Newton's Football

Forbes writer Allen St.John and materials scientist Ainissa Ramirez recently wrote a book titled Newton's Football on various intersections between science and our favorite sport. It's right up ANS' alley. Allen has an article at Forbes with an excerpt from the book:

"The theory that coaches were purely motivated by job security and didn’t want to go against the conventional wisdom, that didn’t quite satisfy me," says Brian Burke of Advanced NFL Stats. Week in and week out, Burke analyzed games and saw evidence that NFL coaches were costing their teams yardage, 1st downs, and, ultimately, games because of the questionable decisions they were making. He further noticed that those coaches almost invariably erred on the side of caution. But why?...

"In terms of team building, risk taking is good," Burke argues. He notes that in any given year the average NFL team enters a season with a Bayesian prior expectation of winning a Super Bowl that’s 1 in 32. "You’re a 31–1 underdog. You want to take chances," Burke explains. "It’s okay to miss the playoffs and win five games instead of seven. It doesn’t hurt you that much. But teams are very conservative. They'd rather win a few more games and avoid having a terrible record."

Cade Massey on Flipping Coins and the NFL Draft

Readers of this site will recall the name Case Massey. Along with fellow noted economist Richard Thaler, he co-authored the Massey-Thaler draft study titled The Loser's Curse. The paper found that, under the previous CBA, "surplus" draft value peaked with picks in the late first round and early second round. Surplus value was defined as the expected performance value above which a team could expect by spending an equivalent amount on a veteran free agent.

Massey has continued research into the draft. His presentation at the 2012 MIT Sloan Sports Analytics Conference outlines his recent findings. (I recommend using IE to view the presentation. Chrome didn't play nice with the video.) The slides from the brief can be viewed here.

If I understand things correctly, Massey has found that:

Roundup 9/23/10

Keyshawn Johnson thinks Romo is average, and he's holding the Cowboys back. Jason Lisk would beg to differ. This year, Romo sports a +30 EPA, meaning his play would be expected to generate 30 points of net point advantage over five games. But he has a negative WPA, meaning he hasn't played well in high-leverage situations.

Jason has been writing at a site called The Big Lead, which, except for JKL's stuff, is mostly pedestrian. The good news is that you can subscribe to Jason's stuff only using this feed link. Here's another neat post in which Jason looks how a few teams compare to historical teams with similar statistical profiles.

Say it ain't so, Phil!

More Phil on how mainstream reporters should report on sabermetric research. I've always had a very good experience working with reporters. They've been open-minded, inquisitive, and willing to accept that sometimes there's no statistical weight to the argument they're trying to make.

How amazing are the 2010 Chargers?

This seems to be a good idea.

Detecting momentum is harder than you think. I've been thinking of various ways to construct a research test for momentum in football games for a while. I have a few thoughts, but more ideas are always welcome.

Roundup 10/16/10

NFL Forecast has fresh playoff probabilities.

Peter King smartly uses efficiency stats (and not total yards or points--awesome!) to diagnose the Saints' troubles this year.

What are the odds?

I recently read this over at Cold Hard Football Facts: "Running is part of football. Always has been, and always will be. The problem from an analysis standpoint is that no one has come up with a way to demonstrate how running helps teams win. But that’s a shortcoming of NFL analysts, not a shortcoming of the running game." Hopefully, now there is one fewer shortcoming.

Platooning QBs? One year when I was at Navy we did that. We had one QB who was a passer who played between the 20s, and one guy who was the runner to played near the goal lines. I think we went 1-10 that year, with the only win against Army.

Last week was a bad one for #1 pick QBs.

Don't sleep on the Titans this season.

Over at the Community site, Chris Alan gives updates his analysis on surviving in a suicide league. Have your own research or analysis you'd like to share? Send it in to Advanced NFL Stats Community.

Roundup 9/25/10

Advanced individual player stats will be updated immediately after each game this season.


Game probabilities will start for week 4. They'll be featured at the NY Times again this season.

Wow.

TJ uses EP to analyze a big play call in the DEN-SEA game from last weekend.

NYT article on the 3-4. 

From the Advanced NFL Stats Community reboot:

Dan Schlauch on placekicker salary distribution. Leave some comments and give Dan some feedback.

John Candido is parsing weekly play-by-play for everyone this season. If you use John's data, be sure to leave behind a thanks. I'll be updating 2010 data periodically, but not every week.

Keep the submissions coming! Thanks again to Ed for tending to 'Community.'

Roundup 9/4/10

In basketball, don't call a timeout at the end of close games. You'll be more likely to draw a foul and win.

A salary cap also needs a salary floor.

The historical distribution of talent in the NFL.

A neuroscientist's struggle to understand regression to the mean.

The Sports Reference sites, including PFR, was named among Time's 50 best websites. Congrats, guys.

Tony Romo is not a mirage.

Advanced Public School Stats. What's next, Fantasy Teachers leagues? ...With his first round pick, Brian Burke selects Jaime Escalante, math teacher, Garfield High School... Stand and Deliver-great flick by the way. Escalante passed away earlier this year.

Roundup 8/21/10

The Roundup feature returns for the 2010 season. The twitter feed over there to the right has served as my voting ballot for interesting football links recently, but the Roundup lets me make comments and explain what I found interesting in each link. There's a backlog of links since the last roundup, so although some of these off-season links might be a little stale, they are still worthy of note.

If a free-agent who brings a certain number of wins comes to a big market team, he'll increase its revenues more than he would to a small market team. So why do teams tend to pay equal prices for free-agents? Phil Birnbaum tells us. Part II.

More Phil. This time a great essay on numeracy. Understanding the world around us requires and understanding of math, but sound logic is just as important if not more so.

Reviving fallen franchises.

What if the draft was an auction? (Off topic, here's a funny/disturbing auction. Apparently they have an edgy sense of humor in New Zealand. Helmet-knock: Mind Your Decisions.)

Player-specific win-loss records. (Part II) A very cool idea from Tango using Win Probability.

Pre-Season Predictions Are Still Worthless

Last year I started my stint at the NY Times by calling attention to just how bad NFL preseason predictions are. I compared the “advanced” projections for team win totals compiled by a fellow stats website called Football Outsiders to two benchmarks. They had predicted doom and gloom for the Jets last year, and my article was intended to relieve Jets fans of needless worry. As it happened, the Jets made the playoffs and went all the way to the AFC Championship game.

The first benchmark was a mindless 8-win prediction for every team. Let's call this the Constant Median Approximation system, or CoMA for short. This benchmark represents zero knowledge. It’s what you would guess if you had no information at all about any of the NFL teams except that they each play 16 games. Certainly anyone can out-predict a coma patient, right?

MIT/Sloan Panel

Here is the video of the panel at the MIT sports analytics conference I referred to in my post about how Bill Polian doesn't get it. The discussion is educational throughout, and despite my criticism of Bill Polian, he has some very wise things to share. The participants are Mark Cuban, Jonathan Kraft, Daryl Morey, Polian, and Bill Simmons, with Michael Lewis as the moderator. It's over an hour long and worth your time. I've embedded it below, but first let me share what I took to be the most interesting points:

Dave Berri Responds

Stumbling On Wins author Dave Berri responds to my analysis of the debate regarding whether top draft pick QBs are really any better than later picks. He has a good point about Elway.

Steven Pinker vs. Malcolm Gladwell and Drafting QBs

Last season you might recall a dust-up between Harvard evolutionary psychologist Steven Pinker and popular science author Malcolm Gladwell over whether teams really have any ability to predict which college QBs will pan out into good pros. You might be wondering what the heck a psychologist and a pop-science author have to do with NFL football.

In his book What the Dog Saw, Gladwell wrote about how hard it is for school administrators to discriminate the better teacher candidates from the lesser candidates. Gladwell used the NFL draft to illustrate how difficult it is for anyone to predict human performance, even in a sport where there is ample performance metrics and every step, throw, and catch is videotaped from 12 different angles. Gladwell was referring to what was reported by economists Dave Berri and Rob Simmons as a "very weak" correlation between draft order and per-play performance by QBs.

In an exchange of letters following Pinker's critical review of What the Dog Saw, Pinker took issue with Gladwell's claim that there was "no connection" between when a QB is taken in the draft and his per-play performance. Pinker wrote that this is "simply not the case."

As has been pointed previously, the problem with the weak correlation cited by Gladwell is that it excludes players who are not judged good enough by coaches during their development to warrant much if any playing time. At its core, the NFL draft is a process of selection, and we should expect  selection bias will taint most attempts at analysis. Gladwell looked at the draft process and (correctly) said:

"Coaches and GMs turn out to be good decision-makers when it comes to drafting quarterbacks when you consider the fact that the quarterbacks who never played aren’t any good. And how do we know that the quarterbacks who never play aren’t any good? Because coaches and GMs are good decision-makers!”

But Gladwell's argument cuts both ways. The only way to see that coaches and GMs aren't any good at drafting QBs is to assume they're no good at choosing which QB on their roster to play in games!

In this post I'll attempt to settle the question of whether NFL scouts really have any ability to identify the better QBs. Do the QBs picked higher in the draft turn out to be better performers on a per-play basis? Is Pinker correct that they do, or is Gladwell correct that they do not?

The CBA and Union Economics

Roger Goodell says veteran players want the rookie pay scale reduced. Even economist Richard Thaler is offended by the salaries of draft picks. He writes, "veteran players would probably agree with the principle that eight-figure salaries should be reserved for players who have already proved themselves on the field."

Of course they would!

People think of unions and corporations as adversaries in perpetual conflict. But there is one thing both groups can agree on.

Stumbling on Wins Giveaway

When I started to get really interested in sports statistics I thought, "Somebody should write a Freakonomics, but about sports." I was woefully uninformed about the vast library of research already done, particularly about baseball. At first I (foolishly) thought, "Maybe I could write that book." I did some clicking around and I was crushed to learn there already was one.

At my first opportunity I ran out and bought Wages of Wins. I thought," This is cool. I could do this too." So I'll always carry a debt of gratitude for authors Dave Berri, Martin Schmidt, and Stacey Brook. I didn't agree with everything in Wages, but it asked all the right questions and got me thinking about sports in a whole new way. Besides, if you're waiting for the sports book that you'll agree with 100%, you'll be waiting a long time.

Rethinking the Massey-Thaler Draft Study

Economists Richard Thaler and Cade Massey authored a widely-read research paper analyzing the value of NFL draft picks, and they've recently published an updated version. The paper's primary finding was that teams are overconfident in their ability to choose the best players. In essence, the very top picks are overvalued relative to later picks, both in terms of what teams are willing to trade to move up in the draft and in terms of salary.

Recently Richard Thaler penned an article for the NYT discussing his paper. But puzzlingly, he goes on to make a claim that clearly contradicts his own research. He writes, "it makes absolutely no sense to be giving so much money to unproven rookies, many of whom turn out to be busts." Further, he writes, "veteran players would probably agree with the principle that eight-figure salaries should be reserved for players who have already proved themselves on the field."

Roundup 3/20

More on advanced stats for golf.

Here is a great application of the Expected Points values I released into the wild last season. This is exactly the kind of stuff I hoped would start happening. It's a look at the Cowboys running game through the lens of EPA. I'd love to see more people take advantage of the EP model.

Here's another article in the same vein. It implores Broncos coach Josh McDaniels to use the EP model to become more aggressive on 4th down.

Sean McCormick at Football Outsiders has a great write-up on the much-hyped Draft class of 2004.

The geometry of free-throw shooting. (Hat tip: M/R)

A strange quirk in how seeding in the NCAA basketball tournament can allow lower seeds to advance more easily. #10 seeds are actually more likely to advance than #9 or #8 seeds. #12 seeds are twice as likely to make the Sweet 16 than #8 seeds.

Turnovers are the key to predicting upsets.

Mathletics

With the football calendar at its darkest nadir--no games, no signings, no draft, just some off-season workouts--and basketball season getting into full swing, maybe it's a good time to broaden our statistical horizons. If you're new to sports analytics or want to become more familiar with the methods used in other sports than football, I recommend Wayne Wilson's book Mathletics.

Wayne is a professor of decision science at Indiana University and has consulted for the Dallas Mavericks for several of the last few seasons. Basketball is his wheelhouse, but Mathletics covers baseball and football analytics as well. The book is really two things. It's a primer on the various principles and techniques used in sports analysis, and it's a how-to book on how to use Excel to do the actual computations. It's perfect for the guy who wants to grab some data off the Web and get his feet wet crunching numbers.

Roundup 3/5

Scientists find the part of the brain that causes coaches to punt too often. (Hat tip: Marginal Revolution)

The Coase theorem says that dynamic ticket pricing is a good idea.

The Chicago Sun-Times says that Jay Cutler's interceptions were all due to poor decisions and not to pass protection deficiencies. Seems KC Joyner was right and I was wrong about Cutler going into last season. The stats show Cutler was a still minor upgrade over Orton, even accounting for all the interceptions. Whether the trade was worth it is another matter.

Jason Lisk defends Joe Namath from the charge he may not be a legitimate Hall of Fame QB. My take--It's the Hall of Fame, not the Hall of Passing Efficiency. He definitely belongs.

Lisk also tells us all about real football. If you read one link from this post, read this one.

What tends to happen to teams that lose the Super Bowl?

Roundup 1/16

Does a playoff bye increase a team's chances of winning in the divisional round? Jason Lisk reminds us that, accounting for team strength, probably not.

Jason also shows that Vinny Testaverde was better than most people think if you consider how bad the teams around him were.

More on QB comebacks from Scott Kacsmar.

Last week we saw the Ravens stomp the Patriots throwing only 10 times for 34 yards. Chase Stuart looks at the reverse. How close have NFL teams come to never running the ball in a game? Could we see something like that in today's Cardinals-Saints game?

Roundup 12/19

If you're snowed in like me this Saturday afternoon, you've got plenty of time on your hands. Early season college basketball doesn't really grab my attention. Neither does the apparently sponsor-less "New Mexico Bowl." (Actually, I often root for Fresno State due to being stationed nearby at Naval Air Station Lemoore, CA for many years.) Here are some links to help pass the snowy Saturday.

Chase Stuart from PFR looks at Steven Jackson's huge year for the struggling Rams. That's very unusual for a RB to have such a big year on a losing team. In a contribution to the Fifth Down Blog, Chase looks at the five least likely playoff teams in history based on their early season struggles.

Another Run-Pass Balance Study

Benjamin Alamar, author of the Passing Premium paper (critiqued here), takes a second stab at comparing the values of running and passing with new research. A brief presenting his methodology and findings was presented at a recent symposium on sports statistics. This time Alamar uses expected points as a measure of value, and compares the EP values gained by passes with those of runs. He defines risk as the probability each play type will result in a negative EP change, and finds that running is both less productive and "riskier" than passing. There are three fairly big problems in the methodology. Fortunately, all three can be rectified.

First, Alamar creates his EP values using a simple linear regression (see slide 10). Using down, distance, and yardline (plus other variables controlling for quarter and other effects), he produces an EP equation. This is a really bad way to estimate EP values. They're not linear, and there are any number of interacting effects within. The Levitt-Kovash paper, in contrast, uses a regression with quintic terms and full interactions to create their EP values. (I prefer a  more direct method--looking at the data empirically and smoothing it using a method called LOESS.)

Roundup 10/24

Two great articles from Chris Brown. Here’s an explanation of the Wildcat he did for Fifth Down prior to the Jets-Dolphins game a couple weeks ago. And at his own site, he explains zone run plays.

Ex-players and coaches are usually horrible analysts. Nowhere is this more evident than in baseball where analysts are forced to fill the endless dead time between each pitch with mind-numbing drivel, superstition, and flat out erroneous statements. Tom Tango points out some of the silliness from the MLB playoffs. It makes you wonder how these players and coaches became successful in the first place.

Roundup 10/18

Which passing stats stay the most consistent when a QB changes teams? Jason Lisk tells us. Keep in mind some stats are naturally more random than others. Really interesting stuff.

The Ravens defense gave up 100 yards to a RB for the first time in 35 games. Chase Stuart tells us that since 1960 only 12 defenses have accomplished that feat.

Longtime reader Ian Stanczyk has luanched a really interesting new website, BookOfOdds.com. I just learned that an MLB player will hit for the cycle in 1 out of 739.2 games. Check it out.

Full Review of Game Theory Run-Pass Balance Study

A new paper on game theory and run-pass balance in the NFL, Professionals Do Not Play Minimax: Evidence from Major League Baseball and the National Football League, says that offenses run too often and play calling is too predictable. The authors, Kenneth Kovash and Steven Levitt, construct a success metric to value the outcome of NFL runs and passes from the 2002-2005 seasons. Then using regression models, they estimate and compare the values of a typical run and a typical pass. They also construct a regression to test if play calls can be predicted to any degree based on the previous play call.

Game Theory

Game theory tells us that in a 2-player zero-sum game, if both players are playing the optimum mix of strategies, the long-term average payoff from each strategy will be the same. If you have two general strategy options, like run or pass, you can’t just choose one of them all the time. That would make the defense’s job pretty easy. So you need some sort of unpredictable mix of strategies. The question is, what’s the optimum ratio?

Roundup 10/3

Neil Paine, the new administrator at Pro-Football-Reference.com ranks all QBs in NFL history by their six best seasons. Ken Anderson, John Unitas, Roger Staubauch, Steve Young, and Peyton Manning come out on top.

Neil also points out that Peyton Manning is dominating the Adjusted Yards per Attempt stat so far this year and since 1998. Kurt Warner, Tom Brady, Drew Brees, and Rich Gannon trail. Some surprises (to me) on the list of top 20 QBs include Chad Pennington, Jeff Garcia, and Doug Flutie.

For those interested in the historical comparisons between the AFL and NFL, Jason Lisk puts a bow on his series on draft classes.

A New Academic Study on Game Theory and Run-Pass Balance

There’s a new study on run-pass balance based on game theory minimax equilibrium. The study is called Professionals Do Not Play Minimax: Evidence from Major League Baseball and the National Football League and it’s from Kenneth Kovash and Steven Levitt (of Freakonomics fame).

The authors created their own version of  Expected Points as their measure of play success. Using a giant regression model that accounts for all sorts of confounding variables, they find passes lead to more success than runs. Game theory would say that, ideally, both strategies should yield the same amount of success.

Roundup 9/26

The roundup is back. Here are some interesting links relevant to NFL analysis. I've been negligent in keeping up with this feature, so although there are some items that are a few months old, they're still good reads.

Verducci Follow-Up

The recent post about the Verducci Effect and Let's Make A Deal didn't elicit the response I was looking for. Reactions ranged from denial to sadness to even anger. I think the game show story hurt more than helped my case of why I think the Verducci Effect is an illusion. And as I said in the original article, I'm not completely certain. But now, after developing my thoughts a little better, I'm more certain than before.

Game shows aside, I'll explain my thought process with an notional example, a mental exercise actually. I'm most interested in the injury aspect of the Verducci Effect, so I'll concentrate on that in this post. The injury rates I'm going to use are created only for clarity, and they are not intended to match the true rates. I'm also going to make some simplifying assumptions to illustrate the broader point. Please keep in mind this example is only intended to demonstrate a concept.

The Example

Assume every MLB pitcher's career lasts exactly 5 years. Also assume that the league-wide injury rate is 1 out of 5 years, defined as however you like--say being on the DL. Also assume that one year out of each pitcher's career can be identified, after the fact, as a "career year," which by definition assures us of two things: no significant injury and an upswing of innings.

Take 200 pitchers and randomly assign a number from 1 through 5 to each of their 5 respective years completely independently. When a 1 comes up, call that an injury year. So far, we've got a 1 in 5 (20%) injury rate across the league. Some pitchers will have multiple injury years, some won't have any, and they are completely independent.

In my head I'm thinking of a table of cards, 200 x 5. For now, the cards are turned up so we can see the numbers 1 through 5. 20% of the cards are 1s--injuries.

Now, take all the "career years" for the pitchers off the table by removing one card from each row, which by definition cannot be an injury year. Let's choose the highest card and remove it. What percentage of cards will now be 1s (injuries)? Before, there were 200 out of 1000 (20%), and now there are the same number of injuries (200) but fewer cards remaining (800). 25% of the remaining years are 1s (injuries). If we now selected a card at random, we'd have a 1 in 4 chance at finding an injury.

Shrink the Sample

Let's do the same exercise but with a sub-sample of 50 pitchers instead of 200. There are still 20% injury years, and if we take each pitcher's known "career year" off the table, 25% of the remaining years will be injury years. Turn over the remaining cards, so you can't see the numbers 1-5. Turn one card face up at random--what are the chances of finding a 1-card (an injury)? It has to be 25%. We started with 250 cards, but there are now 200 cards remaining and 50 of them are injury cards.

Shrink It Again

Repeat the exercise with 10 pitchers. Does this change anything? No. Originally 20% of the cards were injuries, and after removing the career year cards, 25% of those remaining are injuries.

Down to One Player

Now consider a sub-sample of just a single pitcher. Again, turn over all the cards so we can't see the numbers 1-5. There are originally 5 cards on the table, with a probability of 1 in 5 being an injury card. Take away one card, which we know after the fact is not an injury card, leaving 4 cards. Turn one card over--the card dealt immediately following the "career" year. What is the chance it's an injury?

It would be 25%. We had a league-wide injury rate of 20%, but following career/high-inning years we would retrospectively observe a rate of 25%. Even though the injuries were distributed completely at random and completely independently, we'd see a false connection between high-inning years and injuries in subsequent years.

Even a small difference would appear statistically significant with a large data set, but it would be an illusion. The original probability of a year being an injury year was always 20%, but after looking back and removing a year in which we're virtually assured of no injury, we'd see a 25% injury rate.

Try It Yourself

If you don't believe me, you can play the game yourself. Shuffle a deck of cards and deal out 4 face up in row. Those 4 cards represent 4 years of a pitcher's career. Every time we see a diamond card, we'll call that an injury year. We'll say the highest non-diamond card is a career/high-inning year. It goes without saying that, on average, 1 in every 4 cards will be a diamond--an injury. That's our true baseline rate.

After dealing the 4 cards, remove the highest non-diamond card and set it aside. Look at the card immediately to the right of the one you removed. What is the probability it is a diamond? If you said 1 in 4 you'd be mistaken. It's 1 in 3. This is the same illusion.

Try it. I did, 78 times and got a diamond on 26 tries--exactly one third (p=0.04 for the sticklers out there). You have to re-shuffle each time for it to be completely random and independent. Also, if the high "career" card is the right-most card, you can either throw out that iteration or loop around to look at the first card. The effect is the same. In fact, just look at how many of the 3 remaining cards are diamonds, and you'll eventually see that it's 1 in 3.

I'm sure there is a name for this, but I don't know it. If anyone is familiar, fill me in. Otherwise, I'm sticking with the Monty Hall Effect. Also, the Verducci Effect may still be real, but it would have to be shown that the observed injury rates significantly exceed the rate predicted by the effect of the illusion.

Maybe I'm wrong, and that's ok. But every time I deal 4 cards and remove 1 non-diamond, I keep seeing diamonds 33% of the time. Just like the Monty Hall game, you probably won't believe it until you try it yourself.

[Edit: I am now completely certain the paradox/illusion exists as I described. However, after a good discussion with commenter Vince (see below), I'm no longer convinced that the way I set up the question applies to how the Verducci Effect is truly applied. In other words, the illusion is real if you set it up the way I did. It's just that strange, and subtle differences exist in how you look at the problem. For example, if in the pitcher example, you removed the first instance of a non-1, you would see a 1 in the following block 20% of the time, just like you'd expect. But if you select the highest number in the row, or if you remove the final non-1, you'd detect a 1 next 25% of the time.]

Guest Post at the NY Times 'Fifth Down'

I'm a guest contributor for the New York Times Fifth Down blog over the next few days. There will be some fresh articles and some older articles updated with new data. Today's post is a look at just how bad pre-season predictions tend to be.

My thanks to Toni Monkovic for the invitation.

Lucky/Unlucky Baseball Teams

Fangraphs.com, which is best described as the baseball version of this site (actually, the other way around) posted an article today about the luckiest and unluckiest MLB teams at the all-star break.

It's very similar to my own lucky/unlucky breakdown. They're using a simpler runs for/runs against Pythagorean model while I use a logistic regression of efficiency stats. Both systems adjust for opponent strength. I think both are appropriate for the different characteristics of the two sports.

Injury Rates and An Extended Season

At the recent owners meeting, the NFL disseminated a study that concluded an increase in the season schedule from 16 to 18 games would not increase injury rates. The report caught a lot of criticism as a halfhearted attempt to obscure the toll a longer season would take on the players. Judy Battista of the New York Times and Mike Reiss of the Boston Globe both point to flaws in the study.

But I suspect there is a fundamental misunderstanding about what the report says and how it's being interpreted. All I really know about the report is that it says, "the NFL's injury rate doesn't increase at the end of the season." There is no doubt a longer season would result in more total injuries. The bigger question is how many more injuries--does the injury rate itself increase?

Much of the criticism of the study focuses on the use of team injury reports, well known for their deceptive omissions. In an excellent article, Bill Barnwell at Football Outsiders found an additional flaw in the study. It left out players who go on the IR. Before you consider players on the IR, it appears that the injury rate peaks at week 10 before it decreases for the remainder of the season. Barnwell explains why this isn't really the case.

Since team injury reports are notoriously unreliable, the best information is actual games missed. Thankfuly, Barnwell provides that data in his article, and it's very interesting stuff. When you factor in the IR, the number of games missed climbs steadily. He concludes, "the data looks totally different, and in a bad way for the NFL..."

The way I see it, however, is that the NFL report is right, no matter what the intent was of its authors. There is no increase in injury rates toward the end of the season. The injury rate is effectively linear. Of course, as the season wears on, the number of players unable to play due to injury will accumulate, creating an upward climbing injury total. Once you go on the IR, you don't come off. This cuts to the heart of the debate about whether players become increasingly susceptible to injury as the season, along with the number of cuts and collisions, wears on.

Here is a graph of the data included in the Barnwell article.


The blue line is the games missed by roster players (those not on the IR). Except for the uptick on the final week, when playoff bound players nurse their wounds and everyone else has their bags packed for the Caribbean, it's very steady. The green line is the number of games missed by IR or physically unable to perform (PUP) players. Note how its slope steadily increases. The red line is the combination of the injured roster players and IR/PUP players.

Here's what I take away from this data. Players on the IR increase at a (very) slightly exponential rate--specifically it's:

#IR = 0.006w² + 0.1w + 1.6, where w=week.

That .006 term is extremely small, and when combined with the negative camber of the blue line, results in a very linear total, (especially when week 17 is thrown out, although you don't need to.) [Note: By the way, the slight non-linearity of the increase is evidence, however tiny, for the notion that players become more susceptible to injury as they endure the season.]

Ultimately, the total number of players who miss games due to injury is indistinguishable from a linear line (r-squared of .97). Its increase is exclusively due to players going on the IR, which is a one-way check valve.

So will there be more players missing games at the end of the season if the NFL adds two more games? Of course. But it won't be Iwo Jima out there. No explosion of wounded players with "cascading" injuries. It will be a demanding, grueling, even cruel extra two games for the players, but it would barely be noticeable to the fan and to the game itself. I suspect that's what the NFL report is trying to spell out. Even counting the uptick in the final week, each team would average an extra half a missed player by a potential week 19.

Personally, I'm against lengthening the season for a lot of reasons. The nerdiest is that there is a mathematical elegance to 2 conferences, 4 teams per division, 8 divisions, 16 games, 32 teams, and 256 games per season. Please, no 17th game or 33rd team--I'd have to redo all my algorithms and equations! Actually, I just think 16 is plenty. The fewer the number of games, the more unpredictable the season, and I like that.

Are Rookies Overpaid?

I recently looked at what might explain why the top draft picks are paid disproportionately to their expected performance compared to later picks. But that doesn't address the larger issue--are rookies overpaid compared to their veteran counterparts?

A 2005 research paper called The Loser's Curse by economists Cade Massey and Richard Thaler tackled that question. In a nutshell, the paper compares rookie pay to the pay of a 6th-year veteran who could be expected to deliver the same performance as a rookie from each slot in the draft. (Performance is defined by a mix of measures including: being on a team roster, starts, and Pro Bowls.)

The conclusion of the paper is that team executives and scouts overpay for the top picks in the draft relative to the later picks, likely due to overconfidence in their ability to identify the best players. But what might surprise some readers is that rookies at every level of the draft are bargains compared to equivalently performing veterans.

This graph from the paper is the study's bottom line. The red 'compensation' line is the average annual pay for each draft pick. The blue 'performance' line is the salary a team would have to pay a 6-year veteran free agent for the same expected performance. The green 'surplus' line is the difference between the two pay levels.


The surplus performance peaks shallowly at the bottom of the first round and through the second round. That's where teams get the biggest bang for the buck. But still, the surplus is strongly positive throughout the entire draft. According to Massey and Thaler, rookies are a bargain compared to veterans.

There's a good explanation why rookies would be underpaid. Veterans are known quantities while there is a tremendous amount of uncertainty with draft picks. Think of it this way--Peyton Manning has been to nine Pro Bowls and Ryan Leaf to zero, for an average of 4.5 between the two players. Four Pro Bowls--that's not bad. But would a GM pay more for a guaranteed 4.5 Pro-Bowl-type player or for a 50/50 shot between a total bust and Hall of Famer? Just about every modern economic and psychological theory tells us that people will pay a premium for the sure average.

Unfortunately, that's not an option in the draft. Peyton Leaf just doesn't exist. But 6-year veterans do, and GMs will be willing to pay a premium for the reduced uncertainty in performance.

One note of caution on the paper. The draft years studied were 2000-2002, and rookie salaries have increased substantially since then. But veteran salaries have too. The question is whether rookie pay increases have outpaced veteran pay increases since then. However, rookie pay would needed to have increased over 15-20% faster than veteran pay to change the conclusions of the paper.

Reading List

I've been accused many times by many different people of making things up. Friends, family, and coworkers have all raised the B.S. flag on me. My problem is that I remember things both too well and not enough. I'll remember the gist of an interesting magazine article from ten years ago, but the details will be hazy. Someone will say, "where did you get that?" And I'll say, "I don't know. I read it somewhere." "Yeah right," is usually the response.

One of the most common (and favorite) emails I get asks where I get my ideas. Many of them come from the random things I read, so I thought I'd share some of the most relevant books and articles. And with the off-season in full-swing you might have some extra time on your hands come Sundays. Below is my "I read it somewhere" list.


The Hidden Game of Football

Authors Caroll, Palmer, and Thorn were the first to bring innovative statistics on the NFL to the masses in this 1988 book. They explored topics included expected points, win probability, and a "win/fail" model of play success that is the basis of Football Outsiders' DVOA. I didn't read Hidden Game until the beginning of the most recent season, more than two years after beginning this hobby. I'm glad I did because I was able to develop my own original ideas, and the book is so insightful and original that I think it would have put me in a box.


The Wages of Wins

Before I started this site, I had recently read Freakonomics. I thought someone should write a Freakonomics but about sports. Wages comes pretty close. Written primarily by economist, basketball expert, and long suffering Lions fan Dave Berri, the book looks at all major American sports with a heavy dose of the NBA. The centerpiece is Berri's Wins Produced stat for basketball players.


Fooled by Randomness

This is one of my favorite books of all time. Nassim Taleb writes about the role of randomness in the world and our lives. He's part mathematician, part economist, part financial trader, and part philosopher. His prophetic warnings of how Wall Street's risk models were perilously overconfident were sadly unheeded. Fooled by Randomness was a big bestseller, and Taleb's follow-up The Black Swan was an even bigger hit.


Super Crunchers

The alternate title of this book was supposed to be The End of Intuition. 'Super Crunchers' and other titles were tested with quantitative methods before settling on the final name of the book. It's an overview of the many fields being influenced by advanced statistical methods. Airline prices, medical diagnoses, wine vintages, dating services, and even movie script formulas are all now the domain of econometric modeling.


Coincidences, Chaos, and All That Math Jazz

This is a fun, very non-technical book about a wide range of topics, including probabilities, uncertainty, chaos theory, cryptography, notions of infinity, and even aesthetic proportions. It's all interesting stuff, but I learned the most about chaos theory, and it influenced how I think about modeling and why predictions are so difficult.


The Drunkard's Walk

This book is very similar to Taleb's Fooled by Randomness but far less opinionated and with more of a historical bent. Don't read one or the other. Read both.


Games and Decisions: Introduction and Critical Survey

When groundbreaking thinker super-geniuses write books with titles that say "Introduction...," don't be fooled. This book is one of the milestones of game theory and it's highly technical. But if you really want to understand the inner workings of game theory, dig in. I had to read each chapter two or three times before I could understand most of it.


Game Theory: A Nontechnical Introduction

This is the book I wish I had read before Games and Decisions. It is the most interesting 272 pages I've ever read. The implications of game theory relate to so many topics--relationships, economics, psychology, business, diplomacy, war, and even evolution. It's clear, complete, quick, and fascinating. No calculus, I promise.


Moneyball

Michael Lewis' smash-hit book on baseball sabermetrics. This is much better than his attempt at football--The Blindside. Soon to be a movie starring Brad Pitt (I'm not kidding).


Freakonomics

This book has little to do with sports, unless you count sumo wrestling. A runaway bestseller a couple years ago, it's about applying econometric math to things other than economics. A few years before the book was published, I was using logistic regression to predict which midshipmen at the Naval Academy were most likely to violate its honor code. That's how I first learned all this stuff.


Non-books

An Introduction to Utility Theory

This is the best explanation of the concepts of utility theory I've found. It's a survey of all the basic research and ideas of utility theory. It's chock full of great stuff.


GameTheory.net

Want to take courses in game theory from the top universities in the world? You've hit the mother lode. Lecture notes and lots of other great resources are available here. My favorite is this class.


Romer's 4th Down Paper

A groundbreaking application of quantitative football analysis. My summary if it here.


Anthology of Statistics in Sports

This is a compendium of hard-core academic research in sports. The studies cover a wide variety of sports, including football. To be honest, some of it is over my head. But I like stretching my mind, and I learn a lot from studies like these, not just about the subject at hand but about good methodologies too.


If you have any suggestions, please add them in the comments below.

Weekly Roundup 1/29/09

The guys at Cold Hard Football Facts think they've found evidence vindicating the 'frequent running causes winning' fallacy. But I don't think they did at all. Yes, teams that run more often in the Super Bowl (and all other games) also tend to be the teams that win the game. But we all know that it's the lead that allows all the rushing. Take the 2000 Ravens-Giants Super Bowl. The Ravens ran 33 times compared to 15 for the Giants. But 40% of Baltimore's runs were in the 4th quarter after they already had a 24-7 lead. Oddly, the article address the correlation-causation fallacy, but then just says "it's up for debate."

Football Outsiders looks at all the silly prop bets available for the Super Bowl. My favorite is the one about Matt Millen picking the winner in the pre-game show. I have to think that there is so much negativity surrounding that guy that there is an arbitrage opportunity there. (By the way, I noticed FO has been banned from Google. They must have been caught gaming the search algorithms.)

Speaking of silly betting, here is PFR's Super Bowl squares post. And if you're playing SB squares, you'll probably want to keep an eye on the win probability site. The probability of a current drive ending in a TD or FG is available in real-time.

PFR also responds to an article from the Community site asking whether all 10-point leads are equal. Basically, the question is does a 30-20 lead have the same win probability as a 13-3 lead? The answer is no, they're not exactly the same. The 13-3 lead is slightly safer. But it really depends on home field advantage and relative team strength more than whether it's a 30-20 or 13-3 type lead. Pretty interesting, and this kind of stuff has direct applications for the win probability engine.

I wonder who the Derek Jeters of football are?

The Patriots are already 6 to 1 favorites to win the Super Bowl next year.

The Numbers Guy looks at why QBs almost always get named the Super Bowl MVP. A bunch of football stat-heads, including myself, toss in their 2 cents. The author wanted to know if there was a statistical way to isolate the contribution of a single player in a game. My idea was actually "n-player cooperative stability equilibria," but thankfully it was translated into "a market-based approach."

An article from Slate.com about the overtime rules likes the "field position auction" idea. Phil Birnbaum agrees. I think ideas like those are clever and effective solutions, but the NFL is unlikely to make changes that veer too far from tradition.

The problem with overtime isn't really the coin flip, it's the incredible range and accuracy of modern kickers. The entire sport has been slowly warped into fieldgoal-ball. Overtime is just where the problem becomes most obvious. I'd suggest solving the issue by 1) narrowing the goal posts, and 2) moving the kickoff line back to the 40 for overtime.

Weekly Roundup

I was blown away last week when within hours of posting the win probability calculator, reader Zach wrote up an analysis of when to go for a 2-point conversion. Very cool.

Jim Schwartz is the new head coach of the Lions. Besides being a fellow native of Baltimore, I like him because he's known to have a solid grasp of statistics. Like Bill Belichick, Schwartz has an economics degree. The New York Times has a good write up on him from last fall.

The new issue of the Journal of Quantitative Analysis in Sports is out. There's an article on ranking teams and predicting games, including in the NFL. I've only skimmed it. There are a couple of other articles that look interesting too. There is an article on determining the evenness of sports competitions in rugby, essentially doing the same thing--ranking and forecasting. There is also an article on using neural networks to predict NBA games. (I've experimented with neural network software. I can't say I completely understand it, but I was able to get close to the same prediction accuracy from my usual regression model.)

Sometimes the articles in JQAS are crackpot nonsense. So be warned--just because something has a fancy academic title, comes wrapped in a pretty .pdf, and is loaded with references, doesn't guarantee it has any value. These particular articles don't immediately jump out as kooky, thankfully.

Math and stats pay. Check out the top 3 jobs. Funny, I don't see Navy carrier pilot on the list. When I used to fly, I often wondered how much you'd have to pay someone to do that in an open and competitive market. Take away the "serving your country" aspect, and how much money would someone with those skills make? Throw in the danger and the fact that they have to live at sea for extended periods, and you might have to pay them like these guys.

The PFR blog has the usual installments of best-ever, worst-ever trivia. This time, it's best-ever Super Bowl losers (part 2). I'd like to see worst-ever Super Bowl winners too. [Edit: Here it is.] What kills me is that the two biggest championship upsets in American sports history feature an upstart second-fiddle team from New York beating an overwhelming favorite from Baltimore. The Mets upset the O's in '69, and the winter before, the Jets shocked Baltimore in Super Bowl III. I wasn't even born yet, and it still hurts. One thing forgotten about the Super Bowl back then is that it was more of an actual bowl game--a post-season exhibition. Baltimore had already won the NFL Championship. Back then, as I understand it, the Super Bowl was a cross between a meaningless Pro Bowl-type game and the modern championship as we now know it. Not totally meaningless, but not yet considered the championship either. The Jets certainly changed that.

PFR also has a new Super Bowl history page.

Smart Football teaches us about zone blitzes.

Dave Berri has his final rankings of the year, plus he looks at the Lions.

Over at the community site, Denis O'Regan compares scoring frequency in soccer and football using Poisson distributions. Also, Oberon Faelord (real name?) reminds us that not all 10-point leads are the same.

Since the Steelers beat my Ravens last Sunday to reach the Super Bowl, I'm allowed one outburst of sour grapes. When I was in the Navy, I noticed every part of the country seemed to have a sizable stable of Steeler fans. I remember going to watch a Steelers-Browns playoff game at a sports bar in Pensacola and couldn't believe how many fans of each team were there. And here in Northern Virginia, they're everywhere. Now I understand why. I think a lot of it just bandwagon types from the 70s, but the economic dispersion of the rust-belt is also obviously part of the reason.

Weekly Roundup

The two big topics in football stats this week were the BCS and the NFL overtime rules. I've already had my say on OT rules, so let's start with the BCS.

Baseball analyst Bill James made a minor splash with an article urging a boycott of the BCS system by quantitative analysts (Hat tip--PFR). His fourth point is very interesting and goes against conventional wisdom. The BCS is not the result of big conference and big school greed. James says that we would have a Division I playoff system now except for the fact that the large number of small and uncompetitive schools would vote to share the playoff revenue too broadly.

Maybe so, but there is an underlying problem with college football. It's an unstable system. In systems engineering terms, the best example of a stable system is a thermostat. If it gets too hot, the thermostat kicks in to make it cooler, and vice versa. The NFL is a stable system. A team with a top record is rewarded with lower draft picks and a tougher schedule. A team with too many top players will lose some in free agency. But in college, the effect is reversed. College football is like an anti-thermostat. Imagine a room in which the thermostat turns up the heat the hotter the room gets. College football works the same way.

A successful football program will get money, attention, television time. This will lead to better recruits and even more wins. In turn, there's even more money, big name coaches, and better recruits. And every top recruit on one team's roster is a recruit unavailable to competitors. That's why every year we see the same handful of schools competing for championships. Oooh, I can't wait to find out who the 2009 champion is going to be. Will it be USC, Florida, LSU, Texas, Oklahoma, or Ohio State? The suspense is killing me!

While James' point may be true, it's nearly impossible for most schools to become competitive. Maybe the only way to stabilize the system--to create some semblance of competitive balance--is to spread the wealth.

Also on the college front, the Numbers Guy points out that special teams success does not necessarily correlate with winning.

"ZEUS" thinks the Colts should have taken an intentional safety at the end of regulation in their losing effort at San Diego. ZUES is software built by a couple of PhD-types that aids sideline decision-making, such as when to kick or go the 1st down or when to decline a penalty. It's very similar to the win probability system here (except that they're trying to sell it to teams for over $100,000. Good luck with that. Psst Mr. coach, you can have mine for half the price.)

Reader Ed Anthony emailed me to suggest this Monday, but I dismissed the idea too quick. I was going to do up an analysis to prove that ZEUS was wrong. It seemed obvious to me. Taking the safety turns a SD field goal into a game-winning kick instead of a game-tying one. A safety would have made a FG slightly less probable because it would have given the Chargers worse field position, but not nearly enough to risk the loss instead of the tie. What I left out of the analysis is that it also makes a touchdown less probable. And even though a TD would have been fatal in either case, making the TD less probable makes taking the safety a slightly smarter move. It doesn't matter that the TD didn't occur, it would have been the better decision at the time. Good instincts, Ed!

Doug Drinen at PFR looks at whether specific types of match-ups disproportionately affect game outcomes. Suppose there are two equal teams overall, but there is one particular facet where one team is much stronger than the other. Is it decisive? It's a complex question.

A couple years ago, I looked at the same issue but in a different way. I added interaction variables to my game predition regression model. I used all the same efficiency variables I usually do, but added additional factors such as [offensive run efficiency * opponent defensive run efficiency]. I was testing whether any particular match-up of team qualities had a non-linear effect above and beyond just a linear additive effect.

To put it simply, teams just don't put their abilities up on a table and let them play out independently. Team strengths and weaknesses interact with those of their opponenets. I was testing those interactions to see if they were significant. Some were, but the effect was very slight. The model was no more accurate and was far more complex than my original, so I abandoned its use in 2006. Now that I have a lot more data, it might be worth a revisit.

JKL, also at PFR, looks at older QB performance in the latter part of the season. This is a response to what FO looked at last week. The PFR analysis is far more comprehensive and does find a late-season effect. Also check out JKL's clever idea on revamping overtime.

Sometimes, this weekly roundup post turns into a cross-link-fest with PFR, Sabermetric Research, and Smart Football (which features some great college analysis this week). So there's plenty of room for fresh blood. I haven't mentioned it in a while, but the Advanced NFL Stats Community site is up and going strong. There's a new post once every couple days, and the site gets a few hundred visits every day. All contributors are welcome, so if you have an idea you'd like to share, or even just an opinion on stats in the NFL, please join in. There is data available for anyone who wants to kick it around.

Dennis O'Regan has two posts, one on how Baltimore's defense travels (I'm guessing it travels just fine!) and another on starter vs. backup QBs. Derek Singer looks at what kind of teams win championships. Josh Fryman has some observations on how regular season records may not be predictive of playoff success. Bob Burns wonders how a prediction system that doesn't account for wins can actually predict winners. Doug and Patrick Walters share their technical-financial-based system for predicting team fortunes.

Lots of activity this week. Enjoy the best NFL weekend of the year, and don't forget to check out the Win Probability site during the games. There's a special offer--this weekend only--get $100,000 off your first 5 visits!

Weekly Roundup

In his Tuesday Morning Quarterback column from a week ago, Gregg Easterbrook tells us about his favorite high school state champions, the Pulaski Academy of Arkansas. They never punt on 4th downs, and they almost always win. To his credit, Easterbrook has been out in front of the go-for-it movement. (I'm not a regular reader of Easterbrook, and now I remember why. His columns are the length of short novels, frequently meandering into bad politics and pop-culture commentary.) Thanks to all the readers who alerted me to the Pulaski article at Rivals.

FO has a good article on the hidden value of pass interference penalties. Devin Hester is used to illustrate how the value of speedy deep-threat WRs is obscured by the fact that they aren't credited with the penalty yards they draw.

Dave Berri from Wages of Wins posted his weekly QB and RB rankings based on econometric models like my own. Note who the top QB is--Pennington. Dave may have an updated ranking by the time you read this. He also adds his thoughts on an ongoing discussion between amateur/internet sabermetricians and academic researchers.

Last week I wrote that the Redskins collapse this year may have been due to too few interceptions. In other words, their very low interception rate may have become an end in itself, rather than a by-product of a good passing attack.

I wrote, "You can guarantee zero interceptions by playing in an extremely conservative way, tossing short passes, taking sacks, or throwing the ball away anytime a defender is in the same zip code as the receiver. You can minimize interceptions, but you'll lose every game doing it. At some point in risk-reward continuum, there is an optimum level of risk in passing strategy."

The PFR blog appears to have picked up on the theory a few days later and added some evidence that supports it. We appear to be of like mind on the topic, as the PFR post says, "If you never throw an interception, you’re taking too many sacks, throwing too many balls out of bounds, and getting too many four yard gains on 3rd-and-9. So if zero is not the optimal turnover rate, then what is?"

I have a couple small constructive suggestions. The post finds that teams that have high rates of turnovers per non-scoring drive score more points than teams with low turnover rates. First, I'd suggest looking at interceptions per non-scoring drive instead of all turnovers. Interceptions more than fumbles are functions of an offense's risk-reward balance. I'm not sure if it really matters, though. The effect is the same no matter what kind of turnover it is. But it's worth looking at.

Second, and more importantly, I'd look at point differential rather than points scored. In other words, do teams with more turnovers per non-scoring drive outscore opponents? It may be that they score more points themselves, but they may be allowing even more points due to handing favorable field position over to their opponents.

Smart Football, the best Xs and Os site on the web, dissects Paul Johnson's 'Flexbone' offense at Georgia Tech. I'm a big Paul Johnson fan because he brought Navy's program a lot of success over the past several years. I'm not a big Xs and Os guy, meaning I'm not an expert. But I'd like to learn more. Can anyone suggest a good book that digs deep into NFL-style offensive or defensive systems?

Weekly Roundup

This week we see just how bad the NFC West is in 2008, and how team penalties can be an overlooked factor. Plus, a cool Wikipedia page about the Patriots' offensive and defensive systems.

The PFR blog has two good posts this week. First, they compare the intra- and inter-division records of the NFC West. The bottom line is it may be one of the weakest divisions in a long time. The NFC South, on the other hand, may be one of the strongest.

PFR is also trying to establish a sound way of measuring the best defenses of all time. There's points allowed, yards allowed, yards per play allowed, plus turnovers and other considerations. This year's Steelers defense may rank among the best. If you ask me, the 2000 Ravens hold the crown.

This week Football Outsiders look at one of the most overlooked team stats--penalties. They look at playoff contender team penalties and at "penalties against." In my own research, a team 1 standard deviation better than average in penalty yards per play would win and additional 0.4 wins per season. Penalties against appear slightly more important at 0.5 wins per standard deviation.

The Dolphins look like favorites against the struggling Chiefs, except that they'll be playing in some of the coldest temperatures on record. With the weather getting cold, here are a few articles on weather from last season. Warm climate teams don't seem to have as big a problem as dome teams. Dome teams playing in the cold have only won 12% of their games in the last several seasons.