On Nate Silver on ESPN Umpire Study

I was just watching the Phillies v. Mets game on TV, and the announcers were discussing this Outside the Lines study about MLB umpires, which found that 1 in 5 “close” calls were missed over their 184 game sample.  Interesting, right?

So I opened up my browser to find the details, and before even getting to ESPN, I came across this criticism of the ESPN story by Nate Silver of FiveThirtyEight, which knocks his sometimes employer for framing the story on “close calls,” which he sees as an arbitrary term, rather than something more objective like “calls per game.”  Nate is an excellent quantitative analyst, and I love when he ventures from the murky world of politics and polling to write about sports.  But, while the ESPN study is far from perfect, I think his criticism here is somewhat off-base ill-conceived.

The main problem I have with Nate’s analysis is that the study’s definition of “close call” is not as “completely arbitrary” as Nate suggests.  Conversely, Nate’s suggested alternative metric – blown calls per game – is much more arbitrary than he seems to think.

First, in the main text of the ESPN.com article, the authors clearly state that the standard for “close” that they use is: “close enough to require replay review to determine whether an umpire had made the right call.”  Then in the 2nd sidebar, again, they explicitly define “close calls” as  “those for which instant replay was necessary to make a determination.”  That may sound somewhat arbitrary in the abstract, but let’s think for a moment about the context of this story: Given the number of high-profile blown calls this season, there are two questions on everyone’s mind: “Are these umps blind?” and “Should baseball have more instant replay?” Indeed, this article mentions “replay” 24 times.  So let me be explicit where ESPN is implicit:  This study is about instant replay.  They are trying to assess how many calls per game could use instant replay (their estimate: 1.3), and how many of those reviews would lead to calls being overturned (their estimate: 20%).

Second, what’s with a quantitative (sometimes) sports analyst suddenly being enamored with per-game rather than rate-based stats?  Sure, one blown call every 4 games sounds low, but without some kind of assessment of how many blown call opportunities there are, how would we know?  In his post, Nate mentions that NBA insiders tell him that there were “15 or 20 ‘questionable’ calls” per game in their sport.  Assuming ‘questionable’ means ‘incorrect,’ does that mean NBA referees are 60 to 80 times worse than MLB umpires?  Certainly not.  NBA refs may or may not be terrible, but they have to make double or even triple digit difficult calls every night.  If you used replay to assess every close call in an NBA game, it would never end.  Absent some massive longitudinal study comparing how often officials miss particular types of calls from year to year or era to era, there is going to be a subjective component when evaluating officiating.  Measuring by performance in “close” situations is about as good a method as any.

Which is not to say that the ESPN metric couldn’t be improved:  I would certainly like to see their guidelines for figuring out whether a call is review-worthy or not.  In a perfect world, they might even break down the sets of calls by various proposals for replay implementation.  As a journalistic matter, maybe they should have spent more time discussing their finding that only 1.3 calls per game are “close,” as that seems like an important story in its own right.  On balance, however, when it comes to the two main issues that this study pertains to (the potential impact of further instant replay, and the relative quality of baseball officiating), I think ESPN’s analysis is far more probative than Nate’s.

Hidden Sources of Error—A Back-Handed Defense of Football Outsiders

So I was catching up on some old blog-reading and came across this excellent post by Brian Burke, Pre-Season Predictions Are Still Worthless, showing that the Football Outsiders pre-season predictions are about as accurate as picking 8-8 for every team would be, and that a simple regression based on one variable — 6 wins plus 1/4 of the previous season’s wins — is significantly more accurate

While Brian’s anecdote about Billy Madison humorously skewers Football Outsiders, it’s not entirely fair, and I think these numbers don’t prove as much as they may appear to at first glance.  Sure, a number of conventional or unconventional conclusions people have reached are probably false, but the vast majority of sports wisdom is based on valid causal inferences with at least a grain of truth.  The problem is that people have a tendency to over-rely on the various causes and effects that they observe directly, conversely underestimating the causes they cannot see.

So far, so obvious.  But these “hidden” causes can be broken down further, starting with two main categories, which I’ll call “random causes” and “counter-causes”:

“Random causes” are not necessarily truly random, but do not bias your conclusions in any particular direction.  It is the truly random combined with the may-as-well-be-random, and generates the inherent variance of the system.

“Counter causes” are those which you may not see, but which relate to your variables in ways that counteract your inferences.  The salary cap in the NFL is one of the most ubiquitous offenders:  E.g. an analyst sees a very good quarterback, and for various reasons believes that QB with a particular skill-set is worth an extra 2 wins per season.  That QB is obtained by an 8-8 team in free agency, so the analyst predicts that team will win 10 games.  But in reality, the team that signed that quarterback had to pay handsomely for that +2 addition, and may have had to cut 2 wins worth of players to do it.  If you imagine this process repeating itself over time, you will see that the correlation between QB’s with those skills and their team’s actual winrate may be small or non-existent (in reality, of course, the best quarterbacks are probably underpaid relative to their value, so this is not a problem).  In closed systems like sports, these sorts of scenarios crop up all the time, and thus it is not uncommon for a perfectly valid and logical-seeming inference to be, systematically, dead wrong (by which I mean that it not only leads to an erroneous conclusion in a particular situation, but will lead to bad predictions routinely).

So how does this relate to Football Outsiders, and how does it amount to a defense of their predictions?  First, I think the suggestion that FO may have created “negative knowledge” is demonstrably false:  The key here is not to be fooled by the stat that they could barely beat the “coma patient” prediction of 8-8 across the board.  8 wins is the most likely outcome for any team ex ante, and every win above or below that number is less and less likely.  E.g., if every outcome were the result of a flip of a coin, your best strategy would be to pick 8-8 for every team, and picking *any* team to go 10-6 or 12-4 would be terrible.  Yet Football Outsiders (and others) — based on their expertise — pick many teams to have very good and very bad records.  The fact that they break even against the coma patient shows that their expertise is worth something.

Second, I think there’s no shame in being unable to beat a simple regression based on one extremely probative variable:  I’ve worked on a lot of predictive models, from linear regressions to neural networks, and beating a simple regression can be a lot of work for marginal gain (which, combined with the rake, is the main reason that sports-betting markets can be so tough).

Yet, getting beaten so badly by a simple regression is a definite indicator of systematic error — particularly since there is nothing preventing Football Outsiders from using a simple regression to help them make their predictions. Now, I suspect that FO is underestimating football variance, especially the extent of regression to the mean.  But this is a blanket assumption that I would happily apply to just about any sports analyst — quantitative or not — and is not really of interest.  However, per the distinction I made above, I believe FO is likely underestimating the “counter causes” that may temper the robustness of their inferences without necessarily invalidating them entirely.  A relatively minor bias in this regard could easily lead to a significant drop in overall predictive performance, for the same reason as above:  the best and worst records are by far the least likely to occur.  Thus, *ever* predicting them, and expecting to gain accuracy in the process, requires an enormous amount of confidence.  If Football Outsiders has that degree of confidence, I would wager that it is misplaced.

Player Efficiency Ratings—A Bold ESPN Article Gets it Exactly Wrong

Tom Haberstroh, credited as a “Special to ESPN Insider” in his byline, writes this 16 paragraph article, about how “Carmelo Anthony is not an elite player.” Haberstroh boldly — if not effectively — argues that Carmelo’s high shot volume and correspondingly pedestrian Player Efficiency Rating suggests that not only is ‘Melo not quite the superstar his high scoring average makes him out to be, but that he is not even worth the max contract he will almost certainly get next summer.  Haberstroh further argues that this case is, in fact, a perfect example of why people should stop paying as much attention to Points Per Game and start focusing instead on PER’s.

I have a few instant reactions to this article that I thought I would share:

  1. Anthony may or may not be overrated, and many of Haberstroh’s criticisms on this front are valid — e.g., ‘Melo does have a relatively low shooting percentage — but his evidence is ultimately inconclusive.
  2. Haberstroh’s claim that Anthony is not worth a max contract is not supported at all.  How many players are “worth” max contracts?  The very best players, even with their max contracts, are incredible value for their teams (as evidenced by the fact that they typically win).  Corollary to this, there are almost certainly a number of players who are *not* the very best, who nevertheless receive max contracts, and who still give their teams good value at their price.  (This is not to mention the fact that players like Anthony, even if they are overrated, still sell jerseys, increase TV ratings, and put butts in seats.)
  3. One piece of statistical evidence that cuts against Haberstroh’s argument is that Carmelo has a very solid win/loss +/- with the Nuggets over his career.  With Melo in the lineup, Denver has won 59.9% of their games (308-206), and without him in the lineup over that period, they have won 50% (30-30).  While 10% may not sound like much, it is actually elite and compares favorably to the win/loss +/- of many excellent players, such as Chris Bosh (9.1%, and one of the top PER players in the league) and Kobe Bryant (4.1%).  All of these numbers should be treated with appropriate skepticism due to the small sample sizes, but they do trend accurately.

But the main point I would like to make is that — exactly opposite Haberstrom — I believe Carmelo Anthony is, in fact, a good example of why people should be *more* skeptical of PER’s as the ultimate arbiter of player value. One of the main problems with PER is that it attempts to account for whether a shot’s outcome is good or bad relative to the average shot, but it doesn’t account for whether the outcome is good or bad relative to the average shot taken in context.  The types of shots a player is asked to take vary both dramatically and systematically, and can thus massively bias his PER.  Many “bad” shots, for example, are taken out of necessity: when the clock is winding down and everyone is defended, someone has to chuck it up.  In that situation, “bad” shooting numbers may actually be good, if they are better than what a typical player would have done.  If the various types of shots were distributed equally, this would all average out in the end, and would only be relevant as a matter of precision.  But in reality, certain players are asked to take the bad shot more often that others, and those players are easy enough to find: they tend to be the best players on their teams.

This doesn’t mean I think PER is useless, or irreparably broken.  Among other things, I think it could be greatly improved by incorporating shot-clock data as a proxy to model the expected value of each shot (which I hope to write more about in the future).  However, in its current form it is far from being the robust and definitive metric that many basketball analysts seem to believe.  Points Per Game may be an even more useless metric — theoretically — but at least it’s honest.

Favre’s Not-So-Bad Interception

This post on Advanced NFL Stats (which is generally my favorite NFL blog), quantifying the badness of Brett Favre’s interception near the end of regulation, is somewhat revealing of a subtle problem I’ve noticed with simple win-share analysis of football plays.  To be sure, Favre’s interception “cost” the Vikings a chance to win the game in regulation, and after a decent return, even left a small chance of the Saints winning before overtime.  So in an absolute sense, it was a “bad” play, which is reflected by Brian’s conclusion that it cost the Vikings .38 wins.  But I think there are a couple of issues with that figure that are worth noting:

First, while it may have cost .38 wins versus the start of that play, a more important question might be how bad it was on the spectrum of possible outcomes.  For example, an incomplete pass still would not have left the Vikings in a great position, as they were outside of field goal range with enough time on the clock to run probably only one more play before making a FG attempt.  Likewise, if they had run the ball instead — with the Saints seemingly keyed up for the run — it is unlikely that they would have picked up the necessary yards to end the game there either.  It is important to keep in mind that many other negative outcomes, like a sack or a run for minus yards would be nearly as disastrous as the interception. In fact, by the nature of the position the Vikings were in, most “bad” outcomes would be hugely bad (in terms of win-shares), and most “good” outcomes would be hugely good.

The formal point here is that while Favre’s play was bad in absolute terms, it wasn’t much worse than a large percentage of other possible outcomes.  For an extreme comparison, imagine a team with 4th and goal at the 1 with 1 second left in the game, needing a touchdown to win, and the quarterback throws an incomplete pass.  The win-shares system would grade this as a terrible mistake!  I would suggest that a better way to quantify this type of result might be to ask the question: how many standard deviations worse than the mean was the outcome?  In the 4th down case, I think it’s hard to make either a terrible mistake or an incredible play, because practically any outcome is essentially normal.  Similarly, in the Favre case, while the interception was a highly unfavorable outcome, it wasn’t nearly as drastic as the basic win-shares analysis might make it seem.

Second, to rate this play based on the actual result is, shall we say, a little results-oriented.  As should be obvious, a completion of that length would have been an almost sure victory for the Vikings, so it’s unclear whether Favre’s throw was even a bad decision.  Considering they were out of field goal range at the start of the play, if the distribution of outcomes of the pass were 40% completions, 40% incompletions, and 20% interceptions, it would easily have been a win-maximizing gamble.  Regardless of the exact distribution ex ante, the -.38 wins outcome is way on the low end of the possible outcomes, especially considering that it reflects a longer than average return on the pick.  As should be obvious, many interceptions are the product of good quarterbacking decisions (I may write separately at a later point on the topic “Show me a quarterback that doesn’t throw interceptions, and I’ll show you a sucky quarterback”), and in this case it is not clear to me which type this was.

This should not be taken as a criticism of Advanced NFL Stats’ methodology. I’m certain Brian understands the difference between the resulting win-shares a play produces and the question of whether that result was the product of a poor decision.  When it comes to 4th downs, for example, everyone with even an inkling of analytical skill understands that Belichick’s infamously going for it against the Colts was definitely the win-maximizing play, even though it had a terrible result.  It doesn’t take a very big leap from there to realize that the same reasoning applies equally to players’ decisions.

My broader agenda that these issues partly relate to (which I will hopefully expand on significantly in the future) is that while I believe win-share analysis is the best — and in some sense the only — way to evaluate football decisions, I am also concerned with the many complications that arise when attempting to expand its purview to player evaluation.

A Decade of Hot Teams in the Playoffs

San Diego and Dallas were the Super Bowl-pick darlings of many sports writers and commentators heading into this postseason, in no small part because they were the two “hottest” teams in the NFL, having finished the regular season with the two longest winning streaks of any contenders (at 11 and 3, respectively).  Routinely, year after year, I think that the prediction-makers in the media overvalue season-ending rushes.  My reasons for believing this include:

  1. The seeding of many teams are frequently sealed or near-sealed weeks before the playoffs begin, leaving them with little incentive to compete fully.
  2. Teams that are eliminated from playoff contention may be dispirited, and/or players may not be giving 100% effort to winning, instead focusing on padding statistics or avoiding injury.
  3. When non-contenders do give maximum effort, it may more often be to play the role of “spoiler,” or to save face for their season by trying to beat the most high-profile contenders.
  4. Variance.

So the broader question to ask is “does late-season success correlate any more strongly with postseason performance than middle or early season success?”  But in this case, I’m interested only in winning streaks — i.e., the “hottest” teams, for which any relevant sample would probably be too small to draw any meaningful conclusions.  However, I thought it might be interesting to look at how the teams with the longest winning streaks have performed in the last decade:

2009:
AFC: San Diego: Won 11, lost divisional
NFC: Dallas: Won 3, lost divisional

2008:
AFC: Indianapolis: Won 9, lost wildcard
NFC: Atlanta: Won 3, lost wildcard

2007:
AFC: New England: Won 16, lost Superbowl
NFC: Washington: Won 4, lost wildcard

2006:
AFC: San Diego:  Won 10, lost divisional
NFC: Philadelphia: Won 5, lost divisional

2005:
NFC: Redskins: Won 5, lost divisional
AFC: Tie: Won 4: Denver: lost AFC championship; Pittsburg: won Superbowl
(the hottest team overall, Miami, won 6 but didn’t make the playoffs)

2004:
NFC: Pittsburg: Won 14, lost AFC championship
AFC: Tie: Won 2: Seattle: lost Superbowl; St. Louis: lost divisional; Green Bay: lost wildcard
2003:
AFC: New England: Won 12, won Superbowl
NFC: Green Bay: Won 4, lost divisional

2002:
AFC: Tennessee: Won 5, lost AFC championship
NFC: NY Giants: Won 4, lost wildcard

2001:
AFC: Patriots: Won 6, won Superbowl
NFC: Rams: Won 6, lost Superbowl

2000:
AFC: Baltimore: Won 7, won Superbowl
NFC: NY Giants: Won 5, lost Superbowl

From 2006 on, the hottest teams have obviously done terribly, with the undefeated Patriots being the only team to make it out of the divisional round.  Prior to that, the results seem more normal:  In 2005, Pittsburg won the Superbowl after tying for the longest winning streak among AFC playoff teams (though they trailed Washington in the NFC and Miami who didn’t make the playoffs).  New England won the Superbowl as the hottest team twice: in 2001 and 2003 — although both times they were one of the top seeds in their conference as well.  The last hottest team to play on wildcard weekend AND win the Superbowl was the Baltimore Ravens in 2000.

So what does that tell us?  Well, a decent anecdote — and not much more.  The sample is small and the numbers inconclusive.  On the one hand, the particular species of Cinderella team that gets predicted to win the Superbowl year after year by some — one that starts the season weakly but catches fire late and rides their momentum to the championship — has been a rarity (and going back further, it doesn’t get any more common).  On the other hand, if you simply picked the hottest team to win the Superbowl every year in this decade, you would have correctly picked 3 winners out of 10, which would not be a terrible record.

My Favorite Sports?

See the “about” page for information about the purpose of this blog.

At this point in time, my favorite sport, and the one I have done the most research on, is NFL Football.  After that, the other sports I follow fairly closely are, in approximate order: NBA Basketball, Tennis, Golf, Cycling, Olympic Sports, NCAA Football, Major League Baseball, MMA/Boxing, Horse Racing, and Poker (qua “sport”).  Sports I mostly do not follow include Hockey, College Basketball, WNBA, and Bassmaster.

This should not be taken as a promise that I will post about all of the sports I follow, nor that I won’t post on any of the sports I don’t:  I generally choose topics as they strike my fancy, or when they relate to some broader research I’m undertaking.  Thus I can really only guarantee that I will post about football and basketball regularly.  So if you’re looking for a kickass NHL blog, this isn’t going to be it.  On the other hand, if you’re a die-hard NHL fan that loves sports analysis generally, you may still appreciate what I have to offer — and who knows, maybe one day something interesting about Canada’s game will slip out.