Monday, August 5, 2013

Penalties I: Referee Bias

Abstract 
In addition to making the occasional blown call, multiple sources have noted that referees appear to have a subtle, pervasive, likely subconscious, home-team bias. Here I attempt to quantify that bias, using different categories of penalties to highlight any discrepancy between penalties that require no interpretation (and should not be subject to this sort of bias) and penalties that involve the judgement of the referees (and therefore would be prone to bias). I find that there is a small but statistically significant discrepancy between judgement-call penalties on the home and away teams, with the visitors getting flagged an average of ~0.1 more times per game. What is most striking about this result is not its statistical significance but how small it is, a testament to the (often overlooked) fact that NFL referees are generally quite good at their jobs.

Introduction
If you watch football for long enough, eventually you'll see a play that makes you uncontrollably angry—Specifically, angry at the refs. How could they have blown that call so badly? Were they even watching the play?

This outrage, however, usually fades fairly fast—you have some reluctant understanding that what's obvious to you from the super-slo-mo replay is not as crystal clear when seen at full speed, and most individual calls/non-calls have a small impact on the final score. (Of course, there are some notable exceptions).

Individual plays such as these are so infrequent that they are not well-suited to statistical analysis. However, it is also possible that referees can be biased by the location of the game, either because the refs are from the area or are subconsciously influenced by the cheering home crowd. The NFL mitigates the former issue by rotating crews between stadiums, but what about the latter?

Unfortunately, while some work has already been done on this very issue, actual numbers on any bias appear to be thin on the internet ground. General assertions from non-open-access sources1 abound, as do people using studies of soccer(!) officiating to back up their claims about the NFL. I did run across an interesting article that attempted to quantify home/away bias in individual officiating crews, but it unfortunately suffers from a small (13 weeks) sample size and a lack of errors — is calling an average of 1.5 extra penalties on the away team a significant effect or have they just shown how noisy their data is? (The fact that the sum of each crew's 'bias' is close to zero is circumstantial evidence for the latter case).

Data
Once again my data come from the thorough folks at Armchair Analysis. In addition to providing data on individual penalties, they also aggregate the calls into one of several helpful categories. Using their categories as jumping off points, I lumped almost all penalties in the entire data set into one of four categories:
  • Judgement: Penalties like holding, pass interference, and illegal use of hands, for both offense and defense.
  • Timing: False starts, offsides, encroachment, and neutral zone infractions.
  • Positioning: All kinds of illegal blocking penalties (e.g. blocks in the back, crackback blocks, tripping).
  • Dumb: Taunting, roughing the passer, giving him the business, etc.

Results
I split up the penalty data into home and away bins, then computed the average number of penalties per game in each category. To get a sense of the uncertainties, I bootstrapped the data. These averages are shown in Figure 1.
Figure 1:Average penalties per game in each of the four categories discussed in the Data Section.

For both penalties relating to positioning (the illegal blocks) and dumb penalties there is stastically zero referee bias; both the home and away teams get flagged at the same rate (within the errors). This is not surprising, as these calls are fairly cut-and-dried, with little room for interpretation. Also not surprising is that the away team suffers more timing penalties (~0.2 more per game) — despite also being generally black and white, things like false starts and offsides are the fouls most likely to be affected by crowd noise.

For judgement call penalties like holding or pass interference, however, there is a small but statistically significant excess of penalties for the away team, with the visitor receiving an average of 2.70±0.03 penalties while the home team only gets called 2.59±0.03 times per game. These fouls should not be significantly affected by crowd noise, and thus indicate that referees do indeed hold a slight bias in favor of the home team.

Discussion and Conclusions
So it seems that NFL refs are indeed biased. But honestly, one tenth of a penalty per game is a pretty small bias. Since teams only play 8 away games during the regular season, this is less than one extra penalty, and since each team also plays 8 home games over time things should average out. Even in the playoffs, where a #6 seed would have to play 3 away games to make it to the Super Bowl, this bias shouldn't play a large role. The real story here is how fair  NFL officials are, even when calling fouls in front of 80,000 rabid, screaming, angry fans.

1: In an interview with Wired,  one of this book's authors cites this sort of referee bias as the reason why the Seahawks lost Super Bowl XL. I find this frightening, as anyone who writes an entire book about statistics should know that you can't apply statistical trends to individual events. I assume(hope?) that he was just speaking off the cuff and was therefore not very thorough with his answer.

Shout out to Sonographer's Cup winner Andrew "Lulu" Schaffrinna, without whom this post (and indeed, any future studies of penalties) would almost certainly never have happened.

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