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Ultimate Zone Rating (UZR), Part 1

This article will describe the basic methodology of the newly revised fielding system used in Super-LWTS.

Background – RF, ZR, UZR

Bill James introduced us to Range Factor (RF) as, essentially, the number of outs made per game. This was convenient at the time, because we had no other context but the game. The problem is that a game is not necessarily nine innings for each fielder. As well, each fielder is dependent on his pitching staff and "luck" for opportunities.

STATS began tracking Zone Rating (ZR) as, essentially, the total number of outs per balls in a fielder’s "area of responsibility" (i.e., zone). This addressed some of the shortcomings of RF. However, STATS ZR has many shortcomings of its own. For example, each fielder is only given one zone. We know that it’s much easier to convert a ball in play into an out if the ball is hit near you, rather than on the fringes of the zone.

The following table shows the RF and STATS ZR for all 2002 SS in the NL and AL:

National League

Name              Team     GP    RF     ZR
Tony Womack        Ari    149  3.81  0.759
Rafael Furcal      Atl    150  4.87  0.840
Orlando Cabrera    Mon    153  4.89  0.843
Rich Aurilia       SF     131  4.36  0.844
Jimmy Rollins      Phi    152  4.58  0.861
Barry Larkin       Cin    135  4.62  0.828
Cesar Izturis      LA     128  4.18  0.862
Jack Wilson        Pit    143  4.96  0.844
Deivi Cruz         SD     147  4.20  0.843
Edgar Renteria     StL    149  4.28  0.856
Rey Ordonez        NYM    142  4.61  0.864
Juan Uribe         Col    155  5.24  0.841
Alex S. Gonzalez   ChC    142  4.22  0.814
Andy Fox           Fla    112  4.46  0.845
Jose Hernandez     Mil    149  4.93  0.883
American League

Name               Team     GP    RF     ZR
Mike Bordick        Bal    117  5.07  0.904
Omar Vizquel        Cle    150  4.67  0.843
Royce Clayton       CWS    109  4.67  0.875
Alex Rodriguez      Tex    162  4.73  0.919
Cristian Guzman     Min    147  4.33  0.807
Chris Gomez         TB     130  4.74  0.879
David Eckstein      Ana    147  4.26  0.875
Derek Jeter         NYY    156  3.81  0.803
Miguel Tejada       Oak    156  4.64  0.830
Neifi Perez         KC     139  4.85  0.815
Carlos Guillen      Sea    130  4.08  0.856
Nomar Garciaparra   Bos    154  4.60  0.841

STATS expanded on ZR by creating sub-zones. You can take the average out-conversion rates by sub-zone and apply this rate to the number of balls in play for each fielder for each sub-zone to establish a baseline. This baseline will show the number of outs an average fielder would have had, had he received the same number of balls in play for each sub-zone that our specific fielder received. This is, essentially, UZR, or Ultimate Zone Rating. There are other contexts that have not been considered, which we will get to later on.

Defining UZR

The following is the methodology followed in calculating my basic version of UZR (MGL’s basic UZR).

Note: Before I begin explaining the UZR system, keep in mind that there are at least two components of defense that UZR does not address: One, an outfielder’s "arm", and two, an infielder’s skill at turning the double play. Of course, these skills can be measured (and they are in my Super-LWTS system). They are just not included in UZR. Like ZR, UZR is designed to measure and quantify only that skill which enables a fielder to turn batted balls into outs.

UZR rate is expressed as a fraction of 1, the same as a simple ZR (ZR). A UZR rate means essentially the same thing as a simple ZR – namely the number of balls fielded (turned into at least one out) divided by the number of chances; however, UZR rate is a weighted average of a player’s ZR in each of several zones.

As you will see, UZR rate is really a by-product of UZR runs, and UZR runs is the heart of the UZR system. It represents the value of a fielder’s performance expressed as runs saved or cost, in comparison to an average fielder (actually in comparison to the mean performance of all fielders) at that position, in that player’s league, and during that particular year. UZR runs is the defensive counterpart of Palmer’s offensive linear weights (lwts); thus it can be combined with lwts (among other things) to give you an estimate of a player’s total offensive and defensive value. Any player with an average defensive performance will, by definition, have exactly zero UZR runs.

Tracking Data

The entire field is broken down into 78 zones. These are the same zones you can find in the hit location diagram in the documentation section of the retrosheet website ( Of these, UZR uses 64 of them. For infielders, only ground balls, including bunts, are looked at. Pop files caught or landing on an infield zone are excluded, as are line drives caught by an infielder or hit through the infield. For outfielders, all fair fly balls and line drives are included. None of the foul zones are used in UZR except for 3F and 3L, which are near the first and third base bags (for fair ground balls fielded in foul territory behind the bags). Catchers and pitchers are not included in UZR ratings.

For each zone, the computer keeps track of the following on a league-wide (for a particular year) basis:

    1. The number of hits in that zone.
    2. The average run value of a hit in that zone (using traditional lwts hit values).
    3. The number of outs recorded in that zone for each fielding position.

At the same time, the computer keeps track of the total number of fielding errors for each fielding position, but not for each zone individually. Actually it compiles fielding errors in two separate categories: One, ROE errors, are fielding errors that result in an ROE. All other errors, such as on a hit, or a second error on an ROE, are called non-ROE errors.

For example, here is the 2002 league-wide data for zone 56 (the area between the third baseman and the SS):

Zone 56     Hits   Outs    Run Value per Hit
All Plays   1055   1419    .472
SS                  294
3B                 1125

For each player at each fielding position (e.g. Rey Sanchez at SS is one entity and Rey Sanchez at 2B is another entity), and for each zone, the computer also compiles the following information:

    1. The number of hits in that zone while the player was on the field at that position.
    2. The number of outs recorded by that player, at that position, in that zone.

ROE and non-ROE fielding errors are compiled separately for each player, but again, not by individual zones.

For example, the 2002 data in zone 56 for Mike Bordick, while playing SS, looks like this:

Zone 56     Hits      Outs
Bordick       79        18

Remember that these numbers represent ground ball outs in zone 56 recorded by Bordick while playing SS and all ground ball hits in that zone while Bordick was playing SS.

Now, here comes the tricky part.

How a Player’s UZR Runs is Calculated in each Zone

For now, all ROE errors are treated as outs (this is necessary because, at first, we use outs and ROE’s to establish the number of balls that a fielder gets to and because some ROE errors are committed by the receiver of a throw, in which case the fielder needs to get credit for an out). In the above data, "outs" actually refers to "outs plus ROE errors". Errors (ROE and non-ROE) will be accounted for later on.

Let’s use the data to calculate Mike Bordick’s UZR runs in zone 56. First we establish the out rate for all ground balls hit into zone 56. That is 1419 divided by 2474 (1419 plus 1055), or .57. That is, 57% of all ground balls hit into zone 56 in 2002 were turned into outs (by all fielders).

Therefore, the "extra" value of a "caught ball" by a fielder in zone 56 is 1 minus .57, or .43 balls. Since Bordick caught 18 balls in zone 56, he has 18 times .43, or 7.7 "extra" caught balls so far.

Now what about the hits? There were 79 hits in zone 56 while Bordick was playing SS. Surely he is not responsible for all of those hits. How many is he responsible for? Well, since an average SS catches 294 balls in zone 56 out of 1419, or 20.7% of the outs, Bordick is responsible for 20.7% of the 79 hits as well, or 16.4 hits (the third baseman is responsible for the other 62.6 hits). I told you it was going to be tricky!

Now, just like the "extra" positive value of a "caught ball" is 1 minus .57, the "extra" negative value of a hit is the .57 itself (an average ball hit into zone 56 gets caught 57% of the time, so when a ball isn’t caught, the responsible fielders, in this case the SS and third baseman, get "docked" .57 balls). Since Bordick is responsible for 16.4 of the 79 hits in zone 56, he has 16.4 times .57, or 9.4 "negative" caught balls added to his 7.7 "positive" ones, for a total of -1.7 "extra" caught balls. In other words, given the number of balls hit into zone 56 while Bordick was at SS, he caught 1.7 fewer balls than the average SS in the AL in 2002.

Now we want to convert those "extra" balls into runs saved or cost. For that, we use the average run value of a hit in zone 56 - which is .47 runs. Since a 2002 AL out is worth -.29 runs, the "swing" between an out and a hit is .47 plus .29, or .76 runs. Since Bordick caught 1.7 fewer balls in zone 56 than an average SS, he has cost his team 1.7 times .76, or 1.3 runs so far (i.e., his UZR runs in zone 56 is –1.3).

If we do this for every zone in which any SS made at least one out (i.e., the applicable SS zones), and we add up all the runs Bordick saved or cost in each zone, we get a total of +6.2 runs, or 6.2 runs saved by Bordick while playing SS (he must have done well in the other zones).

Including Errors

But wait! What about Bordick’s ROE and non-ROE errors? Remember that I said that a fielder’s ROE errors were thus far treated as outs. Bordick’s 6.2 runs saved assumes that Bordick, and all other SS’s in the AL, turned every ball they got to into an out.

Since that isn’t true (that Bordick and all other SS’s turned every ball gotten to into an out), we now have to factor in Bordick’s ROE errors.

Here’s how (this step is simple):

The average SS committed 169 ROE errors in 5218 balls gotten to (outs plus ROE’s) in all zones. That is an error rate of 169 divided by 5218, or .032. Since Bordick got to a total of 277 balls in all zones, he should have committed .032 times 277, or 8.9 errors. Instead, Bordick committed only 1 error, for a net gain in errors of 7.9. Since an infield error is worth around .49 runs, the swing between an error and an out is .49 plus .29, or .78 runs. Therefore, Bordick saved another .78 times 7.9, or 6.2 runs, by virtue of his "good hands". So far, we have Bordick saving 6.2 runs with his range and another 6.2 runs with his sure hands.

There is one final thing to consider – Bordick’s non-ROE errors. Like ROE errors, that is easily done.

The average SS committed 45 non-ROE errors and Bordick none. If we do the same calculations as above, using .3 as the value of a non-ROE error, we come up with Bordick saving another .72 runs. So it looks like even at the ripe old age of 36, Mike Bordick saved his team last year a total of 13 runs by virtue of his outstanding play (range and hands) at SS!

UZR Runs and UZR Rates

As I said at the beginning, UZR runs is the heart of the UZR system, and that’s really all you need to know. However, if you want to translate UZR runs into a UZR rate, it can be done, although it’s a bit tricky as well. At first glance, it may seem that the simplest way to calculate a player’s UZR rate from the above data is to simply add up all of his outs (not including the ROE errors) in all the zones and divide by his total chances. What is a "chance", though, in a UZR system that surveys all of the zones for every fielding position? For example, if in a certain zone, all SS’s combined field 3 balls out of 300 in that zone, should all of those 300 balls be considered "chances"?

Actually, we were already half way towards calculating Bordick’s "chances" in zone 56 when we determined how many of the 79 hits he was responsible for (16.4). In fact, the number of "chances" for Bordick in zone 56 is 16.4 (his share of the hits), plus 18 (his outs), or 34.4. In other words, a player’s "chances" in any particular zone is defined as that player’s number of outs plus the number of hits he is responsible for. As you saw above, the number of hits a player is responsible for in any zone is the total number of hits in that zone multiplied by that player’s share of the outs in that zone.

If we add up all of Bordick’s "chances" in each individual zone (in most zones, that will be zero, of course), we get his total "chances". If we then divide his total outs by his total "chances", we get sort of a "global" zone rating. Let’s do the math. Bordick recorded 277 outs and errors minus 1 error, or 276 outs. His total chances were 354. Therefore his ZR for all zones combined was 276 divided by 354, or .780.

Unfortunately, this is not his UZR (it does not correspond to his UZR runs), since it doesn’t weight each zone appropriately. For example, if a player happened to get more than his share of "chances" in "high out" zones, he might necessarily have a higher-than-average "global" ZR, while not necessarily being a better-than-average fielder. Basically, using the above method, the resultant "global" ZR is more like a simple ZR, - not really what we are looking for.

Ultimately, the best way to construct a UZR rate which represents the true value of a fielder in comparison to the UZR rate of an average fielder, and is the equivalent of UZR runs, is the following: We’ll use Mike Bordick as the example again.

First we take the simple ZR for all SS’s, including ROE errors as outs. This is the number of total outs plus ROE errors by all SS’s, divided by the total number of "chances" (outs and ROE errors plus the number of hits a SS is responsible for). In 2002, SS outs plus ROE errors were 5218, and SS "chances" were 6786, for an average ZR of .769.

Next, we multiply that average ZR of .769 by Bordick’s total "chances", which was 354. The result is 272. That is the number of outs plus ROE errors that an average SS would make given those 354 "chances". Bordick, on the other hand, got to (outs and ROE errors) 8.1 more balls than the average SS, for a total of 280.1 balls "gotten to" (272 plus 8.1). Of those 280.1 balls "gotten to", he committed only one error, for a total of 279.1 "outs". As you can see, those 280.1 balls "gotten to" and 279.1 "outs" are a "fiction", as Bordick actually got to 277 balls and recorded 276 outs.

Nevertheless, if we divide the 279.1 "fictional outs" by his 354 chances, we get a UZR rate for Bordick of .788, which should correspond almost exactly to his 13 total runs saved (UZR rate doesn’t account for non-ROE errors [UZR runs does], but we could certainly "fudge it in" if we wanted to).

Here is the UZR data for the same NL and AL SS:

National League

Name               Team     GP   Chances   UZR runs     UZR
Tony Womack        Ari     149       422        -22   0.680
Alex S. Gonzalez   ChC     142       382        -10   0.712
Jimmy Rollins      Phi     152       488         -9   0.724
Barry Larkin       Cin     135       425         -4   0.733
Jack Wilson        Pit     143       499         -3   0.738
Rey Ordonez        NYM     142       416         -1   0.744
Rich Aurilia       SF      131       327         -1   0.747
Orlando Cabrera    Mon     153       519          0   0.748
Jose Hernandez     Mil     149       469          4   0.757
Deivi Cruz         SD      147       380          4   0.759
Rafael Furcal      Atl     150       451          5   0.759
Juan Uribe         Col     155       521          6   0.765
Edgar Renteria     StL     149       449          7   0.769
Andy Fox           Fla     112       265          5   0.772
Cesar Izturis      LA      128       290          9   0.786
American League

Name                Team     GP   Chances   UZR runs     UZR
Cristian Guzman     Min     147       378        -16   0.688
Derek Jeter         NYY     156       415        -13   0.702
Neifi Perez         KC      139       405        -13   0.705
Carlos Guillen      Sea     130       334         -3   0.736
Omar Vizquel        Cle     150       461         -1   0.738
Chris Gomez         TB      130       345         -1   0.741
Miguel Tejada       Oak     156       539          1   0.747
Nomar Garciaparra   Bos     154       481          3   0.752
David Eckstein      Ana     147       406          9   0.775
Alex Rodriguez      Tex     162       443         14   0.782
Royce Clayton       CWS     109       278          9   0.783
Mike Bordick        Bal     117       354         13   0.789

If you compare the above charts with those at the beginning of this article, you will see that STATS simple ZR correlates very well with UZR. This suggests that ZR is a pretty good measure of fielder ability, assuming that UZR is the "gold" standard.

On the other hand, RF does not seem to correlate well with either ZR or UZR, suggesting that it is not a good measure of fielding ability (assuming that ZR and UZR are). In fact, if you look closely at the above charts, you will see that a player’s RF is almost entirely a function of his number of "chances".

Where do we go from here?

Earlier, I said that there are a number of contexts that have not been considered in the STATS UZR (or in the MGL’s basic UZR). These are:

    1. park
    2. certain runners/outs combinations
    3. handedness of the batter
    4. groundball/flyball tendencies of the pitchers
    5. the speed (soft, medium, or hard) of the batted ball

In my newly revised UZR, these contexts are considered. In part II, I will discuss these adjustments, incorporate them into the UZR calculations, and present the final UZR results. To see how much of an effect these adjustments have on a player’s UZR, you will be able to compare the initial basic results with the final adjusted ones.

To be continued…

Published on 03/14 at 01:00 AM

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  1. Posted by Craig Burley  on  March 13, 2003 at 09:41 PM (#609440)
    Incidentally, here is a link for the hit location chart.

    Fantastic stuff as always, MGL. Thanks. Looking forward to seeing the nuts and bolts. My primary question is, how is it possible to park-adjust the UZR numbers? Would it be possible to park-adjust this data using the data of only the visiting players?

    My guess is that you would have to park-adjust on a zone-by-zone basis, which starts to look as if you might not have enough data, even over three years, to give even a reasonable amount of accuracy in the park factors.

    I guess we'll find out in Part II.
  2. Posted by Khris Cahrl  on  March 13, 2003 at 09:41 PM (#609441)
    As for Zone Rating, it's a number which conveys very little in a system that is little more than a joke, even to those who invented it. I would not rely upon it for anything. In the end, before cashing out, neither did STATS, since they haphazardly introduced "Ultimate Zone Rating," a repudiation of their previous dingleberry.
  3. Posted by Jonathan Adelman  on  March 13, 2003 at 09:41 PM (#609442)
    Measuring defensive value is indeed a tricky bird, but the two systems I've seen that trust at least a little are Tom Tippett's DMB ratings and Michael's UZR...and those two systems happen to be very similar. I had no idea MGL was still working on improving his system, so I look forward to the second article.
  4. Posted by mooser  on  March 13, 2003 at 09:41 PM (#609443)
    When will the SLW for 2002 season be available? I'm chompin at the bit.
  5. Posted by Depot  on  March 13, 2003 at 09:41 PM (#609444)
    I don't understand why there's a separate conversion dealing with errors. Couldn't you deal with errors in each zone? I would think that certain errors cost more runs than others based on the zone they're committed in.

    Great article!
  6. Posted by Allan Baird  on  March 13, 2003 at 09:41 PM (#609446)
    Ok, so maybe Neifi wasn't as valuable as I thought
  7. Posted by Pete Gillick  on  March 13, 2003 at 09:42 PM (#609455)
    Hey Allan Baird!

    It's not "Allan" it's "Allard", funny guy
  8. Posted by Danil  on  March 13, 2003 at 09:42 PM (#609458)
    Does it work, on a team level? Seems to me that, if these measures matter, somebody ought to be able to take runs allowed, UZR, and DIPS, and demonstrate that it all adds up.

    Yes, I'm fishing for a URL, rather than looking it up myself.
  9. Posted by studes  on  March 13, 2003 at 09:42 PM (#609459)
    This is great, MGL. Dumb question: what's an ROE? Also, how is the run value of a hit in a particular zone established? Sorry if that's covered elsewhere.
  10. Posted by Paul Covert  on  March 13, 2003 at 09:42 PM (#609461)
    It would seem from the context that ROE must refer to errors that put a runner on base, and that non-ROE errors are those that only advance runners.

    Not sure what ROE stands for, though. ("Runner-On Errors"?)
  11. Posted by Dylan  on  March 13, 2003 at 09:42 PM (#609463)
    I believe ROE means "Reached on Error".

    Again, great stuff MGL. I've been waiting for Tango to publish this. I do have a question about IF not getting credit for FBs and only for GBs.

    Was this just to make the analysis easier? Did you find FBs for IF to be insignificant compared to GBs? I would think there is some value in having a SS or 2B who is able to cover certain plays in shallow LF/CF/RF.
  12. Posted by tangotiger  on  March 13, 2003 at 09:42 PM (#609464)
    Danil, click the above link. We discuss it about halfway through.

    ROE = Reached base On Error
  13. Posted by George Steinbrenner  on  March 13, 2003 at 09:42 PM (#609465)
    Surprise, Surprise...My favorite Party Boy Jeter ranks close to dead last in defensive excellence in yet another system.

    He sure is worth every beautiful penny I am paying him ($18.9 million/year).

  14. Posted by tangotiger  on  March 13, 2003 at 09:42 PM (#609466)
    Jeter, from 1998 to 2002 according to the published versions of UZR:
    +8, -1, -1, -17, -13

    Does Jeter have old man legs?
  15. Posted by UZR  on  March 13, 2003 at 09:42 PM (#609469)
    Actually, under the "new and improved" UZR, Jeter's UZR runs for the last 4 years (99-02) are -5, -2, -15, -12. As to whether that implies a degradation in defensive ability or is simply year to year random fluctuation (or some combination, of course), I don't know. I'm normally not a big fan of inferring anything (that he is improving or declining, etc.) from a player's year to year "pattern", since there is just too much random fluctuation year to year and it would be virtually impssible to separate the year to year noise from any actual pattern of improvement or decline. I am in the process of seeing if there might be a steeper (and different, in terms of peak age) age curve with defense than with offense. I suspect there might be. On eof the difficulties is that if I use UZR, I am going to have a limited database. Most of the age/offense research uses a pretty big database.

    As far as park factors for UZR, as you will see in the next article, the park factors I use are not that "granular". I certainly don't use PF's per zone. As someone mentioned, the sample sizes would be too small, plus there is no reason to think that a park would affect the "out percentage" of a fly ball or ground ball differently in each separate zone to any signifcicant degree (although that's probably less true for the OF than for the IF). Again, as you will see, I basically use a "ground ball factor" for the entire IF, and a fly ball and line drive factor for each of the three segments of the OF - LF, CF, and RF (those are defined by the retrosheet zones). In computing the PF's I use as many years as possible, but only going back to 1993 (for no particular reason). I also regress the sample park factors, depending upon the sample sizes. You might be surprised, however, at how little variation there is in the sample park factors, once we get into large sample sizes (e.g., almost all infields are between .98 and 1.02). There really are only a couple of parks that have extreme PF's, and they are all in the OF (BOS LF and COL).

    As far as using only visiting team data for the park factors, when you calculate PF's (be it for defense or offense), you usually use data from both teams combined simply to have the maximum possible sample size. The only drawback in doing this is that each team (home or visitor) probably has its own unique true park factor. IOW, and for example, the Rockies' Coors Field park factor (how Coors Field affects the Rockies players) is definitely different from how that same park affects the visiting players, therefore technically there should be two separate PF's - one for the home players and one for the visiting players. This is more true in some parks than in other parks. Also, this idea of 2 separate park factors - one for the home team and one for the visiting team should not be confused with batting park factors (BPF's) versus pitching park factors (PPF's). That is something completely different, and in fact has nothing to do with park factors at all. Also, the idea of different PF's for the home and visiting teams is inextricably related to home field advantage. In fact, they are so related that they are almost interchangeable. For example, you can use the same PF for the home and visiting players in Coors Field and then give the Rockies a much larger than normal home field advantage (HFA), OR you can use a different PF for the Rockies' players in Coors than you use for the visiting team players in Coors and then apply the normal HFA to the Rockies. Either method should yield the same result, so it may be a matter of semantics.

    As far as the treatment of errors, yes they could be handled on a zone by zone basis. And yes, an error in one zone may be worth more or less than an error in another zone (mostly in the OF), but I doubt (I know) that it would affect a player's overall UZR by any appreciable amount.

    I think someone asked how I calculate the value of ahit in each zone. That is easy. The computer simply keeps track of the number of s,d, and t in each zone and uses the lwt value (for that league and year - it could certainly do it by park also if we wanted to get even more "granular") for each type of hit...
  16. Posted by MGL  on  March 13, 2003 at 09:42 PM (#609470)
    One more thing...

    I constantly grapple with whether or not to use anything but GB's for IF'ers. I don't like using line drives to or thru the IF because even though there is some level of skill (positioning and reaction time) involved in catching a line drive, it is mostly luck.

    IF pop files are almost all caught (96 or 97% I think), there doesn't seem to much skill involved and who catches which pop flies probably varies considerable from team to team.

    If I use pop flies caught by an IF in the OF, there is definitely skill invlolved there (some IF'ers are better than others at going back on pop flies and/or making those over the shoulder catches). I just don't think I can isolate and capture that skill because there is too much of an interrelationship between the IF and the OF in catching pop flies in the OF. Basically I eliminate pop flies that are caught or land in the IF zones completely for better or for worse.

    One more thing. I did not mention in the article (because I hadn't thought of it at the time) that there is one other defensive skill (besides OF arms and IF DP) that UZR does not cover (and I don't cover at all). That is ability of the first baseman to catch (or not) bad throws from the infielders. For example, it had been suggested that J.T. Snow (who has not have a good UZR rating for several years, BTW) is so good at catching bad throws, that he may save 5-15 errors or hits per year with that skill. That may be true, and I am working on seeing if I can somehow measure and quantify that skill to any reasonable degree...

  17. Posted by MGL  on  March 13, 2003 at 09:42 PM (#609471)
    As far as STATS ZR, I can't agree with Khris. UZR seems to correspond to ZR quite well, while RF (and Palmer's batting runs, since it is essentially a RF type metric) is all but worthless, at least without some kind of denominator indicating total "chances".

    When STATS came out with their UZR, I don't think they repudiated simple ZR, I think they were merely trying to refine it.

    In the hierarchy of fielding metrics, and in comparison to batting metrics, I would say that RF is akin to BA (maybe worse), ZR to OPS (maybe a little worse) and UZR to linear weights (worse).

    The best idea I have seen for a fielding metric without using PBP data (except for the initial research) was suggested by the person that wrote that multi-part series on fielding, I think. The idea (at least for the IF) was to use the initial PBP data to determine what percentage of GB's each infield position fielded, on the average, depending on whether a RH or LH pitcher is on the mound, and then to apply this to each team's data, using the G/F ratio of their pitching staff, the number of BIP outs, and the L/R composition of their pitching staff. This is sort of like a "poor man's" ZR. If this is a decent pitching metric (which I think it is), then sureely ZR, which basicaly takes it one step further, is a better than decent metric.

    We can all certainly disagree on the quality of the various metrics (both offensive and defensive) and whether something is bad, decent, good, very good, etc., can be a matter of semantics as well (e.g., what does "decent" actually mean?), but to state or imply that STATS ZR is meaningless or worthless can't possibly be right...
  18. Posted by Shortie  on  March 13, 2003 at 09:42 PM (#609473)
    MGL--Great, clear explanation. One (maybe two) questions. Using the Mike Bordick example (quoted below), why wouldn't the calculation simply be Bordick's percentage of balls he successfully fielded that were hit in zone 56, minus the league average rate for shortstops in the same zone, multiplied by the total balls hit in zone 56? The numbers would be (18/(18+79), or 18.6%, minus the league rate -20.7%, times (18+79), or -2.1%*97, or 2 extra "hits" allowed? The following quote indicates that a two-step process is used instead:

    "Let’s use the data to calculate Mike Bordick’s UZR runs in zone 56. First we establish the out rate for all ground balls hit into zone 56. That is 1419 divided by 2474 (1419 plus 1055), or .57. That is, 57% of all ground balls hit into zone 56 in 2002 were turned into outs (by all fielders).

    "Therefore, the "extra" value of a "caught ball" by a fielder in zone 56 is 1 minus .57, or .43 balls. Since Bordick caught 18 balls in zone 56, he has 18 times .43, or 7.7 "extra" caught balls so far.

    "Now what about the hits? There were 79 hits in zone 56 while Bordick was playing SS. Surely he is not responsible for all of those hits. How many is he responsible for? Well, since an average SS catches 294 balls in zone 56 out of 1419, or 20.7% of the outs, Bordick is responsible for 20.7% of the 79 hits as well, or 16.4 hits (the third baseman is responsible for the other 62.6 hits). I told you it was going to be tricky!

    Now, just like the "extra" positive value of a "caught ball" is 1 minus .57, the "extra" negative value of a hit is the .57 itself (an average ball hit into zone 56 gets caught 57% of the time, so when a ball isn’t caught, the responsible fielders, in this case the SS and third baseman, get "docked" .57 balls). Since Bordick is responsible for 16.4 of the 79 hits in zone 56, he has 16.4 times .57, or 9.4 "negative" caught balls added to his 7.7 "positive" ones, for a total of -1.7 "extra" caught balls. In other words, given the number of balls hit into zone 56 while Bordick was at SS, he caught 1.7 fewer balls than the average SS in the AL in 2002."

    Under the two-step calculation, what would happen if Bordick was playing with a very good third baseman, who fielded an above-average number of batted balls in zone 56, so that the total number of *team* hits allowed in zone 56 was below average? Wouldn't Bordick's rating go up, because he only gets docked for a fixed "shortstop" percentage of a smaller number of "team" hits allowed in zone 56?

  19. Posted by MGL  on  March 13, 2003 at 09:42 PM (#609480)
    Shorty, very good questions! You are probably one of the few people who actually carefully went through the methodology to see if it makes sense or if it is the best methodology (or has any flaws, etc.). Beleive it or not, figuring out the proper methodology is extremely difficult. I have to go to dinner right now, but when I get back, I'll try and explain why your "method" isn't the best, and what happens with the various methods when the adjacent player (like in Bordick's case, the third baseman) is better or worse than average. I went literaly through many months (any many sleepless nights) going back and forth on the various methodologies. I think I came up with the best, but I could be wrong...
  20. Posted by MGL  on  March 14, 2003 at 09:42 PM (#609488)
    Shorty, by golly, I think you are right! Rather than the 2-step process, I should simply be using the 1-step much simpler process that you describe, which is simply a STATS-type ZR turned into a balls saved or cost for every zone. You did make a slight error in your illustration, but it is not important (you used league outs for SS divided by total league outs rather than league outs for SS divided by total hits plus outs).

    Well, all those months and sleepless nights for naught! Anyway, I'm glad you caught the error and I thank you (and the sabermetric community should thank you as well). This is one of the reasons why new and important metrics should not be proprietary. Peer review and open source is a must!

    I will explain my error in part 2 of the UZR series and present revised UZR ratings for the SS's.

    Thanks again! I'm glad that someone took the time to really scrutinize the math and the logic. As Tango likes to say, when you write an article laden with formulas and the like, everyone tends to skip them over and assume they are correct. Can't really blame anyone. Who's got the time to pour over someone else's work!
  21. Posted by Charles Saeger  on  March 14, 2003 at 09:42 PM (#609503)
    Great stuff. Most of the details are obvious, when you think about them, but there were some things I did not know. I await part 2 ...
  22. Posted by Shorty  on  March 14, 2003 at 09:42 PM (#609507)

    I think you deserve a Primey(?) award for you latest post, even more than for UZR. Gracious consideration such as yours of the ideas of others is what advances knowledge. Your graciousness is *especially* impressive considering the amount of work you've devoted to your system.

    The good news is that I firmly believe UZR will work much better now, with better per-player serial correlations from year-to-year. Moreover, a host of defensive rating conundrums will be solved. Finally, UZR will now be a better benchmark for testing defensive rating systems that don't use UZR data, so that we'll be able to generate much better defensive ratings for periods during baseball history for which we *don't* have UZR available.

    We all have Mike Emeigh to thank for this latest breakthrough, though he might not know it. (By the way, he deserves a Primey, too, for the Jeter series.)

    I didn't have time to join the e-mail discussion of Mike's series on Jeter when it came out (someone should generate a post to that series here), but about a month afterwards I went through his eight articles and all of the e-mail threads. I wrote him an e-mail (which must have gotten lost in the blizzard of e-mails he receives) in which I posited a reason for the seeming contradiction between UZR ratings for Jeter and the Jeter ratings under all of the other systems that rely upon old-fashioned statistics (Bill James' Win Shares, Clay Davenport's system, and, I think, Charlie Saeger's Context-Adjusted Defense).

    Before going through the whole analysis, the key finding appeared (to me at least) that Yankee third-basemen were subsidizing Jeter by fielding an above-average number of balls in the SS/3B "hole", and that the current UZR "accounting" system did not take this into account. In other words, Jeter managed to field an only slightly below-average percentage of the *remaining* ground balls in the SS/3B zone (which may be zone 56) *after* taking *out* of consideration the 56-zone balls fielded by Yankee third basemen. Since Jeter was adequate in the other zones, his ratings for a few years were basically average, when every other system showed him as terrible. I think Jeter's recent drop toward a -15 to -20 rating probably reflects a decline in Yankee third baseman quality or their willingness to help him out by shading towards the hole. This I believe is Jeter's "true" level of ability, which has been consistently reflected in the Davenport and Saeger systems (as well as a system of my own that I had developed and have recently streamlined in part to address legitimate criticisms you had offered).

    Mike's "bottom-line" factual findings that led me to this conclusion seemed to be as follows:

    1) There was a mysterious "gap" in ground balls against the Yankees reaching both the SS and 2B "zones" on each side of the second base bag. For some mysterious reason, which no one could figure out, the Yankee pitchers did not allow ground balls up the middle. Thus, Jeter had legitimately fewer opportunities on his side of the bag.

    2) Jeter had average "rates" of making plays available to him near the bag, as well as in the zones near the traditional position for shortstops.

    3) Jeter had only a slightly below average assists totals "in-the-hole" between short as calculated under UZR. "Table 15" in Part 6 of Mike's Jeter series was entitled: "Outs Made by Yankee/AL SS in hole after removing 3B plays, 1999-2000". This got me thinking about the UZR calculation, which I tentatively confirmed based upon your old description of the system. Your invaluably clear description in the latest article confirmed this for me.

    (I also believe that the Yankee pitchers had a pretty high rate of generating flyballs instead of ground balls.)

    Given the above four factors, it made perfect sense that Jeter had shockingly low assists totals, but an average UZR rating.

    Some studies that I had done indicated that Yankee pitchers had *fielded* about 50 more ground balls during 1999-2000 above the average rate for pitchers, given their GB/FB tendency, which I believe entirely explains the "gap" in ground ball distribution near the bag. In short, Yankee pitcher *fielding* prevented a normal number of ground balls from *reaching* SS and 2B zones near the bag. I believe it is entirely correct, however, to take this into account for the benefit of Jeter and Yankee second basemen. They literally didn't have a chance to field those "missing" ground balls.

    At third, the problem seemed fundamentally different. As the posters seemed to say, Yankee third basemen appeared to be drifting over towards the hole, ostensibly to "help out" Jeter. One indirect cost of this was that they fielded only one out of twenty ground balls hit down the third-base line. Then it occurred to me that under the current "accounting" system, third basemen could earn extra points helping out the shortstop (without penalizing the shortstop), which would "make up" for their "failures" down the line. The net effect would be average ratings at third and short for the Yankees, when in fact the third basemen were OK or good but Jeter was terrible. The "sum" seemed to be greater than the "whole" (pun intended).

    Mike Emeigh also ably argued that there are other complexities to using the rich UZR database, which you'll be writing about in the next installment. I would imagine, based on your posts to Mike's series, that UZR will make adjustments for contextual factors that limit the ability of fielders to position themselves optimally. The clearest example of this is that, with a runner on first, middle-infielders have to shade toward the bag, which hurts their ability to field balls in the holes on the left and right sides of the infield. Likewise, first baseman literally have to plant themselves at first, which must drastically reduce their range.

    A great system is about to become greater. Congratulations.

    If you'd like to chat off-line, I've posted my e-mail address.

    Many thanks again.

  23. Posted by tangotiger  on  March 14, 2003 at 09:42 PM (#609509)
    One way to determine if the 3B is helping Jeter is to look at those conditions where the 3B would not try to help him. Say in late innings of close games, where the 3B is covering the line, especially with runners on base.

    So, how do we find these things? Well, look at the out-conversion rates *for the league* for each zone, by the inning/score/base/out situations. Pick out those game states where the out-conversion rate for the "down the line" is 50% higher than average. You've now identified those game situations where the 3B is more likely than not to cover the bag.

    Now, how did the *SS* do during these game states? How did Jeter do relative to other SS.

    If the sample size is too small, change that "50%" to "30%" or something.

    Look for the opposite as well. Look for those game states where the 3B would *not* cover the line. So, in this case, the 3B will shade towards the SS. How did Jeter and the other SS do in these game states?

    I agree, thanks much to MGL for parsing and putting in the effort on the PBP database.
  24. Posted by Shorty  on  March 14, 2003 at 09:43 PM (#609515)

    Good points. I think there might be an easier way to approach the problem, however. Let's first review how we should quantify Jeter's contribution based upon the method I've suggested to MGL, and then quantify how his third base teammates had been "helping" him under the current UZR "accounting" system as described in Mike Emeigh's Jeter series and MGL's latest article.

    As MGL rightly pointed out, my calculation was a little off in my first post. All we need to do is look at the number of 3B/SS "hole" (let's call it "Zone 56") plays made by Jeter out of *all* of the Zone 56 batted balls allowed by Yankee pitchers, *whether or not* fielded by Jeter *or* his third base teammates. We would then compare *that* percentage against the percentage of gross Zone 56 batted balls fielded by American League shortstops. My guess is that Jeter's percentage is very low. We would multiple the (negative) percentage difference by the gross Zone 56 balls allowed by Yankee pitchers to find the number of gross Zone 56 balls Jeter failed to field that an average shortstop would have.

    Now let's do the same thing for Yankee third basemen in 1999-2000. We would look at the Zone 56 plays made by Yankee third basemen as a percentage of the gross Zone 56 batted balls, subtract the league average percentage, and multiply by the gross Yankee Zone 56 batted balls. We'll find that Yankee third basemen successfully fielded (substantially) more balls in Zone 56 than average third basemen would have.

    Under the existing UZR accounting system, the extra hits saved by Yankee third basemen in Zone 56 are effectively eliminated from consideration in determing Jeter's total opportunities in Zone 56. But the "credit" for those plays should only be granted *once* to Yankee third basemen, not indirectly a *second* time to Jeter by reducing his "denominator" of opportunities.

    The "proof" that the Yankee third basemen were helping Jeter would be the fact that Yankee zone ratings down the third base line were below the league average, as I believe they were. In that sense, Yankee third basemen were sacrificing their performance in the zone that is entirely theirs (the third base line) in order to compensate for Jeter's weakness in going to his right.

    One could quantify the "unfair" "help" that Jeter got from his third basemen as the excess of the third base Zone 56 rating over the "down-the-line" zone rating. If the third basemen were playing their positions "normally", they should have roughly equally good or bad ratings in both Zone 56 and "down the line" (leaving aside, for the moment, the fact that going to your left and right are different skills).

    If in fact Yankee third basemen actually managed to field the line adequately, that would just mean that they were so good that they could field their own position adequately and also help out Jeter. But, again, they should get the credit, not Jeter.

    Note that it is entirely possible for the process to go the other way--that is, for shortstops to "subsidize" third basemen. For example, Chipper Jones has unembarrassing UZR ratings for the seasons he played at third, despite the fact that his assists rates were very much below average (taking into account the GB/FB tendency of his pitching staffs and their Righty/Lefty split) and the fact that his own team decided to move him to the outfield. I suspect that Atlanta shortstops were reducing *Chipper's* "denominator" for Zone 56 plays by making extra plays in Zone 56.

    One fascinating strategy the Mike Emeigh's article reveals is that the Yankees had a great (missed) opportunity to improve their infield defense. If my theory is correct that Yankee pitchers were above-average fielders, Jeter should have shifted slightly *towards* the hole (because there were fewer opportunities "up-the-middle"), which would have given the Yankee third basemen the opportunity to shift *towards* the line, and cut off more ground balls.

    Furthermore, such strategic positioning would properly be credited under a revised UZR system to the appropriate fielders, and the sum performance of the team would correspond to the team's (higher) Defensive Efficiency Rating, or (lower) BABIP. Jeter's rating would still be low (but perhaps slightly higher, as he would be more effectively positioned), the pitcher UZR rating would be the same, and the third base UZR rating would be higher (not only because they would make more plays, but also because the extra saved doubles down the line would have a higher UZR linear weight).

  25. Posted by tangotiger  on  March 14, 2003 at 09:43 PM (#609517)
    I think the way MGL did the splitting of the zones is to look at the league average plays made for the shared zones for each of the fielders. Whether he did or not, let's consider it.

    Let's say zone 56 is split so that 60% of the plays made are by the ss, and 40% by the 3b. Let's infer that 60% of the plays not made in that zone also belong to the SS. Let's say the league average was to make 80 outs out of 100 plays there.

    So, if the Yankees had 100 plays there, 60 "belong" to Jeter and 40 to Ventura.

    Let's say that Ventura shaded greatly in that zone. Let's say he made 42 outs, and Jeter made 38. According to the split above, Ventura made 42 outs in 40 "opps" and Jeter made 38 in 60.

    The league average 3b makes 30 outs, and the lg average ss makes 50 outs. So, Ventura is +12, and Jeter is -12 outs per 100 balls in the 56 zone.

    I would even say then that you don't have to worry about splitting the zones in 40/60. Just consider all 100 plays in that zone, and compare to the league average. This might be what Mike is talking about when he says NOT to split the shared zones.

    Regardless of what the split in the shared zones are, just make the comparsion to league average for that position/zone.

    We still have the possibility that Ventura is stealing plays from Jeter. Jeter should be stealing plays on his other side, but he doesn't (if I remember Mike's article on the subject).

    Since the question being asked at the beginning of the article is "how would an average fielder do, giving this player's playing conditions", I suppose we should consider not only the pitcher on the mound, the batter at the plate, the runners on base, but the fielders next to him. So, what would an average fielder do with Ventura next to him?
  26. Posted by Shorty  on  March 15, 2003 at 09:43 PM (#609521)

    I think I’m with you on this, with some minor computational points, but let me know if I am. Sorry for repeating back your thread, but it may make it easier for readers to keep up with the math and the many subtle points you're making.

    TANGO: I think the way MGL did the splitting of the zones is to look at the league average plays made for the shared zones for each of the fielders. Whether he did or not, let's consider it.

    Let's say zone 56 is split so that 60% of the plays made are by the ss, and 40% by the 3b. Let's infer that 60% of the plays not made in that zone also belong to the SS. Let's say the league average was to make 80 outs out of 100 plays there.

    So, if the Yankees had 100 plays there, 60 "belong" to Jeter and 40 to Ventura.

    Let's say that Ventura shaded greatly in that zone. Let's say he made 42 outs, and Jeter made 38. According to the split above, Ventura made 42 outs in 40 "opps" and Jeter made 38 in 60.
    The league average 3b makes 30 outs, and the lg average ss makes 50 outs. So, Ventura is +12, and Jeter is -12 outs per 100 balls in the 56 zone.

    SHORTY: Here’s the computational detail. If:
    1) the Yankees are spot-on average as a *team* and have 100 “plays” (batted balls?) in Zone 56, and
    2) the Yankees are spot-on average as a *team* in converting 80 of such plays into *outs*, and
    3) The league average split of SS/3B for plays *made*, i.e., outs, is 60/40,
    1) The expected number of plays made by the league average shortstop playing for the Yankees should be .60*80, or 48. Jeter made 38 in your example, so he should be down -10, I think, not -12.
    2) The expected number of plays made by the league average third baseman playing for the Yankees should be .40*80, or 32. Ventura made 42 in your example, so he should be up +10, I think, rather than +12

    TANGO: I would even say then that you don't have to worry about splitting the zones in 40/60. Just consider all 100 plays in that zone, and compare to the league average. This might be what Mike is talking about when he says NOT to split the shared zones.

    Regardless of what the split in the shared zones are, just make the comparsion to league average for that position/zone.

    SHORTY: Exactly. We save ourselves a lot of work by simply saying that for every 100 batted balls in Zone 56, the average baseman turns 32 into outs. One hundred batted balls were in Yankees’ Zone 56, and Venture turned 42 into outs, so he’s up +10. Likewise, Jeter is -10. The sum +10 – 10 equals zero, which is correct, because the Yankees as a *team* were exactly average in Zone 56.

    TANGO: We still have the possibility that Ventura is stealing plays from Jeter. Jeter should be stealing plays on his other side, but he doesn't (if I remember Mike's article on the subject).

    SHORTY: I don’t know whether there’s a definitive answer to that problem, but here’s an attempt at supporting a “common sense” belief that Ventura is not “harming” Jeter by taking plays away from Jeter that Jeter was able to make. (In other words, Ventura made plays that Jeter wasn’t able to make.)

    First, it is in general much less likely for infielders to “fight over” infield ground balls than for infield pop-ups, which MGL wisely leaves out of his ratings. The decision as to which out of two or three infielders catches a pop-up reflects an election, not a skill. How many times does one see an infielder “waive away” another infielder before fielding a ground ball (not a Sac Hit)? Not many. It all happens too fast.

    Second, there is not a statistically significant negative correlation between assists by third basemen and shortstops, while there is a strong, statistically significant negative correlation between assists by middle-infielders and by pitchers. Going back to my explanation for the strangely low number of groundballs against the Yankees in 1999-2000 in the SS/2B zones near second base, good fielding pitchers obviously come between the batter and middle-infielders, and reduce the latter’s chances to make plays. Though third basemen are closer to home than shortstops, it’s not nearly so strong an effect. Of course, the lack of a statistical relationship between all league shortstops and all league third basemen doesn’t prove what was going on with the Yankees, but it’s suggestive.

    Third, the only way definitively to prove the point would be for STATS Inc. to subdivide Zone 56 yet again. Then we would see whether Ventura was making plays in Jeter’s “side” of Zone 56. We’ve got 78 zones already; I don’t think we want to go down that route.

    TANGO: Since the question being asked at the beginning of the article is "how would an average fielder do, giving this player's playing conditions", I suppose we should consider not only the pitcher on the mound, the batter at the plate, the runners on base, but the fielders next to him. So, what would an average fielder do with Ventura next to him?

    SHORTY: The “easy” answer first. Since I don’t think Ventura covered the line well and did not “take away” plays from Jeter, but Jeter’s pitchers “took away” plays from Jeter, Jeter should have shifted slightly towards the hole, made more of the Zone 56 plays that he was supposed to make (possibly offset entirely by fewer balls in the other direction), and allowed Ventura to cover the line better. Net/net, the Yankees would have fielded the same number of batted balls as before, plus more of the down-the-line doubles.

    Now the hard part. My sense is that we should not "model" all of these weird contextual factors except to the extent they *force* a fielder to take a position in the field that is *per se* suboptimal given the likely batted ball distribution. In other words, we *delegate* the job of "modeling" anomolies in ball distributions to the fielder, and let him position himself optimally. I think, under UZR, that the players who position themselves well will have higher ratings, even if the distribution of batted balls is unusual; i.e., he may have lotsa plays in a weird zone and fewer plays in a common zone, but net/net, he's ahead.

    Where things get tricky is when game factors *constrain* the fielder from taking the *best* position given the most best estimate of where the next batted ball is going to land. One “context” I would consider relevant is runners on base. They definitely force fielders to take suboptimal positions. It’s also an easy factor to factor in. On the other hand, the relative quality of fielding teammates should not, except in truly bizarre cases, per se disadvantage a fielder. If he’s smart, he’ll make an adjustment and make more plays, just in slightly different zones. In a world in which a .750 DER is exceptional, there are still plenty of batted balls to go after.

    As the hour is late, I may not be expressing myself as clearly as I should. Bottom line, don't over-model, let the fielder do his job, and adjust only if there are frequently occurring, significant factors that vary widely from team to team--such as variation in runners on first--that keep the fielder from doing the job the best way he knows how.

  27. Posted by MGL  on  March 15, 2003 at 09:43 PM (#609524)
    SHORTY: "Exactly. We save ourselves a lot of work by simply saying that for every 100 batted balls in Zone 56, the average baseman turns 32 into outs. One hundred batted balls were in Yankees’ Zone 56, and Venture turned 42 into outs, so he’s up +10. Likewise, Jeter is -10. The sum +10 – 10 equals zero, which is correct, because the Yankees as a *team* were exactly average in Zone 56."

    Yes, that is the correct (and easiest - funny how it occasionally works out that way) way to do it! I used to do it that way, but for some reason after cogitating for months, I decided to change my methodology and do it the other way, which turned out to be wrong. I should have listened to my 6th grade teacher who told me to always go with my first answer on the test - the more I think, the worse it gets.

    As far as one fielder (Ventura) stealing chances from another fielder (Jeter), if you use Shortie's method (the correct one), that can never be a problem, unless one fielder can field a ground ball that another fielder can also field, which I agree is rare and probably inconsequential.

    As far as pitcher's snagging balls up the middle, I had never thought of that (more thanks to Shortie). Off the top of my head, I;m not sure how that affects things. Let's see...

    Those snags by the tyhe pitcher would be credited to zones 13 and 15 and occasinally zones 6MS and 4MS I guess (I would have to check the database). Let's first see what happens if they are credited to zones 13 and 15...

    Let's say an average team has 100 balls hit into the 6M zones and the SS fields 20 of them. If on one team (the Yankees) the pitchers snag a lot more than their fair share, whether it helps or hurts the SS (Jeter) sepends on what percentage of those balls normally go thru for hits and what percentage normally get caught by the SS. IF 5 extrta balls are snagged by the pitcher (out of those 100) and 4 would have gone thru and 1 would have been caught, we now have 95 balls into the 6M zones with the SS (Jeter) catching 19, which is exactly the same as 20 out of 100. It does seem likely (I think) that for every extra ball that is snagged by the pitcher, 80% of the time it would have gone thru and 20% of the time it would have been caught by the SS, so that it shouldn't affect the SS's UZR at all.

    Now what about if those extra pitcher snags are in zones 6MS and 4MS? Now I thionk we have that rare situation where a fielder is in fact "stealing" balls from another fielder (the other fielder might catch them) AND causing that fielder to have an unfair drop in his UZR rating. (In the last case, where the snagged balls were in zones 13 and 15 it didn't affect the SS's rating - I don't think - unless of ocurse the ones that the pitchers snag are the most catchable balls for the SS, which could be the case I guess.) Anyway, let's see what happens with extra balls snagged by the pitcher in zones 6MS...

    Now even if the pitchers snag extra balls, we still those balls reaching a SS zone (I guess it is a shared zone with the pitcher). SO let's say for an average team, we have 20 balls hit into the 6MS zone, the SS makes 10 of those and the pitcher makes 5 (the other 5 stop short in that zone for a hit). The SS ZR for that zone is then .500. IF the pitcher now makes 6 and the SS only makes 9 (or 9.25 - 4.75 are hits - the pitcher also took away 1/4 of a hit), then I guess that the SS;s (Jeter's) rating gets unfairly reduced (.450 or .4625) in that zone. This is the classic case of a fielder "stealing" a hit from anoteh fielder, which we think is a rare occurrence. One of the ways to check that, of course, is to look at the database and see what's going on in zones 6MS (and 4MS).

    I guess the bottom line is to identify zones in the field where it is possible for more than one fielder to field the same ball (like 4MS and 6MS). If one fielder is above (or below) average in that zone, should we automatically adjust the other fielder's rating? What if they are both above or below average? Is this prevalent in the infield?

    What about in the oufield? This probably goes on much more often in the OF? Should automatic adjustments be made in the OF? If yes, what is the formula (methodology)? DMB says that they do this (adjust one fielder's rating due to an adjacent fielder's rating), but of coure, they don't explain HOW they do this...
  28. Posted by tangotiger  on  March 15, 2003 at 09:43 PM (#609525)
    Shorty, we're mostly on the same wavelength.

    Let's say we COULD establish responsibility, and that of those 100 plays in the hole, 40 belong to 3b and 60 to SS. I also said that the lg avg out-conversion rate (ZR) was 30/40 for 3b, and 50/60 for SS.

    There's no reason to think that their ZR in the same zone would be the same. After all, the 3b is playing in, but he's got the more natural throw. I don't even know if this particular zone would be an advantage for the 3b or ss.

    But it doesn't matter! Ventura made 42 plays there, and the avg 3b made 30. That's +12. It doesn't matter if the split was 60/40 or 70/30 or 50/50. All we know is that the avg 3b made a certain number of outs per total plays there. And it becomes irrelevant what we think the shared split of BIP might/should be. Unless we know, don't consider it.
  29. Posted by tangotiger  on  March 15, 2003 at 09:43 PM (#609526)
    Just to expand on my comment, which I discussed at fanhome last year and I'll repeat it here for those who missed it, consider all 78 zones for every fielder. Determine the out-coversion rate by POSITION for each zone. Take those out-conversion rates, and apply them to the opps while Jeter was on the field foe each of the 78 zones. No need to worry about "shared responsibilities".

    You can figure out the extent of "shared responsibilities" impact by looking at situations as I described with my game state example. You can also do it by looking at players that get a "shift" from fielders, like Bonds. There's no "shared" impact between the SS and 3B in this case.
  30. Posted by MGL  on  March 15, 2003 at 09:43 PM (#609532)
    Here is the data for zones 13 and 15 and zones 6MS and zones 4MS for 2002 NL:


    zone 15: 931 balls, 820 outs, 802 by pitcher, 11 by third baseman, and 3 by SS.

    zone 13: 994 balls, 912 outs, 900 by pitcher, 8 by first baseman, and 2 by 2B'man.

    zone 6MS: 279 balls, 253 outs, 8 by pitcher, 232 by SS.

    zone 4MS: 160 balls, 133 outs, 4 by pitcher, and 102 by 2B'man.

    Similar results for AL. I don't think there should be much if any of a problem with the pitcher "stealing" outs from either the second baseman or SS AND unfarily affecting their UZR, at least according to the way the zones are set up...

  31. Posted by Shorty  on  March 15, 2003 at 09:43 PM (#609533)
    MGL and Tango,

    Looks like a consensus is emerging. That's great! Your most recent posts raise some interesting issues.

    MGL-I think it would be worthwhile trying to find the zones in which fielders could "steal" opportunities from each other. I guess the next step would be to try to quantify the possible range of distorted outcomes. We might find that it really doesn't matter in the long run. Of course, if we can "model" "play-stealing" and the computer can do the work without complaining, we might as well do it.

    Regarding outfielder ratings, the key difference is that outfielders "share" zones with players (infielders) who do *not* get credit for catching the ball, which introduces a new complexity, especially for Andruw Jones, who probably fields a lot of short flies that middle-infielders would normally get. Here's my tentative solution, for what it's worth. (MGL--you've probably already figured this out, because your AJ ratings are sensibly much lower than raw putout data would predict.) First, isolate the zones in which some fly balls are caught by infielders. Second, only give credit to the outfielders to the extent that the *team* rating in such zone is superior. Third, for short outfield zone in which there is an overlap between center/right/2B and center/left/SS, I think we could allocate the credit between center/right and center/left in the same way we did Zone 56, provided that we limit the upside/downside to the *team* rating, and account for the much greater chance with a high fly that one outfielder could "steal" the play from his teammate.

    Or, what might even be simpler, one might ignore non-line-drive hits in all zones that involve overlaps between outfielders and between outfielders and infielders, on the theory that *somebody* on any normal team would catch the ball. Or maybe one simply ignores zones in which non-line-drives fly balls are "always" caught. Come to think of it, maybe it was this consideration that led to the "two-step" process, because inherent in the two-step process is a threshold determination of the percentage of times in which *somebody* on the team makes the play.

    Tango--I now understand your example. The -12/+12 ratings result from the fact that the expected play conversion rates for short and third are different.

    The Bonds-shift example introduces a new complexity, which, fortunately, probably has little practical effect. In the admittedly ridiculous example in which a third baseman only played when Bonds was hitting and there was *no* Bonds shift, he would literally always have a zero rating, because he would have no chances. (The Bonds shift gives him a chance to earn points in the "up-the-middle" zones, which demonstrates nicely the "good" insensitivity of UZR to weird ball distributions.) Similarly, if a great third baseman played for a team with very little left-handed pitching (which happens from time to time) would have so few opportunities that his "gross" rating would suffer. Now I guess that still makes sense, because the "gross" rating accurately reflects the actual impact he had over the course of the season. It's like a guy with a high OPS+ who doesn't get enough at-bats. I guess this is a long-winded way of asking the question whether a legitimate "rate" stat can be generated by UZR and how relevant it might be as a practical matter.

    My parting thought, in case we're done here, is that we should step back a little and appreciate the big picture. Is there "play-stealing" "noise"? Probably. Is there infield/outfield flyout "noise"? Probably. But the important thing that more people need to appreciate is that all of the good systems of defensive evaluation--UZR, Davenport, Saeger, Dick Cramer's still-proprietary system, the Diamond Mind system--are showing for the first time how significant fielding can be. It really is the case that outstanding fielders at all positions (except maybe catcher and first base) can measurably save their teams 25 runs a season, at least for a few years of peak performance. When you also factor in the impact of replacing such a player with a poor defensive performer, the "swing" value is very significant--easily a few wins a season.
  32. Posted by tangotiger  on  March 15, 2003 at 09:43 PM (#609535)
    I didn't mean to take the Bonds as the good example, jsut as an extreme example.

    You should be able to go through the PBP and look at the BIP in each zone BY BATTER. That will tell you what kind of shift a batter should get. Look at those batters who are skewed to one way or the other, or who forces the CF to play more to the RF but leaves the LF in place. You should be able to see how much overlap really exists.

    I don't think there should be much overlap with infielders, even for Jones. This again is easy enough to figure by doing jsut what MGL did for the stealing pitchers.
  33. Posted by MGL  on  March 15, 2003 at 09:43 PM (#609541)
    I am reprinting a post that Bernard Shakey made on Fanhome regarding this discussion (the discussion - a good one - has become fractured, much like the UZR ratings themselves)!

    That was an interesting suggestion that "Shortie" made on BPrimer, by eliminating an extra step you can still get your net outs calculation. But I am surprised, mgl, that you gave in as quickly as you did! His formula seems clearer and simpler, but I don't know if it's necessarily better. The step that is being eliminated is essentially, the prorating of average fielders in the gray zones which more than one position is active in, to figure out who's responsible for what hits (and chances). By eliminating this you are eliminating an extra control in measuring the subject to "league average", which is the whole basis behind UZR.

    As I understand what was being suggested was to take the Bordick's outs/opp. (or "chances") and subtract that from all the league SS outs/lg opp. in zone 56, and multiply that by Bordick's opp. Where "lg opp" is defined as *all* hits in zone plus *SS* outs, in zone. So Bordick's calculation would be as follows:

    (18/(79+18) - 294/(1055+294)) *(79+18) = -3.1 net outs, which is more that the -1.7 you came up with.

    Technically this equation is sound, and the zero baseline is maintained. (re the sums of net outs equal zero). But theoretically by eliminating the SS and 3B "share" of hits allowed by the prorating method you used, you no longer are comparing Bordick to lg averages. Instead of comparing Bordick to league average SS with league average 3B holding equal, which you did originally . . . you would now instead be comparing league average SS AND the ability level of his own third baseman, I think, which is really what you don't want.

    The biggest consideration in accounting for gray zones where more than one different position is active, is to try to minimize the ability levels of those other adjacent fielders involved. For example: let's say Tony Batista is a better thirdbaseman and fielded two balls that Bordick would normally have fielded. So instead of making 18 outs in z56 he makes 16 . . . so league SS fielded 292 balls instead of 294, and league 3B fielded 1421 outs instead of 1419, and hits allowed in that zone remain the same at 1055.

    The calculation for Bordick becomes:

    (16/(79+16) - 292/(1055+292)) *(79+16) = -4.6 net outs (from -3.1)., where if you allow for the prorating for hits allowed it's -2.5 (from -1.7). It still goes up to a higher negative number because Batista increased the league avg for 3B, but not as much as you would doing the simpler calculation. I also note there is a greater range in net outs (and therefore using the simpler formula.

    So the problem is that Bordick's net outs would be prejudiced by a better fielding third baseman, and even moreso if there is also a better fielding second baseman. That's minimized by using that extra control. Now, the simpler formula would work well enough if we are measuring "value", but since UZR is an "ability" measure (at least I think it is), we should context neutralize the averages as much as possible. Also, it may not be that big a problem with infielders because the fielder closer to the ground ball is going to make the play anyway (and "compete" with the adjacent fielder). It may, however be an issue for outfielders where the zones converge toward cf, where of's do tend to compete.

    Prorating is an artificial way of allocating responsiblity of hits and may not be a true measure because it assumes the lg average 3b and lg average SS have the same ZR in that zone, (which probably isn't true), but when estimating the control it still may be better than no control at all because you will be estimating on the side of conservatism.
  34. Posted by Shorty  on  March 16, 2003 at 09:43 PM (#609545)

    I'm having a little difficulty "unpacking" Berney's post, but I'll attempt to address some of the points. I'm really looking forward to hearing what you think.

    First, I had always assumed that UZR *was* meant to be a "value" rather than an "ability" stat. ("Runs saved".) In other words, as is the case with offensive linear weights, which fortunately don't have the interactive issues of defensive UZR, we count the plays made by each player and the plays made by each player "add up" to the total value of the team. I think we're in agreement that the "two-step" procedure can result in the sum of the individual fielder UZRs exceeding the team UZR. This may be a matter of taste, but I strongly prefer systems in which everything adds up. (For all its limitations, Win Shares is notable for this quality.)

    Second, as we've discussed, there is much less risk of infielders stealing plays from other infielders--almost, from what we've seen thus far, no risk. Ventura is unlikely to be taking plays away from Jeter; rather, he is more likely to be making more plays on "his" side of Zone 56. The fact that Ventura makes more plays on his side of Zone 56 shouldn't cause Jeter's rating to go up.

    Third, I readily acknowledge that one would guess that the "play stealing" risk would be greater in the outfield. I'm not sure there is a solution that doesn't implicate Point One. MGL, do you have data on outfielder "play stealing" analogous to the helpful information on pitcher "play stealing"? If we can verify that it's not in fact a big deal . . .

    Fourth, if Bernie is concerned that an outfielder might be "harmed" by having a good player "next" to him, shouldn't said player shift away from the "encroaching" player to catch more balls on the "other" side, so that his team will catch more batted balls in total? The two-step approach seems to penalize smart positioning. As I've said before, in a world in which a .750 DER is exceptional, there are a lot of batted balls for everyone to field.

    Fifth, maybe the ultimate trade-off is as follows: which is more distortive of value *or* "ability" ratings: the "Jeter"-type of distortion we've been discussing, or the "Batista"-type of distortion as Bernie sees it. My strong sense, absent a lot of calculation, is that the Jeter-type of distortion seems potentially much larger, although as "play stealing" increases, the trade-off may change.

    Sixth, if increased volatility is a concern motivating the "two-step" calculation, I think the way to deal with that is to use the (I believe) less distorted one-step "value" number, and then, as you have wisely suggested in the past, separately "regress" the "value" for purposes of rating *ability*. I think what you'll find under the one-step approach is that the annual standard deviation in ratings goes up, but the year-to-year serial correlation per player, which is more important, will go up as well. In other words, I'm still confident in the vast majority of cases that the one-step number is less "biased", if even, assuming Bernie is right, it is more variable.

    Looking forward to learning more about Bernie's points.

  35. Posted by MGL  on  March 16, 2003 at 09:43 PM (#609548)
    Shorty, why were you Shortie and now you are Shorty?

    Anyway, first of all, I am almost positive that the two-step method adds up properly to coincide with a team UZR just as well as the 1-step process. In fact, it is specifically designed to make sure that the net number of balls in any zone for all fielders sums to zero. So I don't think that is a problem.

    As far as value versus ability, I don't think that is an issue either as far as the 2 methods are concerned. Value and ability are almost the same anyway. The differences are that ability must be "value regressed" (to account for sample error) and that, as David suggested, technically ability should take each fielder's ZR in each zone and apply league average distributions, rather than the other way around, although as Tango and I pointed out, there are some practical problems in doing that. In any case, I don't think the tension between the 2 methods has much if anyhting to do with value versus ability.

    I am also not convinced that the tension between the 2 methods is solely about whether fielder's "overlap" (can steal plays from one another) or not. If it is, then I think that it is clear that your method is best in the infield and that the other method could be better for the outfield.

    As far as checking if there is much out stealing in the OF, you can't realy verify it, like I could with the pitcher/SS and pitcher /2B stuff. We just "know" that there isn't much stealing in the IF even though there are plenty of shared zones (like 56 and 34). As you said, if there were too much stealing in the IF, it would probably behoove one infielder to move over.

    In the OF, OTOH, we "know" that there are lots of lazy fly balls, or even moderately difficult fly balls or line drives, whereby one fielder can call off another fielder. You can't really verify the extent of this in the OF by looking at the data. All you will see are shared zones like 78 and 89, which will look like shared zones in the IF (56 and 34). In the IF we assume that in most of those shared zones, the fielders do not steal ground balls from one another, and that if those shared zones were broken down further, much of the sharing would disappear.

    In the OF, however, we don't think that even if we broke down the OF shared zones, like 78 and 89, we would see most of the sharing disappear. We assume that there is much out stealing or at least out "calling", especially on lazy fly balls. How to account for that is another story. The suggestion that we perhaps separate the fly balls from the line drives, at least in the shared zones is a good one. Or we ignore or minimize the zones where most of the balls are caught (for example if in a shared zone 98% of the balls are caught, should we be calculating a ZR for each fielder in that zone? Probably not, since whether oen fielder catches 60% and the other catches 38% or vice versa probably has not much to do with their fielding abilitities in that zone, and mroe to do with who calls of whom, kind of like pop flies in the IF.) In fact, the more that I thinkof it, perhaps certain zones and types of balls should be eliminated from the analysis besides infield pop-ups and line drives. Perhaps any zone that has a high out rate should be eliminated altogether?

    Anyway, this is an interesting topic, not to metnion the fact that it is driving me crazy. I will solve it though, perhaps through my computer defensive sim work. I appreciate the help...
  36. Posted by David Smyth  on  March 16, 2003 at 09:43 PM (#609550)
    As far as the OF plays, it would either be between the CF and RF or the CF and LF. There is a long-standing convention that the CF is the "captain" and is supposed to take those common balls. So if you are comparing CF to other CF, we can assume that they all get the benefit of those extra balls, and can be fairly compared to each other. And just the opposite when looking at LF or RF. There are occasionally times when the RF might take a common ball, such as when a strong throw is needed, but again that is more of a *positional* thing, rather than an *individual fielder* thing. As long as you are only making within-position ratings, I don't see why there is much of a problem. And if you are trying to compare players from different positions...well, this is just one more reason why the most reasonable way to do that is with a proper offensive positional adjustment.
  37. Posted by tangotiger  on  March 16, 2003 at 09:43 PM (#609551)
    If there is no stealing, then I don't see why we should be making things more complicated than they should. Here's my explanation:
    ...consider all 78 zones for every fielder. Determine the out-coversion rate by POSITION for each zone. Take those out-conversion rates, and apply them to the opps while Jeter was on the field for each of the 78 zones.

    As for value or ability, unlesss we define these words, we don't know what we are arguing over. Ability is the manifestation of a player's tools in a context-neutral game. Value is the actual manifestation of a player's tools in a game, after considering context. Sammy Sosa's 3-3 3HR 9 RBI game has alot of value, but, by itself, has little impact on determing his ability. Value is about past accountability, and ability is about future potential. So, as MGL is doing UZR here, he's doing value. To do ability, he'd have to first apply a player's out-conversion rate againt the league average number of opps in that zone. And then, he'd have to regress that total to some degree. He's not doing the first part, and he's certainly not doing the second. This UZR is a value measure.

    And anytime you do a value measure, you must ensure that everything adds up. It's about past accountability. (Whether you decide to include a luck bin is a topic for another discussion).

  38. Posted by tangotiger  on  March 16, 2003 at 09:43 PM (#609554)
    I think David's right on the money here. His insight, while seemingly obvious, is rather remarkable.

    The bias in sharing zones in the OF will always be towards the position, and not the player. And if all CF have the same bias, well then don't worry about it. In the IF, the bias is based on individual positioning. But if there's less stealing in the IF (a number that we should try to quantify, but we can make a good guess that we can ignore), then again, let's not worry about it.

    As for errors, as Mike pointed out in Article 8, the rate of errors in the "easy zones" as opposed to the "hard zones" is not as much as you'd first figure (you might figure that errors are on plays in the easy zones). So, you might not need to treat the errors separately, and just treat them as hits.

    I know that we are trying to establish responsbility for plays that are ambiguous (non-outs, non-RBOE), but this leads us to more trouble than is (currently) worth. Taking a step back will lead us 2 steps forward. I think we should apply the KISS principle here.
  39. Posted by Dylan  on  March 16, 2003 at 09:43 PM (#609557)
    I would be curious to see some sort of concrete evidence that "stealing" in the IF isn't happening. Does anyone have any laid out to show that a good fielding 3B isn't stealing from the questionable SS or such?
  40. Posted by Mike Emeigh  on  March 16, 2003 at 09:43 PM (#609566)
    I've been staying out of the discussion until I see part 2, mostly because the devil is in the adjustments, but I do want to make one point about the shared responsibility problem.

    If the 3B is taking more of the plays in the shared zone than normal, the chances are that the plays left for the SS in that zone will be harder plays than normal. There are two reasons for this:

    1. Positioning. As I suggested earlier, if the 3B is playing to get to more balls in the hole, then it's likely that the SS is cheating up the middle, and will have to take an extra step or two just to get to the ball in the hole in the first place.

    2. The effect of the 3B "flashing in front of" the SS. If the 3B gets in front of the SS but doesn't make the play, he's probably going to affect the SS's field of vision, causing a hesitation. This isn't likely to have much of an effect when the players are playing normally, because almost all balls deep in the hole that the 3B doesn't get are hits anyway. But with extra 3B range, there will be some plays closer to the SS normal position that the movement of the 3B could affect.

    These particular issues are (IMO) pretty unique to the 3B/SS combo. Theoretically they could affect the 1B/2B, but because the 1B usually needs to play pretty close to the base I think it's less likely that he'll range far over toward the 1B/2B hole.

    -- MWE
  41. Posted by tangotiger  on  March 16, 2003 at 09:43 PM (#609568)
    I read this a couple of weeks ago, so I'm glad Ryan posted it on BP.

    "Definitely, I think last year was my best year... You can't go by number of errors, but I know I got to more balls that I didn't get to in the past. I felt my range was better and all-around agility was better by far."
    --Derek Jeter, Yankees shortstop, on his defense in 2002 (Sports Illustrated Online)

  42. Posted by MGL  on  March 16, 2003 at 09:44 PM (#609576)
    I agree with DS about the outfield stealing thing of course. In fact that's why I never worried about it too much. However, I do worry about it a little, and do think that any problem that does exist is rectifiable to some degree, for the following reasons:

    As David says, if all CF's takes 75% (or whatever percentage) of all fly balls that could be caught by either of 2 fielders, we have no problem of course. But we know that this will vary by team, depending upon who is considered either the surest handed fielder of the two or who is the "designated captain", notwithstanding the fact the CF is usally the "captain" by default. As well, we have lots of fluctuation (the measurement error in those shared OF zones will be greater) from player to player in terms of whether those either/or fly balls were closer to the CF or closer to the other fielder. Again, this is not a huge problem, but it is a problem nonethelsess.

    One way to address the problem is to see whether the overall out % in a shared zone is greater or lesser than the league average. If it is around leageu average and one fielder is below average and the other is above average, then I think that suggests that one fielder is indeed stealing outs from the other. If the overall is above average and one fielder is above average, then I think that suggests that the above average fielder is NOT stealing from the other fielder.

    Tango, also don't forget that while you say that UZR is strictly a value stat, once I do the adjustments it becomes more ability based, or at least context-neutral value based. The reason I don't like value stats (wihtout at least some kind of context adjustment) is that no matter what people say about wanting to know the actual "value" of a player, and no matter how much "cleaner" a value stats is, it always ends up being a discussion about ability (who is better or worse than whom, etc.)...
  43. Posted by Dylan  on  March 16, 2003 at 09:44 PM (#609577)
    I think to a much lesser extent the SS could potentially steal plays from the 2B in the same manor as he's coming across the diamond with the better throwing position. This would also be something I would be interested in seeing.
  44. Posted by tangotiger  on  March 16, 2003 at 09:44 PM (#609579)
    Value = actual manifestation of ability +/- context +/- luck
    Ability = expected manifestation of ability in a neutral context

    So, if you strip out the context to neutralize it (by adjusting for opponent, park, etc), you have to decide what to do with luck. Say, Shane Spencer's 1998 September had alot of (probable) luck, or Pat Tabler's bases loaded performance had alot of (probable) luck. You can decide to keep the luck portion with the player that "caused" it or "benefited" by it. In any case, that package is value.

    You can have a guy with lots of ability, say Mickey Mantle. But if he doesn't perform to his level for whatever reason (luck, design of being drunk or being hurt), then you can have a player whose expected ability would not match his actual value.

    (I don't have a good example in baseball... Mick wasn't a good example, but in hockey, it would be Stephane Richer.)

    MGL, based on how you are doing it, and unless you define your words otherwise, this version of UZR is describing value.
  45. Posted by tangotiger  on  March 16, 2003 at 09:44 PM (#609584)
    that should read "manifestation of talent".
  46. Posted by Shorty  on  March 16, 2003 at 09:44 PM (#609585)

    I switched to Shorty because you addressed me as such in your first response. Then it occurred to me that you were "right" to call me Shorty, not only because that version has the masculine ending ("y" rather than "ie"), but also because it has a "one-step" ending instead of a "two-step" ending. ;-)

    Sorry for the long post and sorry if this is a double post--couldn't be sure the first one went through. The good (new ideas) part is toward the end.

    Regarding UZR "adding up", I know realize, based upon a cursory glance at the Fanhome website, that a team UZR was never meant necessarily to equal or "match up" against a team DER. That's probably a good thing, as UZR reveals ways in which pitchers, either by accident or skill, generate easier- or harder-to-field ball distributions. It's very useful, for example, that UZR keeps track of line-drives, flyballs and ground balls, each of which have different out conversion rates.

    But setting aside the issue of the relationship between UZR and DER, the application of UZR as I understood it in Mike Emeigh's Jeter article (and in your most recent article, MGL) seemed to result in an OK Yankee '99-'00 UZR rating at both third and short, when it seems as though collectively the Yankees fielded a below average amount of ground balls at all of the third and short zones on a combined basis. (This could probably easily be verified.)

    Generalizing from that example, it seems inevitable that the effect would remain at the team level, as there was no way that other position interactions would necessarily correct the fact that the "whole" was greater than the "sum of the parts" at short and third. Furthermore, I can see no limit to how these interactions can play out at the other positions, at least in the infield.

    To repeat, for those such as David who might just be joining the thread, my reading of Mike Emeigh's Jeter articles and MGL's latest article seemed to indicate that Yankee third basemen had shifted over to cover Zone 56 (the "hole" between short and third) better, at the cost of allowing more hits "down the line" at third. The "points" earned by the third basemen (let's call him Ventura) in Zone 56 presumably offset the points lost "down the line", presumably resulting in an average UZR rating for Ventura. The "extra" Zone 56 plays by Yankee third basemen increased *Jeter's* rating by effectively decreasing his "denominator" of opportunities as UZR is currently calculated, thereby permitting him to earn, in those years, an essentially "average" UZR rating.

    Again, as I understand the "two-step", Jeter was given full credit for each play that he made in Zone 56, based upon the out conversion rate in that zone *for all position players*, and then was charged a fixed "league average shortstop" percentage of the total hits allowed in Zone 56, which were affected by Ventura's performance.

    The problem seems to be that he was charged a percentage equal to the league average percentage of *total* SS plays made in Zone 56 out of *total* batted balls in Zone 56, *whether or not* caught by the third basemen. The more balls Ventura fielded, the lower the hits charged to Jeter, because Jeter's "percentage" responsibility was fixed. As I write this, I *think* I'm seeing better how this methodology *helps* when a zone is *truly* shared, i.e., *either* player has an *equal* chance of making a play *anywhere* in the zone.

    But as we're discovering, Zone 56 and other infield ground out zones really cover two separate zones for which there is little overlap. The fact that player A fields well in his "half" of the zone should help him, but not help player B's rating. And the problem of the sum of the parts exceeding the whole remains.

    In the outfield, the risk of overlap is much greater in theory. However, David's "real world" comment that there is a convention that "center fielders don't share"; i.e., they take all the chances that they can, should prevent individual ratings from being distorted. I'm trying to think of ways in which we could verify this.

    But maybe the problem is self-correcting in the outfield in a way that it is *not* in the infield. And maybe the two-step approach is not particularly problematical for flyballs (*not* line-drives) to the outfield, or maybe just the "medium" distance left/center and right/center zones. Why?

    The two-step begins with a threshold determination of the likelihood of a ball being caught anywhere in the zone by anybody. Note how *low* the *out* rate is in Zone 56! That makes sense, because ground balls have low out conversion rates, and Zone 56 is the "hole" on the left side. Therefore the *stakes* are *very* high for player ratings in terms of allocating credit and blame for Zone 56 ground balls. Furthermore, the fact that out conversion is relatively low *collectively* is excellent indirect evidence that there is little *overlap* between the two fielders!!!

    If there are truly outfield zones in which flyballs are "shared", that is, it is highly likely that two outfielders can reach them, the likelihood of at least *one* outfielder reaching them is *extremely* high. Therefore the points "won" for "taking" such plays will be very low under the two-step procedure, and the "points" lost for ceding them will be lower. And since the gross number of hits will be very low, the fact that the "second step" results in effects of the type described in the Jeter example should result in the sum of the parts more closely approaching the value of the whole.

    However, it might get even simpler than that! Could we still, for the sake of simplicity and keeping the sum equal to the whole, stick to the one-step procedure, confident that any "hogging" won't help the hogger, because the *collective* out conversion rate is so high? In other words, shouldn't the *run value* per play made or not made above or below the league average rate for such position in such zone be quite low for the "truly" shared medium-depth outfield flies? Stated one more way, if we use the one-step approach to determine how many plays made by position player A in zone X above or below the league average, what is the run value we multiply that by? Wouldn't that run-value be very low in highly shared zones in which the likelihood of *somebody* catching the ball approaches 100%

    The decision to ignore pop-ups is just an extreme example of the dynamic described above. Since two, or three or four infielders can each reach the ball, the chance of any one of them getting it is nearly 100%. So we just ignore it altogether.

    Net/net, I'm back to thinking we can, through the "one-step" procedure, maintain simplicity, the principle of the parts equaling the whole, and not reward outfielders with idiosyncratic habits about claiming easy fly balls.

    Sorry again for the long post.
  47. Posted by tangotiger  on  March 16, 2003 at 09:44 PM (#609588)
    In terms of run value, you would do the following:
    - for each zone, determine the run value of the hit and out (let's assume it's a static .80 run difference, but we know that's not true)
    - for each fielder/zone, determine the number of outs made and BIP for each fielder and for the league
    - multiply the lg out-conversion rate by the BIP for the fielder in question, and take the difference
    - multiply the difference by the .80 value (or the dynamic value for that zone)

    That's it. That'll answer this question: "Given the ball distribution and context of Derek Jeter, how many runs better/worse is he compared to a lg average SS?"

    This assumes that sharing is not an issue.


    The other thing we are trying to do is figure out how to "share" the zone. You can
    a - share all BIP and split them based on the outs made by each fielder in that zone
    b - share all NON-OUT and split them based on the outs made by each fielder in that zone
    c - share all non-out, and non-RBOE, and split them based on the outs and RBOE made by each fielder in that zone

    For b, you add a fielder's outs made to determine "balls responsible for".

    For c, you add a fielder's outs made and RBOE to determine "balls responsible for".

    Each of these 3 options have certain validity to them. You can even compute them each way if you like. My guess is that you will find little difference overall. If that is the case, take option a. It's the easiest one, it's clean. In all cases, you can make the sum of the parts equal the whole.
  48. Posted by tangotiger  on  March 16, 2003 at 09:44 PM (#609590)
    The thread that Shorty refers to can be read by clicking the above link.

    Essentially, DER = fielding (or UZR) + pitching (or PZR), and we can figure this out using the zones. Check the thread for a longer explanation.
  49. Posted by MGL  on  March 16, 2003 at 09:44 PM (#609593)
    Slapshot, I don't mind changing the direction of this thread. I'm not sure where you are going with your quotation (whether you agree, disagree, or something else).

    If the Yankess were to acquire Tejada, since he is probably a much better SS (defensively), I think it would be correct to move Jeter to third, assuming that he was willing and could play third. The assumption is that if you move a bad SS to third, that he will perform better at third realtive to the other third basemen, of course. That's a general rule, and since third and SS require different skills (quick reactions, better hands at third, and more speed and range at SS), I suppose it is entrirely possible that a SS (good or bad) could not play an adequate third base (and vice versa). For example, I doubt that one of the small wirey good SS's, like Ordonez or Sanchez, could play a good third base (I'm not sure why, but you rarely see a small wirey player at third, though that may be because they are not good enough hitters).

    In any case, since both Jeter and Tejada are bif strong guys, there is no reason to think that one or the other would be better suited for third base. In the absence of any information in that regard, you clearly want to move the worse SS over to third, don't you? There is almost no doubt that no matter how you look at it, that Jeter is one of the worst defensive third basemen in baseball.

    In fact, there has to be a point at which you move a good hitting SS to another position, just like you would move an old SS or any other old fielder to first or to DH. What that point is I don't know off the top of my head. As Tango once explained, you would have to go through all the combinations on your team, look at each player's offensive and defensive ratings, and see which combination gives you the best overall runs scored and runs allowed (also keeping in mind that a run saved is slightly better than a run earned). If you have Jeter and Tejada on your team, whom you put at SS should be a no brainer I would think, unless, as I said, one or the other shows some great talent or complete inadequacy at third for some reason. For example, Jeter is probably worth around -15 runs or so per year at SS and Tejada is worth around 0. So if you assume that Jeter would be worth, say -5 at third, and Tejada +5 at third, you would prefer Tejada over Jeter at SS (to the tune of 5 extra runs).

    On the other hand, if the 15 runs difference between the 2 players shows up at third (such as if Jeter is -5 at third and Tejada is +10, or Jeter is -10 at third and Tejada is +5), then I guess it's a wash where you put them. When I say that the decision is a no-brainer, I am assuming that this is NOT the case - that the spread between a good and bad third baseman is not the same as the spread between a good and bad SS, which is a good assumption, I think (becuase the SS gets more chances and because range is a big factor at SS and not so big at third).

    Getting back to at what point you move your good hitting, bad fielding SS to another position, Jeter has to be somewhere close to that threshold (I am assuming that the worst SS in the league has to be somewhere close). When the Yankees had Tino at first, he was not a very go0d hitter (-8 batting lwts in 00, I think). If they moved Jeter to first, and got an average SS, and benched Tino, they would have, say, lost, say 15 runs in defense, but picked up like 35 runs in offense at first, for a net gain of 20 runs at first. If they put in an average SS, they would have picked up, say 15 runs in defense, and lost 40 runs in offense, for a net loss of 25 runs at SS. So while this switch may be a 5 run loser, it is close enough to a wash (if you get a better than average SS or Jeter is pretty good at first, etc., it might be a gain) to be worth considering.

    There are of course, at least 3 reasons why Jeter would not be moved from SS, at least at this point in his career: 1) He might be greatly offended, 2) He is not perceived by the Yankees (I don't think) as nearly as bad on defense as he probably is, and 3) It would probably be a bad public relations move (what would the Yankees say - "We like Jeter's offense, but he just stinks at defense, so we had to move him...").

    OTOH, if the Yankees did acquire someone like Tejada or A-Rod (I don't think they would), and they didn't trade Jeter, then I think they could come up with a diplomatic way to move him to third or somewhere else (DH?)...
  50. Posted by MGL  on  March 16, 2003 at 09:44 PM (#609595)
    That should be "one of the worst SS", not "third basemen", in the third paragraph of my last post.

    And Jeter and Tejada are "big" strong guys, not "bif" strong guys. Bif is the guy in "West Side Story", isn't he?

    And what the heck is going on with everything being italicized? Is it just my browser (older version of Netscape)? I thought that Tango was just trying to indicate how important his posts were compared to everyone else's! :)
  51. Posted by Italics Police  on  March 16, 2003 at 09:44 PM (#609596)

    Good reading.
  52. Posted by Slapshot  on  March 16, 2003 at 09:44 PM (#609600)
    MGL, thanks for addressing the Neyer comment. The way you and Tango, et. al. would practically look at a positional move makes quite a bit of sense. My only quibble is that you have used one year of stats to analyze the matter, and we do not know for example if Jeter and Tejada's value in your system last year varied more than their ability or past and projected performances. After reading Mike E's pieces dealing with some other seasons I had not expected that Jeter would come out as poorly as you make him out to be based on 2002, but that is the most recent data. Personally, I believe Jeter was at his defensive worst last year, and that frankly, he has been injured since the 2001 playoffs versus the A's and even earlier than that from a weightlifitng injury suffered after the 2000 season, from which he may or may not recover--it remains to be seen.
  53. Posted by Chris Dial  on  March 16, 2003 at 09:44 PM (#609602)
    Well, I waited it out it appears.

    First, David makes a correct observation wrt the "taking of discretionary plays" by CFs. Except Andruw Jones takes *all* of them. That's very important. When the CF is not just the CF, but the "defensive rep" he gets far more than 75% of the discretionary plays - he takes 90%. And when pop-ups are included to take eaway from MI, then stats get padded in a hurry. Hell, I forgot if MGL is removing pop-ups from OF. If not, you have a serious inequity on a team with a rookie SS (Furcal) and a GG CF like Jones, vs,say, the Mets with GG Ordonez and random CF. Isolating hte dominant personaltiy CFs isn't necessarily easy, but AJones is one, and that can be demonstrated in MGL's data wrt the consumption of FBs shorter than 220 feet.

    I used to score for STATS, so I have a good understanding of the raw data. In addition, I have a book of the ZR zones for every ballpark, and I've looked at the overlay diffrences between STATS and Retrosheet (which is Project Scoresheet's diagram, of course).

    As Shorty *perfectly* observes, what if the zones were smaller? Well, Shorty, I haven't actually seen the data MGL has, but if it's STATS data, then it is probably desseminated in smaller zones. He may have contractual obligations not to use the data "just like" STATS would.

    Here's the basic breakdown: Zone 56 represents 10 ZR sub-zones for the 3b and 5 for the SS. There are another 5 zones that are designated "no man's land" in ZR. One of the bigger differences between Defensive Average (please google rsb for Dale Stephenson's DA/DR work - not that he did the work, but that he has the data at his fingertips).

    You can see that 57% of plays are made (1419/2474). In reg. ZR 75% are the "responsibility" of either the SS or the 3B - usually, each defender misses ~10% of his zone opps, which would make up the difference between 57% and 75% (9% for 3b and 9% for SS). Of the 1055 hits, ~600 of them are in no-man's land.

    What this suggests is - *no*, other than *possible* positioning (which I disagree with Mike about - see no groupthink), the 3B's defense does not impact the SS defensive play making. The STATS zones of responsibility are assigned because those are the areas where 50% of plays are made. There's another 10 feet between the 3B zone and the SS zone - in ZR. Basically, no, Brosius and Ventura do not damage Jeter's ZR. He's not very good. But he isn't as bad as Clay says either.

    So, no, the Braves SS couldn't impact Chipper's rating. The SS can't play balls the 3B is responsible for. It's too far away and the SS couldn't be in front of the 3B and the SS couldn't throw anyone out from over there and deep anyway. Chipper did okay in ZR. He fared poorly in some systems because his team was a GB staff, but didn't throw GBs to 3B. That sounds screwy, but Chipper didn't have GBs hit into the ZR zone of assignment. It was dramatically depressed. Much moreso than Jeter's numbers (which aren't being impacted by the 3B either). Put it this way - if Chipper fielded *every* ball hit into the 5 and half of the 56 zone you are looking at and got the runner every time (100% efficiency), his Range Factor would still be lower than Aramis Ramirez' - the Pirates just threw more GBs to 3B. And systems that rely on "expected chances" fall in the dumper right here. That happens to Jeter to a lesser extent, *and* favors Andruw Jones in a similar way.
  54. Posted by tangotiger  on  March 16, 2003 at 09:44 PM (#609604)
    Let's say you have the hypothetical zone 65. For the league, there's an average of 200 BIP in this zone, with 80 outs recorded, 50 from the SS and 30 from the 3B. There's also 10 errors, 6 from the SS and 4 from the 3b. The average safe play is +.50 runs, and the average out is -.30 runs.

    Our team has a SS named Derekson, and a 3B named Robinson. Derekson recorded 40 outs and made 10 errors, while Robinson recorded 40 outs and made 0 errors.

    That's all we know. What do we do?

    Method 1A
    Derekson is 40-50 = 10 outs worse than average (or 8 runs worse) for his position in that zone, and Robinson is 10 outs better (or 8 runs better).

    Method 1B
    Of the 200 BIP, the SS gets 5/8 responsibility, or 125 plays. 3B gets 75 plays. The avg SS made 50 outs and 75 safe plays for a LWT run value of +22.5 runs. Jeterson made 40 outs and 85 safe plays for a LWT run value of +30.5 runs. That's 8 runs worse than average. Robinson works out to 8 runs better than average.

    As you can see, Method1A and 1B are the same thing. 1A is much more straightforward, and you don't have to consider the "sharing" on zones.

    Method 2
    Of the 120 non-outs, we give 5/8 to the SS as his responsibility, or 75 safe plays. The 3B get 45. Derekson was responsible for 40+75=115 plays, and Robinson 85.

    The average SS has, as you remember,+22.5 LWT runs. Derekson is +25.5 runs, or 3 runs worse than average. Robinson was 3 runs better.

    Method 3
    Of the 110 non-outs, non-RBOE, we get 56/90 to Jeterson, or 68.4. Adding in his 40 outs and 10 errors, and that gives him 118.4 BIP (40 outs and 78.4 safe plays). That's a LWT run value of +27.2 runs, or 4.7 worse than average. Robinson was 4.7 runs better than average.

    Method 4
    The avg SS, of the known plays that were not fielded by the avg 3B (166 of them), 50 were outs, 6 were errors, and 110 were hits. So, the avg SS has a LWT run value of +43 runs.

    Jeterson's 3B fielded 40 plays, meaning that 160 plays were up for grabs. He recorded 40 outs, 10 errors, and 110 were hits. That's a LWT run value of +48 runs, or 5 runs worse than average.

    In this case, the 3B is not the reverse, so let's do Robinson. The avg 3b, of the known plays not fielded by the avg SS (144 of them), 30 were outs, 4 errors, and 110 hits. The avg 3b has a LWT run value of +48 runs.

    Robinson's SS fielded 50 plays, meaning that 150 plays were up for grabs. He recorded 40 outs, 0 errors, and 110 were hits. That's a LWT run value of +43 runs, or surprise, 5 runs better than average. Even though we double-counted, we still end up with the result that the team overall was zero.

    So, where does that leave us? I don't know. But, in this example, which I guess is a bit extreme, we're talking about a 5 run swing per 200 BIP. I don't know how extreme the real Jeter/Ventura is, or how many shared plays you need to worry about.

    So, we have to decide which method best captures the contributions of our players.

    Anybody else left dizzy with these math gyrations? Sorry about that, but it had to be done!
  55. Posted by MGL  on  March 16, 2003 at 09:44 PM (#609605)
    Slapshot wrote:

    "My only quibble is that you have used one year of stats to analyze the matter, and we do not know for example if Jeter and Tejada's value in your system last year varied more than their ability or past and projected performances..."

    Slapshot, any analysis of a player's defense must be informed by their true ability, rather than by measures of their sample ability, so I don't diagree. What goes into "translating" a player's sample defensive rating to an ability rating is regression based on sample size (luck), age adjustments, and injury adjustments.

    Here are Jeter's and Tejada's last 4 year's (99-02) adjusted UZR runs per 162 games:

    Jeter: -14, -8, -22, -27
    Tejada: 9, 7, 0, 4

    I think that the numbers speak for themselves...
  56. Posted by Shorty  on  March 16, 2003 at 09:44 PM (#609606)

    I was unaware of the availability of further subdivisions in Zone 56. It sounds like you're saying that Yankee third basemen did not take plays from Jeter in his "mini-zones", and that in general there is a clear no-man's land running down the middle of Zone 56. If that's right, then in cases in which we're analyzing "aggregate" Zone 56 data, we have additional evidence why we should not use the "two-step" calculation analyzed at length in the Shorty/MGL/Tango threads above. As the the threads above indicate, extra plays made in the *third base* side of Zone 56 cause *Jeter* to be charged--under UZR--with *fewer* hits allowed in Zone 56.

    In other words, we haven't been saying that Ventura hurt Jeter by taking plays away from Jeter; we've been saying Ventura *subsidized* Jeter's *rating* by making more plays on the third base side of Zone 56. This subsidy resulted from a "two-step" calculation mechanism designed for situations in which two position players have an *equal* opportunity to reach batted balls *anywhere* in a *shared* zone. That mechanism *may* have a good role to play in dealing with Andruw, but the trade-off is that it may result in the sum of individual outfielder ratings (plus infielder ratings) exceeding the *team* UZR. (For reasons explained in the threads above.)

    Regarding Chipper, I didn't mean to imply by my prior post that Chipper's rating *had* to be the result of a "subsidy"; I just posited the possibility. The probable explanation is that Atlanta's pitching staff, which was remarkably stable during Chipper's tenure, probably had a persistent lefty-fly ball / righty-ground ball composition. Those things happen. Just curious--if Chipper is an OK third basemen, why did they move him to left?

  57. Posted by MGL  on  March 16, 2003 at 09:44 PM (#609608)
    Well, I tried 4 different UZR accounting methods in my "defensive sim". Only one of them achieved the correct results for all 9 combinations of two fielders (poor/poor, poor/average, poor/good, etc.). It is the simplest. It is a fielder's outs divided by the total BIP's (hits plus all outs) in a zone MINUS the league outs for that position divided by BIP's in that zone, MULTIPLIED by the total BIP's for that player. This is Shorty's method.

    BTW, this yields the exact same results as the folloiwng method:

    Take the total BIP for a player (in a certain zone) and prorate them according to that player's share of the total outs in that zone. Call this number that player's "chances". Then take that player's outs divided by his "chances". Do the same for the league. Then subtract that number (the league outs at that position divided by the league "chances" for that postition) from the player's "outs divided by chances" and multiply the difference by the players "chances". The answer you get is always exactly the same as the first, much simpler method.

    It is NOT correct to divide player and league outs by total outs. It is NOT correct to do my "prorate the hits" method (my method in Part I of the article).

    This applies to all zones, shared or not, whether one fielder steals outs from another fielder or not, as long as the out stealing is the same for all players, as David points out (becuase the out stealing will show up in the league totals).

    The problem arises, as Chris points out, when a certain player, like A. Jones, steals outs more or less than the league average. Then something else needs to be done, and I'm not sure what that is right now. I will work on it eventually, but I don't have any mroe time to devote to tweak UZR until after I come out with my Super-lwts and finish my projections for Tango (if that is even possible at this point).

    BTW, I have STATS data (so I have data from STATS smaller zones), but I do the UZR from the retrosheet type data (larger zones). Actually I transpose the STATS data into retrosheet format and then I do the UZR analysis.

    Eventually, I will use the STATS data to address the A. Jones out stealing issue...
  58. Posted by Shorty  on  March 16, 2003 at 09:44 PM (#609610)

    I confess to feeling dizzy and I'll try to re-examine the examples tomorrow. Just to help me focus, which one is designed to replicate current UZR calculations?


    Are the "revised" Jeter UZR ratings based upon the one-step calculation? Do they include his DP rating? Many thanks again.
  59. Posted by Slapshot  on  March 17, 2003 at 09:44 PM (#609587)
    I realize this is not exactly where this thread is right now, but I would appreciate commentary on the following comment by a well-known popularizer of the sabermetric approach, who apparently is not following the good work being done by the good folks of Baseball Primer.

    Sure, it's not hard to imagine the Yankees signing Tejada (though the notion that Tejada should move to third base so Jeter can continue to sort of play shortstop is laughable, if not sublimely absurd).
  60. Posted by MGL  on  March 17, 2003 at 09:44 PM (#609611)
    Everything from now on reflects the "new" (simple, Shorty) methodology. They are only UZR ratings, which do not include DP ratings. DP rating, at least as I calculate it (I split the credit for every DP above or below league average 50/50 between the fielder who starts it and the pivot man), does not affect a player's overall defensive rating much (around +-1 run)...
  61. Posted by Doug  on  March 17, 2003 at 09:44 PM (#609613)
    Was thinking about your future centext adjustments, and started wondering about distinguishing infield hits from others in terms of hits allowed in a zone. Is this one of those adjustments?

    My thinking is that just getting to a ball to knock it down is a desirable skill, as opposed to not getting to the ball and allowing it to go through to the outfield. Clearly, there is less opportunity for runner advancement, and hence more "saved-run" value in the former case. Yet, UZR appears to treat both cases as just a hit allowed, with equal "cost" charged. Meaning, a player who can get to more balls (even if he can't turn all of them into outs) may not be receiving all the credit he is due.

    In a similar vein, for a player who gets to a lot of balls other players don't get to, but throws away that advantage (pun intended) with more wild throws, he would presumably end up with fewer hits allowed, but more ROEs than his more typical counterpart who never got to the ball in the first place. Which guy is going to come out further ahead in UZR? Which guy should?

    Something's been bugging me about how errors and hits are dealt with separately - can't quite put my finger on it, but here goes.

    might get dealt with
  62. Posted by tangotiger  on  March 17, 2003 at 09:44 PM (#609617)
    To recap: the method that MGL last mentioned is exactly Method 1A that I have shown, which is equivalent to the longer more complicated Method 1B. Method 1A is also the (I think) exact same method that Mike Emeigh mentioned in his fielding series about not worrying about splitting the shared responsibilities, and I think this is the same method Shorty proposed.

    So, from where I sit, Mike, Shorty (who is also named Michael), Mitchell (lotsa Mickeys around here), and I have all agreed that Method 1A is the simplest method, probably most accurate. This looks like the one that MGL is going forward with.
  63. Posted by Chris Dial  on  March 17, 2003 at 09:44 PM (#609620)
    Well, if you guys read my DPI methodology, Method 1A seems to be what I do without access to smaller zones. I did it four or five years ago. I don't know why it is largely ignored. It's on this site, even. If it isn't, let's discuss why we do or don't think so.

    I guess super-genuises aren't recognized in their own time. ;-)
  64. Posted by Slapshot  on  March 17, 2003 at 09:44 PM (#609621)
    There is something strange goin on in this thread: my question to MGL now appears to be answered before it is asked. That is mighty impressive.

    Thanks to MGL for posting Tejada vs. Jeter UZR's for years prior to 2002. The conclusion seems to be somewhat at odds with Mike E's series regarding Jeter's defensive reputation. I appreciate the many additional insights and look forward to Part II.
  65. Posted by tangotiger  on  March 17, 2003 at 09:44 PM (#609623)
    Yes, those numbers look strange, since from 98 to 2000, he was pretty average, and it was in 2001 and 2002 that he s-cked rocks.

    Perhaps with the newly revised UZR, his somewhat average rating from that time period were biased by the other factors that MGL is considering.
  66. Posted by tangotiger  on  March 17, 2003 at 09:44 PM (#609624)
    Chris' article can be found in the link.

    So, let's add Chris to the list in terms of support for how to handle the zones.

    Dan, if you are out there, you might want to add Mike, Chris, and Mitchel's past articles on this subject in the "related links".
  67. Posted by Bernard Shakey  on  March 17, 2003 at 09:44 PM (#609629)
    Hi. First time posting here. I'm the guy that MGL referred to from fanhome "defending" the "extra step". I think the Shorty equation is an excellent on IF we know for sure that there is no "stealing" in the gray zones. Based on the anectdotal "logic" plus the important Chris Dial post which offered some substantive evidence that there is *probably* no sharing in the infield (at least the zone in question, we can assume the same holds for other zones) . . . then there is no need to use the extra step, which essentially is a fudge.

    Shorty, you're correct that the extra step is essentially a "subsidy" for particulary the less dominant fielder in the zone. You can also look at it as a "regressionary" equation that "pulls back" the player (slightly) toward the zero base-line. The effect is less volatility if sharing does come into play. I don't know if that was what MGL originally intended for it or not . . . or perhaps he was doing housekeeping to get his net outs to "add up". I gather he wasn't too sure why he used it.

    The example I used in my post assumed something different, but the principles remained the same, that this formula is more sensitive to sharing than the 2-step method. Going by MGL's post on what the formula actually is (using Bordick as an example):

    (Borick outs/tm opp - SS outs/lg opp)*tm opp
    =(18/162 - 294/2474)*162

    (The number 162 was provided by MGL on fanhome so I assume Batista and co. made 65 outs)

    You get a net out of -1.25. If Batista "hogged 2" the net out goes up
    to -3.12. So it's sensitive to sharing, to range factorish proportions. But, here's the good part. It has absolutely *no effect* on the performance level of the adjacent fielder. If Batista made two extra outs (or two less outs) and Bordick made his same 18 . . . and opps held constant, there should be no effect on Bordick's net outs. Using the two step method there is some because the prorating based on hits to outs is factored in).

    So bottom line the method 1A is the best one IF there is no sharing...

  68. Posted by Chris Dial  on  March 17, 2003 at 09:45 PM (#609638)
    I just want to speak up to thank Bernard and Shorty for dropping in and bringing some excellent observation and critique to the discussion. When I complain about peer review on others' methodologies, this is the discussion that should take place. MGL cannot be commended enough on his acceptance of the input and willingness to listen. That's very hard to do in a published public forum *with* immediate feedback where the author is expected to respond. Bravo, MGL.

    Other than that, I'm really looking forward to the Part II. I hae a few quibbles that I'll get to later tonight.
  69. Posted by tangotiger  on  March 17, 2003 at 09:45 PM (#609643)
    I second Chris' point. Some analysts present their findings, and then leave, for whatever reason. Thankfully, MGL is not one of them. Effort + intelligence + changing approach + access to data = GREAT!!!
  70. Posted by MGL  on  March 17, 2003 at 09:45 PM (#609662)
    Doug, looks like your post got cut off (I think there has been a poltergeist in Primer lately).

    Good point about the infield hits! The value of an infield hit (when an infielder knocks down a ball heading for the outfield) is obviously less than that of an outfield hit (because of the baserunner advances). It would be interesting to see if infielders with greater range do in fact allow more infield hits (knock down more ground balls).

    OTOH, if I included that it UZR, how much difference would it make? OTOOH (how many hands are there?), I am including things in the adjustments that have little overall influence (like pitcher G/F ratios).

    As far as doing the errors (ROE's) separately (I could just lump them in with the hits), there are several reasons to do so. One, they have a slighly different value than a hit. BTW, I could separate fielding errors from throwing errors (for IF'ers) if I wanted to, since throwing errors may have a higher value. Two, I wanted to present a fielders UZR "fielding" runs, which is his "range", and his UZR "error" runs, which is his "hands", even though it makes no practical difference - defense is defense. Perhaps, however, as a fielder gets older, his "hands" get better and his "range" gets worse. I don't know. Or perhaps you can teach, or a fielder can learn with practice, to get better with his hands, but not with his range. SO it might be important (for a team at least) to know the breakdown of a player's UZR runs (hands and range). Also, there is probably a different standard error for "range runs" and "hands runs", although I'm not sure which would be higher. An error is very certain - we know that the fielder reached the ball with reasonable effort and then "booted it" or threw the ball away. With a hit, we have all the problems that we were discussing (is that fielder really responsible for every hit he is "charged" with). In that sense, it would seem that the hit would have a much higher standard error (uncertainty) than the error.

    OTOH, an error is often the result of a bad hop (maybe 50% of the time), in which any fielder would have made the same error. So how much do a fielder's errors reflect his fielding (hands) ability? What is the year to year correlation for errors? Look at R. Ordonez. One year he has like 3 errors and the next, like 20. On the other hand, you had fielders like Sandberg and Elster who were known for few errors every year (I think). Part of that was that they had limited range, of course. Anyway, the hits and outs, even with all the problems apportioning the hits, do reflect a fielder's range, which is a reflection of his ability. So in this sense, maybe the erros have MORE of a standard error (correlate less with ability) than the hits (Maybe throwing errors correalte well with ability, but fielding errors do not because of the bad hops).

    In any case, I don't think it can hurt to calculate the errors separately (and I THINK I did it correctly, although now I'm not so sure about anything) - it can only help...
  71. Posted by MGL  on  March 17, 2003 at 09:45 PM (#609665)
    I re-read Chris Dial's article from Tango's link (than God someone knows how to do things like that - create links, etc.). Two things come to mind:

    1)I long for the day when a player's defensive rating (be it ZR or UZR or some other reasonaby accurate metric (NOT RF!) is uttered in the same breath as his offensive rating (be it OPS, lwts, xRuns, RC, or BaseRuns), rather than as an afterthought! Yes, these defensive metrics (ZR, UZR, etc.) are not as accurate or reliable as the offensive ones, but they should be far from an afterthought - including them is far better than not including them, IMO!

    2) It never ceases to pop up, in discussions about infield defense, how "important" a player's DP rating is (particularly for those that pivot also - the 2B and SS). It is NOT important (relatively speaking)! It is paled in "importance" by a fielder's fielding ability! A typical SS or 2B'man is a MAXIMUM of plus or minus 3 runs (pivot and starting DP's), and a typical first and third baseman is at most plus or minus ONE (yes, including the all "important" 3-6-3 DP) run! I guess the assertion that DP skill is "so important" falls into the category of the assertion that a great fielder saves his team "a run or two" per game...

    BTW, I'm not sure what category OF arms fall into (are they undervalued or overvalued?). They are, in fact, more important than DP defense. The typical OF'er has an "arm lwt" of plus or minus 4, with an occasional 6.

    Keep in mind that when we talk about "plus or minus" 3 for infield DP skill or "plus or minus" 4 for OF arms, these are one-year sample spreads, which means that the typical spread in "ability" is much less!

    In fact, the more that I think of it, I long for the day when a player's "complete package" (read: Super-Lwts) is uttered in the same breath as his offensive value. As someone pointed out in the Dial article, Piazza is a good example of how you must consider a player's total package. As good a hitter as Piazza is, his other numbers are so bad across the board (throwing, GDP, baserunning, moving runners over), that he is NOT a great player overall. When discussing Piazza (and many other players (read: Jeter on defense), his other numbers should not be an afterthought...
  72. Posted by Slapshot  on  March 17, 2003 at 09:45 PM (#609671)
    Re "complete package" (read: Super-Lwts)" and "When discussing Piazza (and many other players (read: Jeter on defense), his other numbers should not be an afterthought...

    But some numbers are less "definitive" than others so breaking them out is perhaps more practical than a total package a la super-Lwts. You need to know the individual components since some are more prone to variation and may be less reliably predictive. Also, I believe that Jeter, unlike Piazza, would do well in many/most of the other skills you mentioned other than overall defense, as he makes good use of his speed, is an excellent base runner and stealer, has a good arm which plays its part in relays, hits the other way and is thus likely decent at moving runners over, and is not prone to GIDP. Including him in the sentence with Piazza, whom you say is weak at everything else across the board, could be a bit misleading IMO. I am not suggesting that all the other factors make up for his defensive deficiency, but they probably offset a few runs per year, which brings us back to his being a superior shortstop overall, and perhaps still a great (if not anywhere near AROD-great) player. As I may have said earlier, I think it will be most interesting to see how Jeter performs this year.

    Leaving all the Steinbrenner commentary aside, Jeter has said that he hurt himself weightlifting two off-seasons ago and that this is the first time he has been able to enter the season completely healthy since. We may see if the last two years are part of a long post-peak decline phase that will continue or perhaps were deviations from his more normal path, and which may have derived inpart from his injuries. This is where scouting and traditional information needs be married to the tremendously insightful analytics being developed by sabermetricians such as MGL, et. al.

  73. Posted by MGL  on  March 17, 2003 at 09:45 PM (#609676)
    Actually, Jeter is a great example of why you need the "total package" rather than just the offense and the defense or just the offense.

    If you just look at his offensive numbers (say, including his base stealing), he looks like a GREAT player, considering he is a SS, and worth every penny he is making.

    If you then include his defense, he no longer looks like a GREAT player - he looks like a GOOD player.

    If you then include his baserunning and advancing runners, he is now a VERY GOOD player.

    Jeter and Piazza are examples of players whom we know have major non-hitting deficiencies (although we tend to ignore or at least minimize them). The players that most concern me are the ones whom we don't for whatever reason know or consider their non-hitting deficiencies (or their non-hitting benefits, though this seems to be less prevalent). Two that come to mind are Womack and Bernie Williams. Womack can't hit and I've never heard him referred to as a terrible defensive player, which he is. His last 3 years' adjusted UZR runs per 162 games at SS were -16, -10, and -27. He does not belong on a major league team.

    Bernie Williams is usually referred to as a good or excellent CF'er, as far as I know (although probably those in the "know", other than sabermetricians, know otherwise). This is because he is (was?) fast and graceful, or perhaps once was a good or great CF'er. His adjusted UZR runs for the last 4 years are -20, -14, -16, and -33 and his arm runs are -2, -6, -5, and -10 (wow, I didn't realize his arm was that bad, and that baserunners aparrently know that)!!

    Despite his great offense, he is no better than an above average CF'er, and I'm sure he is overpaid.

    Yes, I recognize that defensive metrics are less "definitive" in many ways than offensive ones. Again, that does not mean that they should be ignored or mentioned as an afterthought! As far as the other components in my Super-lwts, they are as "definitive" (and reliable) as any offensive metric, and if nothing else, should be lumped in with a player's offensive lwts, so that we can get at least the "total package" sans defense.

    One more thing: If we all had a nickle every time a player, coming off a bad year or years, said something like "I'm finally healthy..." (if you get my drift)
  74. Posted by tangotiger  on  March 17, 2003 at 09:45 PM (#609678)
    Bernie williams and Rondel White. I'm surprised that two such strong guys could have such poor throwing arms. Anyone think of an OF with a worse arm than these two?
  75. Posted by MGL  on  March 17, 2003 at 09:45 PM (#609683)
    Yes, upon a quick look at White's arm runs for 99-02, it looks like he was also around -5 runs per 162. Between them that's around one win per season given up by their arms alone!. At least White showed a good UZR runs for 01 and 02 (+19 per 162) to offset Bernie's terrible UZR runs...
  76. Posted by tangotiger  on  March 17, 2003 at 09:45 PM (#609684)
    I think we could all pick out say 80% of the good fielders visually. I don't think we could determine the impact of their fielding. There's another 20% that might surprise us. And then there's the reverse.

    I think this is a good Bill James rule. A stat that never surprises is boring. A stat that always surprises is wrong. 80/20 is a good split.

    So, is Torii Hunter part of the 20?
  77. Posted by Chris Dial  on  March 17, 2003 at 09:45 PM (#609689)
    MGL, I'm not sure how those two things come to mind after reading my articles. I am somewhat well known around USENET for being tyrannical wrt making people *always* consider defense on any "player X is better than Y" commentary.

    And how position always matters - although I know that is a point of argument at fanhome.

    As for turning the DP, the Defensive Average work indicated that DPs were largely over-rated wrt importance. I ignored them and your work agrees with DA findings.

    Piazza is a catcher. Is he not the highest ranking catcher?

    Womack, in the sabermetric circles I run, is considered to suck on defense.

    While the noise level is high on USENET, some of the sharpest minds around cut their teeth there, and most still frequent. And the peer review there is outstanding. There's one guy in rsb that is _the_ expert on the Wizard of Oz. I honestly belive he can claim that, if he wanted to - but it isn't Ty Cobb.

    But you have the right view, and work like yours goes a long way to help - the total player contribution is what's important.
  78. Posted by MGL  on  March 18, 2003 at 09:46 PM (#609696)
    Chris wrote:

    "MGL, I'm not sure how those two things come to mind after reading my articles. I am somewhat well known around USENET for being tyrannical wrt making people *always* consider defense on any "player X is better than Y" commentary."

    My "musings" had nothing to do with you per se. In fact, you are one of those advocating presenting the "whole enchilada", right? Those 2 thoughts just popped into my head while I was reading your article, which was very good, BTW. In fact, I think that ZR and RC (or whatever offensive metric you want to use) should have been combined, as you sugggest, a long time ago, when talking about a player. I've never had a problem with ZR. I think it captures a fielder's value, albeit not perfectly, 90% of the time. Outside of sabermetric circles, even though ZR has been around for a long time (15 years?), it either gets mentioned as an afterthought, not mentioned at all, or scorned.

    As far as Torii Hunter, he is very much in that 20% (like J.T. Snow), although you always get someone saying, "Yeah, I knew all along he was not a good fielder" - I would like to one time hear someone say that BEFORE the metric comes out..."

    Hunter's UZR runs, per 162, 99-02:

    -2, -8, +10, -17

    He does have a good arm:

    .4, 2.3, 1.4, 3.7


    -1, -12, +3, -8

    (He is about a wash in DP runs)
  79. Posted by MGL  on  March 18, 2003 at 09:46 PM (#609697)
    I ran across this quote on BP. Most of you probably heard this - I haven't. It's humorous.

    "Definitely, I think last year was my best year... You can't go by number of errors, but I know I got to more balls that I didn't
    get to in the past. I felt my range was better and all-around agility was better by far."
    --Derek Jeter, Yankees shortstop, on his defense in 2002 (Sports Illustrated Online)

    Jeter's "range" (errors not included, since, as Jeter says, you can't go by errors - whatever that means) UZR for last 3 years:

    -5 (116 "games"), -19 (129 "games"), -26 (147 "games")

    "Games" are Jeter's chances divided by league average SS chances per game.
  80. Posted by David Smyth  on  March 18, 2003 at 09:46 PM (#609702)
    Tango wrote, "I think we could all pick out 80% of the good fielders visually."

    Well, if Jeter is -20 runs per 162 games, at -.75 runs a pop, that comes to one play every 6 games that an avg SS makes that Jeter doesn't. And that's assuming that you are watching all of the games to form your impression. Furthermore, it's not like these criteria nail down BIP difficulty with real precision. Just because a ball passes in zone 56 with "medium" velocity doesn't mean that we have really captured the difficulty of every ball meeting those criteria. So it's entirely possible that the 1 ball every 6 games was more difficult, just by chance.

    Every fielder handles almost all of the easy-routine plays. Every fielder occasionally makes plays the "look" great, and every fielder occasionally screws up. The only fielders that we can be pretty sure of how they rank just by casual observation might be the fat 1Bmen, like Vaughn or Thomas.
  81. Posted by tangotiger  on  March 18, 2003 at 09:46 PM (#609708)
    David, I moved to NY/NJ in fall of 97, having hardly seen the Yanks or Mets play. After watching a dozen games, Brosius reminded me of the good ole days of Tim Wallach. Tino looked good for a 1B. Jeter also looked good. Piazza has an arm as strong as Bernie, and I don't know why. Reyrey was great to watch. Olerud was similar to Tino. (Though both of these were slightly below The Big Cat in his heydey.) Fonzie was excellent, whether at 2b or 3b. I was impressed with Derek Bell and I always liked Brian McRae, but maybe their poor positioning made their plays look better than they should?

    So, if the numbers tell me something, and my impressions tell me another, then there must be a reason. I guess McRae's numbers weren't that good, and so maybe I have a certain bias for flashy plays in CF, having been subjected to Dawson, Grissom, and "Puck" White all my life. If Big Cat's numbers (in his prime) don't look good, then I'd say there's a problem with the numbers (I don't know what they are).

    Maybe the most revealing things about UZR is with the OF, because positioning, speed, and hang time of ball are alot harder to judge in the OF than in the IF. Since 3B is very reactionary, and arm strength is easy to spot, I'd guess that 3B and 1B (scooping glove) should be the easiest positions to qualify visually, without supporting numbers. Maybe CF is the hardest.

    So, maybe you can make a good guess at 90% of the 1b down to 60% in CF? The "visual fielding spectrum" (VFS) might be 1b,3b,c,2b,ss,rf,lf,cf,p ??
  82. Posted by Shorty  on  March 18, 2003 at 09:46 PM (#609709)
    Thanks again to MGL for considering our input. I'm with all of you on (i) the importance of considering everything that we can measure (including defense) when rating a player, (ii) the relative unimportance of DPs and (iii) the surprisingly high importance of outfielder arms. I think there was a Clutch hit a while back about how bad Bernie Williams' arm is.

    Regarding the treatment of errors and infield hits, the UZR database is probably rich enough to quantify the difference in value between certain types of errors, the allowance of "infield hits", and the failure to make any play at all. My limited research using non-PBP data suggests that "raw" errors (i.e., not broken out between throwing and non-throwing errors, and excluding WP, PB and BK) have no statistically significant effect on runs allowed, *after* one takes into account plays made out of the total of batted balls in play.

    I also find this thread's latest application of the 80/20 rule amusing and probably right.

    MGL, do you have a rough idea when it might be possible for the revised UZR results for 1998-2002 to be posted? I know you're a busy guy (I don't know how you do it, being in law school and all), but you seem to be a wizard at programming. ;-)

    Also, have you ever considered having just defensive stats shown by position over the past five-year period, with players ranked in descending order of playing time at that position, so that long-term performance and trends can be easily spotted? I think such a summary would have a *tremendous* impact in the sabermetric community in terms of correcting and forming fielding reputations.

    For example:


    Player / 5-year innings played ("IP") at position / 1998 IP-UZR-DP / 1999 IP-UZR-DP / 2000 IP-UZR-DP / 2001 IP-UZR-DP / 2002 IP-UZR-DP


    Player / 5-year IP at CF / 1998 IP-UZR-AR (arm rating), etc.,

    If it would be easy to do, I'm sure we'd all be very grateful.

    Many, many thanks again.
  83. Posted by tangotiger  on  March 18, 2003 at 09:46 PM (#609712)
    In terms of RBOE, whether on a miscatch or misthrow, and the difference in LWT value, relative to a single:

    If you don't catch the ball properly, it's the same as an infield single. The LWT value of an infield single or a miscatch would probably be about .40 runs.

    The LWT value of a misthrow would probably be similar to an outfield single, with sometimes being equivalent to a double. I'd guess therefore about .50 to .55 runs.

    Suppose you have a guy with 5 catching errors and 25 throwing errors, and the reverse: what's the difference? Using the above numbers, you get a difference of 2 runs. I'll guess these are pretty extreme numbers, and you wouldn't get that kind of split on throwing/catching errors by *position*.

    My guess is that distinguishing between catching and throwing errors will give you an "error range" (no pun intended) of 1 run.
  84. Posted by Craig Burley  on  March 18, 2003 at 09:46 PM (#609716)
    It never ceases to pop up, in discussions about infield defense, how "important" a player's DP rating is (particularly for those that pivot also - the 2B and SS). It is NOT important (relatively speaking)! It is paled in "importance" by a fielder's fielding ability! A typical SS or 2B'man is a MAXIMUM of plus or minus 3 runs (pivot and starting DP's), and a typical first and third baseman is at most plus or minus ONE (yes, including the all "important" 3-6-3 DP) run! I guess the assertion that DP skill is "so important" falls into the category of the assertion that a great fielder saves his team "a run or two" per game...

    If this is the case, with double plays being worth about half a run apiece (as compared to forceouts... a run apiece compared to all-hands-safe), it follows that the difference between a very good 2B and a very bad one is about ten double plays a year.

    I'm not saying that's wrong, but that seems highly unlikely to me; I would have thought the difference would be greater, at least twice that.
  85. Posted by tangotiger  on  March 18, 2003 at 09:46 PM (#609720)
    Craig, that's exactly right.

    I've got Craig Biggio at one end and Jose Vidro at the other end, and the difference between the two is about .20 DP turned as pivot / dp situation. There's about 100 of those opportunities to turn, so that makes the swing 20 DPs, or +/- 10 DP.
  86. Posted by MGL  on  March 18, 2003 at 09:46 PM (#609721)
    Yes, I'm more than happy to make available complete UZR ratings for 99-02 (I don't have batted ball speed for 98).

    I talked to Dan Szymborski of this site about putting up the complete UZR files (on this site), but he hasn't gotten back to me on that. I don't think it will be a problem. He's been very helpful with everything else. (BTW, I submitted part II of the UZR article, so that should be up on this site shortly, I assume.)

    Maybe Tango can put up the UZR files on his web site and Primer can link to them if they want.

    I'll put them in the best format I can think of, something similar to what Shorty suggested (also Tango is a magician in terms of being able to "do" things on a web site, like sorting data with one click of the mouse)...
  87. Posted by tangotiger  on  March 18, 2003 at 09:46 PM (#609723)
    MGL: Sure, sounds good.
  88. Posted by MGL  on  March 18, 2003 at 09:46 PM (#609725)
    Oh and BTW, my DP ratings assign half of the credit to the pivot man and half to the fielder who started the play (I probably should assign a higher percetnage top the pivot man). That may be one reason why the DP runs for SS and 2B seem a little low (they get half credit for the extra DP's they start and half credit for the ones they are a pivot on)...
  89. Posted by Shorty  on  March 18, 2003 at 09:46 PM (#609730)

    Thanks for considering the idea of a report of defensive ratings over time. The '98 scores would be valuable, even if we have to discount them somewhat for the fact that batted ball speed is not available.

    Assigning credit for DPs *is* tricky. Although I agree that the "pivot" rather than the "feed" is probably more relevant, it's hard to prove whether that's true in general and probably very hard to prove in particular circumstances. Fortunately, the amount of credit at stake is (correctly) rather low. I think that the old STATS Inc. books had coded team DPs above or below expectations. Most were within the +/- 10 plays band. One or two teams a season might have been +25 or -25. Since each DP is worth half a run and the half run is split in two, we can see how low the maximum stakes are per player. It's also probably extremely unlikely that scores of +/-25 would persist for a double play combo over time.


    Thanks for the run estimates for miscatches/infield hits and throwing errors. They sound about right. And I think you're probably right that it is unlikely that a particular player's "mix" of errors will have a meaningful impact on his rating.
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