The Paul Millsap Doctrine


Our last baptism of per-minute eroticism surfaced some valid concerns regarding causation; we studied year-to-year jumps in minutes, which served to shroud our evidence players don't get worse when they get more minutes by failing to control for situational changes and summertime improvement. Fair enough. Free Darko's Silverbird5000 offered a suggestion for more lucid study:

One way to do this would be to look at cases where a starter gets injured mid-season and see what happens to the PER of the player who replaces him. A kind of natural experiment for TOIH.

While the reagents bubbled on my own TOIH experiments, Silverbird went another direction to prove his theorem. In his post, he lays out further theory: player performance suffers against better opponents, and more minutes means a greater percentage of time played against better opponents... thus more minutes mean worse performance. The findings are significant (statistically and in terms of our debate), but enough questions remain to leave the cloud of skepticism hovering over both TOIH and its 'opposing' philosophy, what I'll now refer to as The Paul Millsap Doctrine.

No one would question the impact of opponent strength in player performance; of course Kobe Bryant and Ronny Turiaf would rather play the Kings than the Spurs. This is the reason TOIH was rather immediately accepted and the burden of proof placed on us in the 'per-minute camp.' (That Silverbird found an innovative way as well as a motive to formalize this is commendable.) Realistically, however, his study found relatively small production drops. Bench players never play strictly against bench players or vice versa, so the difference in average opponent PER is unlikely to be quite as dramatic as Silverbird hypothesizes (an increase from an average PER of 10 to 20, which would cause the player in question to, on average, lose two points of normalized Win Score).

To satisfy Silverbird's previously requested natural experiment, Kevin Pelton and I (but mostly Kevin Pelton -- he watches way too much basketball) compiled a list of players who got stretches of starter-level playing time due to injuries to starting teammates. We came up with 17 such cases for 2006-07. Note that we were very wary of expected criticisms, thus leaving out possibly viable players like Tyrus Thomas and Matt Carroll (players who would have reinforced our findings). The problems with Tyrus and Carroll (and Walter Herrmann and Sasha Pavlovic) -- they clearly earned further extra minutes from performing so well when needed. We wanted to erase (as much as possible) causation problems stemming from increased production resulting in increased minutes, as detailed in a criticism from Brian M. (Knickerblogger addresses those concerns on a parallel but distinct avenue as I in this post.) The majority of our players saw their big-minute stint come bookended by low-minute stints; these are not cases where minutes come from production -- minutes are coming from necessity. All the players included had starting teammates who were injured or suspended; thus, the minutes increases. Games were not cherry-picked -- we took the entire span of games from the stretch of necessity, not just the games in which the player got a lot of minutes. We've worked to isolate the issue of changes in playing time/role versus player efficiency. While the sample size is understandably small and every case is not perfect, I think we've done a pretty good job in controlling for the stated factors of concern. We used 17 players. The range of MPG increases were 9.5 and 21. A full list of the names and situations is in this appendix.

The results:

Shooting percentage: On average, effective field goal percentage and True Shooting percentage both increased by .003. Eight players saw their shooting percentages improve with the extra minutes; nine saw declines.

Points per 40 minutes: +1.82 on average; 15 improved, 2 declined.

Rebounds per 40 minutes: -0.01 on average; 11 improved, 6 declined.

Assists per 40 minutes: +0.48 on average; 10 improved, 7 declined.

Steals + Blocks per 40 minutes: -0.11 on average; 4 improved, 13 declined.

Turnovers per 40 minutes: -0.10 on average; 9 improved, 8 declined. (Of course, improved means lower turnovers here.)

Fouls per 40 minutes: -0.92 on average; 13 improved, 4 declined.

And finally... PER: +2.38 on average, 15 improved, 2 declined.

Let's take a closer look at what we have here. Shooting percentages, rebounding -- these tend to stay equal regardless of minutes. It's actually remarkable how level the shooting percentages stayed -- all but two of the cases stayed within 10 points of the low-minute rates. Rebounds had a bit more variance -- Alonzo Mourning got a big boost from the starting role while Mikki Moore's boarding suffered. Steals and blocks took a hit from more minutes, which makes sense: starters are better ball-handlers on the whole, and steals/blocks are so few already they'll be more susceptible to wild variation. A common thread among the anti-Millsap population is the argument players like him  -- so-called 'energy guys' -- would foul out if they played 30-40 minutes. Well, when minutes increase, foul rate goes down substantially. Scoring rate surprisingly (based on TOIH) jumps, as does PER. The majority of players perform better when they get their minutes in bigger chunks... despite the evidence they should perform worse given the apparent but possibly overstated disparity in opposition skill level. To me, that says per-minute statistics are a good indication of a player's true talent level and decidedly not nonsense.

And before we shake hands and break souvlaki, I would offer the data of one beauteous case in our study here: Paul Millsap himself. Carlos Boozer was injured from late January through the All-Star break. During that span, Millsap's minutes went from 16.3/game to 28.5/game. His PER in the combined 71 games before and after Boozer's injury was 16.1. His PER during the Boozer injury was 18.4, a 14% increase. Yes, Paul Millsap helps prove his own quandary, giving him naming rights on the doctrine.

Players perform better in most measurable categories when they get more minutes.  The possible causes? They can get into a flow with extended stints (versus chopped up minutes here and there), roles are more stable/defined in the starting lineup, they aren't looking over their shoulder and worried about making a mistake (Deron Williams, 2005-06) or pressing too hard to impress (Francisco Garcia, forever). This logic all makes as much sense as Silverbird's equally sensical findings.

In fact, the two theories -- the Theorem of Intertemporal Heterogeneity (not all minutes are created equal) and The Paul Millsap Doctrine (the production of low-minute players typically improves or remains the same when given substantially more minutes) -- can coexist, if we realize and admit how contextually based and situationally complex this game is. (And for those who call 'bullsh*t' on our ability to aptly dissect this game through statistical methods -- imagine using Silverbird's 'quality of minutes' data combined with per-minute numbers to correctly identify the inflated and assign more tightly predicated prognostications as to expanded worth on the misused.) Only through continuing to explore the intricate relationships between players, their teammates, their minutes, their opponents and their performance can we hope to unveil the skeleton which ties Tom VanArsdale and Nick Van Exel together.

A million thanks to Kevin Pelton for help on this study and post.

Tags: NBA Paul Millsap John Hollinger

Comments (9)

  • Jason Jason

    Thanks, Tom (& Kevin)--this is more interesting stuff.  And it's good to see that the namesake fared well in this study ... Free Millsap!  A couple of questions:

    - Was there a minimum number of high-MPG games required for inclusion in this sample?  I can understand the need for this, but I'm wondering a minimum might exclude players who received a quick hook after performing poorly in the first handful of games of increased minutes.  For instance, Josh Boone and Mikki Moore played similar minutes shortly after Krstic went down, but Coach Frank clearly favored Moore after those first few games.

    - Would it be fair to attribute some of the foul rate drop to the fact that the study was restricted to players whose minutes increased substantially?  To use the Nets as an example once again, perhaps Frank tried to help fill the Krstic void with more PT for Jason Collins, but failed because of his ridiculous foul rate (more PF than PTS, AST, & BLK combined in 06-07).

    (new) Posted 9/18/2007 [reply] [flag]
    • tziller tziller

      Thanks Jason. There was no minimum GP; I believe the lowest was nine games. You're hinting at something that keeps the sample from being perfect -- it's not a perfect world where there's only one backup option when injury strikes (a la Krstic). But I think in most cases we chose folks who were getting minutes out of necessity more than production, with the understandable but brief battles between Mikki and Boone et al. Also, most of our players' minutes came back down at the end of the run of necessity, which I think tempers any concerns about winning the coach's heart.

      You're right about foul rate -- the minutes jump makes that a bit of a self-fulfilling prophecy. We made sure to look at a variety of numbers, and I'm glad we did. Foul rate might need to be looked at separately -- say, by taking some high-foul players and breaking down their playing time by segments (1st four min, min 5-8, min 9-12, etc.) to see if fouls taper off.

      (new) Posted 9/18/2007 [reply] [flag]
  • TheSecretWeapon TheSecretWeapon
    Great stuff guys. Terrific analysis.  Any thoughts of attempting to replicate this study on previous seasons to see if the results are similar?
    (new) Posted 9/18/2007 [reply] [flag]
    • tziller tziller
      Thoughts, yes. Hopefully, this data set can form a base to which we can add future and past cases which apply.
      (new) Posted 9/18/2007 [reply] [flag]
  • mcwelk mcwelk
    I can't quarrel with any of the finer points of your analysis, because I love that you have named it after Mansap so much.
    (new) Posted 9/18/2007 [reply] [flag]
  • kpelton kpelton

    It should be noted, in regards to earlier seasons, that the genesis of this study was a similar one by Hollinger in his first Pro Basketball Prospectus. It dealt with the 2001-02 season and looked only at overall performance, finding similar results.

     In picking players, I used a de facto cut-off of about eight games, since anything below that would be too small. Most of the time I think the changes were too quick to really be about performance (Boone's game-by-game numbers show him playing well at first ... and then not at all, which is strange.)

    Foul rates may have restricted coaches options, but there are some high-foul rate guys in this study, starting with Millsap (6.6 pf40 in low-minute games). Mourning, Mutombo and Moore (M&M&M&M?) also had foul rates over six when they didn't play heavy minutes.

    (new) Posted 9/18/2007 [reply] [flag]
  • goathair_3 goathair_3

    The only problem I have with all of these analyses is that each researcher is looking for something to support their idea in the data.  If you're looking for something, you're going to find it.  That's one of the reasons why every scientific trial is blinded.  Investigator bias plays a HUGE role in study design.

    That being said, good work. 

    (new) Posted 9/18/2007 [reply] [flag]
  • silverbird5000 silverbird5000

    Great work all around. As I mentioned to TZ in an email, I think this kind of research design has a lot of potential. One very small quibble I have is with your strong claim that "these are not cases where minutes come from production - minutes are coming from necessity". Yes, to a certain extent, this is true: it is, after all, the reason for using injury replacements in the first place (rather than just mpg increases per se). Still, it isn't true that the entire increase in these players' minutes can be explained by necessity. Players like Boozer or Pierce pretty much have to play 30+ minutes a night, every night, no matter how bad they're playing. When they get injured, yes, bench players will be forced to play more - but so long as the bench is sufficiently deep, how much they play will still partly depend on how well they're playing on any particular night – at least, more so than the starters they replace. So, if you look at the variance in mpg for your players during their replacement stints, it's still pretty high. For instance, the doctrine's namesake (who still didn't actually start in Boozer's absence) split time with Jarron Collins, with minutes ranging anywhere from 17 to 38. I do think the injury approach is much better at picking up "necessity" increases, rather than "production” increases. For cases like Mikki Moore, it will work very well. Still, it has its problems.

    That said, I'm all for the kind of doctrinal synthesis you allude to at the end. As you say, in many ways our findings are complementary (i.e. the fact that stl/blk40 goes down with minutes sense in terms of the better-defense theory). Insofar as PER is highly biased towards scoring, and most of the PER-mpg relationship in your data is being driven by higher point totals, which in turn are being driven by higher shot attempts per minute (not higher tsa%), what this really comes down to is what one's philosophy of scoring is. Are these players shooting and scoring more per-minute because the more they play, the more they find their groove. Or is it because the role they step into (say, the Paul Pierce role) is that of a player who has to shoot and score more. Though here again, your conclusion that all these things vary with context still applies. I think the way forward would be to try and pick out regularities in the variation, and see if we can't predict which kind of players will improve with minutes, and which will decline. Discovering a general rule at this point seems more and more like folly.


    (new) Posted 9/19/2007 [reply] [flag]
    • tziller tziller

      Amen. It was interesting to me how PER really magnifies scoring -- of course it has all the other stuff in there, but in that mid-range of players -- say PER 13 to PER 20 -- scoring is the difference-maker. Perhaps it's because other statistics are relatively similar across the board; perhaps it's the way Hollinger counts assists.

      (new) Posted 9/19/2007 [reply] [flag]

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