College football, voting, and the law of large numbers

October 25, 2012
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(This article was originally published at Statistical Modeling, Causal Inference, and Social Science, and syndicated at StatsBlogs.)

In an article provocatively entitled, “Will Ohio State’s football team decide who wins the White House?”, Tyler Cowen and Kevin Grier report:

It is statistically possible that the outcome of a handful of college football games in the right battleground states could determine the race for the White House.

Economists Andrew Healy, Neil Malhotra, and Cecilia Mo make this argument in a fascinating article in the Proceedings of the National Academy of Science. They examined whether the outcomes of college football games on the eve of elections for presidents, senators, and governors affected the choices voters made. They found that a win by the local team, in the week before an election, raises the vote going to the incumbent by around 1.5 percentage points. When it comes to the 20 highest attendance teams—big athletic programs like the University of Michigan, Oklahoma, and Southern Cal—a victory on the eve of an election pushes the vote for the incumbent up by 3 percentage points. That’s a lot of votes, certainly more than the margin of victory in a tight race.

I took a look at the study (I felt obliged to, as it combined two of my interests) and it seemed reasonable to me. There certainly could be some big selection bias going on that the authors (and I) didn’t think of, but I saw no obvious problems. So for now I’ll take their result at face value and will assume a 2 percentage-point effect. I’ll assume that this would be +1% for the incumbent party and -1% for the other party, I assume.

I agree with Cowen and Grier that this sort of pattern among voters is disturbing, similar to Chris Achen and Larry Bartels’s famous study of the electoral effects of shark attacks.

Not as bad as it sounds

That said, I’d like to defend democracy a bit and argue that the college football effect isn’t quite as bad as Cowen and Grier imply. Here’s what they say:

The key to victory could come down to . . . Florida, Ohio, and Virginia. On Oct. 27th, a little more than a week before the election, the Ohio State Buckeyes have a big football game against Penn State. The University of Florida Gators have a huge match up against the University of Georgia Bulldogs. If the election remains razor close, these games in these two key battleground states could affect who sits in the White House for the next four years. Can you imagine Ohio State head coach Urban Meyer getting a late night call from the Obama campaign suggesting a particular blitz package? Or maybe Romney has some advice for how the Gators can bottle up Georgia’s running game. The decision of whether to punt or go for it on that crucial fourth down could affect the job prospects of more than just the football team’s coaching staff.

Unless I’m misunderstanding something, I think Romney’s staff should be giving advice to the Bulldogs, not the Gators (unless Cowen and Grier are subtly riffing last month’s “hapless Romney” meme to imply that the candidate’s best chance to help the Florida team lose is to give them advice). Details aside, though, I don’t think this adds up to so much.

I have two reasons for making this argument, even conditional on assuming that a local win really does count for 2 percentage points of the vote. My reasons are:

1. Locality. My quick reading of the Healy, Malhotra, and Mo is that all their analysis is at the county level. Ohio State University is in Columbus, Ohio, which is in Franklin county, which according to Wiki has 1.2 million people. 1.2 million is a lot, but it’s only 10% of the population of the state. So a difference of +/- 1 percentage points in Franklin county corresponds to only +/- 0.1 percentage points in the state of Ohio. An increase or decrease of 0.1 percentage points isn’t nothing, but even swing states are unlikely to be divided that closely. (Just to calibrate, 0.1% of 5 million votes is 5000 votes, which is very close for a state election.)

As for Florida . . . the Gators are in Gainesville, in Alachua county, population 250,000, that’s less than 1.5% of the population of the state. OK, maybe there’s some influence on other nearby counties but then you have to be careful, as you’re going beyond the bounds of the research study, also one might expect the effect to decline as you move away from the location of the game.

2. Averaging. The article under discussion includes two Ohio teams—Ohio State and Cincinnati. According to the schedule, the Bearcats are playing Louisville this Friday and Syracuse the Saturday after that. And, after to their upcoming Penn State game, the Buckeyes are playing Illinois before the election. So these are 4 Ohio games, not just one. Florida has three teams (Florida, Florida State, and Miami). Even lowly Virginia has two teams in the list: Virginia and Virginia Tech. And here are a few more football teams in swing states: Colorado, Iowa, and Iowa State.

There are multiple games in multiple weeks in several states, each of which, according to the analysis, operates on the county level and would have at most a 0.2% effect in any state. So there’s no reason to believe that any single game would have a big effect, and any effects there are would be averaged over many games.

In summary, it is indeed disturbing that people are more likely to vote for the incumbent party if their local team wins—sure, 2% isn’t much, but it’s a nontrivial proportion of the undecided voters. But the claim, “It is statistically possible that the outcome of a handful of college football games in the right battleground states could determine the race for the White House,” while literally true (if the election happens to be extremely close) is overstated.

P.S. In addition, Avi suggests that the electoral effect of a football game is likely to be smaller in an intense election such as Ohio 2012, compared to an average election in the dataset.



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