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Statistically Speaking: Home Field Advantage as a Function of Crowd Size

Sunday, June 26, 2011

Home Field Advantage as a Function of Crowd Size

A few weeks ago I finished reading the fantastic book Scorecasting. One of the more interesting chapters in the book deals with home field advantage and what actual advantage(s) it confers to teams. I won't spoil the conclusion, but its not what you think. The authors later look at how crowd size may have accounted for these advantages. Feeling inspired, I decided to take a look at how crowd size affected home field advantage in 2010. I didn't look at any particular telling stat (penalties, yards, touchdowns, etc.), I simply looked at whether or not the home team won, and then what the crowd size for that game was. I then, very unscientifically I might add, divided the crowd attendance into ranges of 10,000 and calculated the winning percentage for each range. The results are summarized in the table below.That looks like an almost perfect relationship. As crowd size increases, the home team is more likely to win (up to a certain point--adding a few thousand more folks north of 100,000 doesn't appear to make the home team more likely to win). However, there are some caveats. First, sample size is an issue for a few ranges. Only 12 games were played involving 10,000 or fewer spectators. These were all games involving either MAC, Sun Belt, or WAC schools. There were also only 57 games played in front of more than 90,000 fans. These games all involved SEC, Big 12, or Big 10 teams playing at home (some of their opponents were mid-majors). This brings up a second issue. Better teams tend to have bigger stadiums. It doesn't make sense for Akron to have an on-campus stadium that seats 96,000 fans. Likewise, it doesn't make sense for Ohio State to have a 30,000 seat stadium when they have more undergraduates than that currently enrolled at the university. If only there were some unbiased way to look at two teams and determine whether or not the home team is more likely to win in the first place. Thankfully, for our purposes, and for degenerates nationwide, there is. Its called the point spread. This next table summarizes the home teams record Against the Spread (ATS). For those who do not know what this means, I present a quick example. Lets say the road team is favored by seven points against the home team. If the home team loses the game by six points, they cover the spread and 'win' for our purposes. If they lose by eight points, they 'lose', and if they lose by exactly seven points its a push, or for our purposes, a 'tie'. Now, here's that table I promised.Based on their record against the spread, home team's performed better as crowd size increased. However, once again this was only up to a certain point, and that point is much lower than the previous threshold for simply winning the game. As the crowd size inched north of 50,000 or so, the added fans provided no real boost to the home team's hopes of covering the spread. Here's another way of looking at the data.Any gambler worth his salt would give his best parlay card for a guaranteed winning percentage of 57%. If you occasionally make plays on college football, keep crowd size in mind when placing your bets. And you can feel free to send any large windfalls my way.

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