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Monday, August 16, 2010

Crowd Size Doesn't Matter

It is a truism of sports that spectators influence the outcome of the game. Fans encourage the home team and disrupt/distract the road team. They are the 12th Man. Right?

Wrong. At least as it applies to college football, the effect of the crowd seems to be massively overstated.

First, larger crowds do not disrupt road teams. In conference games*, road teams are slightly more likely to be penalized than home teams (1 extra penalty every four games, 2.5 extra penalty yards per game), but crowd size has no effect on the number of penalties or penalty yards for road teams. Using multiple regression, we find that increasing the number of fans in a stadium by 1,000 increases the average penalty yards for the road team by -.187 to .033 . In other words, it is just as likely that larger crowds lead to fewer penalty yards as more penalty yards for road teams. 

But fans also encourage the home team to play harder, right? If this were the case, we would expect home teams to average more yards than road teams - and they do, about 19 extra yards per games - and we would expect the size of this difference to be influenced by crowd size. Unfortunately, not true. After controlling for the number of yards that a team gains on the road, every 1,000 fans at a home game increases a team's offensive output by 1/20 of a yard - a whopping 1.8 inches. Because every yard, on average, is worth about .1 points, 1,000 fans in your stadium is worth 1 point every 35 years or so. The 12th Man isn't pulling his weight.

And, finally, do butts in the bleachers help a team win. Whether or not they influence penalty or yard totals really doesn't matter if they can help the home team get over the hump when it matters, right? In 2009, home teams facing conference opponents won 57.7% of the time (and, consequently, road teams won 1-.577=42.3%). But this does not mean that crowd size is the cause. To test the contribution of crowd size on winning and losing, we use logistic regression to predict the probability that the home team will win given its winning% on the road, the opponent's winning% and the number of fans in attendance. Remarkably, this simple model predicts the winner 80% of the time, but crowd size is, again, not a factor. Even in close games decided by less than 7 points, when crowd noise should be most important, the size of the crowd has no effect in choosing winners from losers.

Bigger crowds do help a program in other ways. They generate revenue and lead to greater media exposure. Atmosphere is important for recruiting, even if it isn't important for performance. And crowd size may be missing the point - what really matters is crowd noise, not just size. It may be true that Oregon's 55,000 are louder than Michigan's 110,000. But crowd size and noise are correlated - as one increases, the other tends to increase as well. 

But home teams win 57% of the time, right? There has to be some explanation. My theory is this - home field advantage is principally of product of travel. The the longer the road trip, the better. Living in the boonies helps, too. Crossing times zones is especially important. Travel causes tight, tired muscles, dehydration, interrupts normal eating patterns and preparation ceremonies, and the new surroundings can be distracting to less-experienced athletes. The crowd is just another piece of that new environment.  

*All calculations are based on non-neutral conference games in 2009 - 466 games in all. Using only conference games is a simple and reliable way of controlling for the relative strength of home and road teams.

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