Monday, September 16, 2013

Penalties II: Crowd Noise

Abstract
Crowd noise is generally considered to be a contributing factor in causing false-start penalties on visiting teams. Some stadiums are well-known for focusing deafening amounts of noise on the field, usually near the endzones. To determine if crowd noise really does cause false-starts, I compared the discrepancy between false-starts called on the home and away team as a function of distance from an endzone. While distance from midfield and likelihood of visiting team false-start penalties is correlated, it is not strongly significant.

Introduction
In Part I of my investigation into penalties, I found that there was a statistically significant discrepancy in the number of false-start penalties between the home and away teams. At the time I chalked this result up to crowd noise and focused my analysis on other types of penalties, but I later realized that, while frequently quoted as fact, I've never seen any hard evidence on the subject.

If crowd noise does affect a visiting offense's snap count, it's logical to expect that the effect will be largest when fans surround the field on three sides—near the endzones. This provides a way to isolate crowd noise from other variables surrounding false-starts, e.g. the possibility that traveling to away games makes teams more prone to jumping before the snap, or that referees are somehow biased even for such apparently cut-and-dried calls.

Data
As usual the data come from Armchair Analysis. For this project I created a new table containing information on the field location of all plays as well as whether a penalty was called—because of the huge number of plays in the database this query took ~8 hours and therefore was not feasible to do on the fly during the analysis.

Results
The percentage of plays that result in false-start penalties as a function of field position is shown in Figure 1. I'm not sure what's going on when the offense is backed up by their own endzone; I've checked the data and didn't find anything out of the ordinary. It's possible this is due to the relatively small number of samples that close to the goal line—regardless of the cause, it doesn't appear to affect the rest of the data, so I will simply exclude this bin from the remainder of the analysis.
Figure 1: Percentage of plays which result in false-starts as a function of distance from the offense's goal line. Black points are for the home team, while red points show penalties committed by the away team. X error bars show the range of yards included in each bin, while y error bars are the bootstrapped uncertainties.
At just about every point on the field the away team commits more false-starts, which is unsurprising given what we already knew. If you squint just right, however, it does appear the away team gains 'penalty parity' around midfield.

As always, trusting your eyes is a poor way to do statistics. Therefore I ran a correlation analysis, folding the data at the 50 to test raw distance away from the nearest endzone rather than position on the field. The result is a fairly weak correlation (Spearman ρ of 0.28) that is far from statistically significant (p-value of 0.24).

Discussion and Conclusions
Our eyes do lie, apparently, at least about the statistical significance of the correlation. It's difficult to figure out what to make of this (non) result—the original hypothesis certainly seemed reasonable, and I don't believe that crowd noise has zero effect on false-starts. You can certainly make a strong argument for a correlation based on watching some of these false starts happen.

So why no significant correlation? Well, it certainly is possible that crowd noise actually isn't playing a huge role after all, although I don't have another explanation for why referees would be more likely to call a false-start on the visiting team. It's also possible that my original assumption, that crowd noise is amplified near endzones, is incorrect. Another option is to look at Figure 1 and note that the correlation appears to be more significant in the offense's own end of the field: maybe fans are more vocal when the away team is starting a drive, but as the offense moves down the field they get quieter.

Ultimately, the only way to know for sure just how crowd noise affects the game would be to attach sound meters to the players. The NFL may already do this, for all I know; they already mic the players and coaches, so at the very least crowd noise information should be (in principle) recoverable from these recordings. If I ever get my hands on this sort of data I will certainly try this sort of analysis again, but for now the stats I have on hand are are just too rough to make any definitive conclusions.

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