How Much Does Home Field Advantage Matter?

Everyone knows that home field advantage exists in football. Some say it’s because the crowd helps the home team play at their highest level. Others say it’s that the crowd subconsciously influences the referees. Yet another theory is that players play better when able to follow the same routine, starting from sleeping in their own bed the night before. But whatever the reason (or combination of reasons), I’m hardly breaking new ground by saying that it’s better to play at home than on the road.

But how much does home field matter? Or, put another way, is there a way to quantify home field advantage to use in analyzing football? Let’s find out.

Game Projections

One way computer ranking systems demonstrate their accuracy is by making game projections. In doing so, each projection system is putting its credibility on the line. Be off by too many points, or be off in the same direction consistently, and something is wrong with your numbers. On the other hand, a good projection system can predict games well enough to score as high as 55% against the spread*.

*Believe it or not this is really, really good.

In my last post I used Bill Connelly’s SP+ rating, which analyzes on a per play basis. Today I am going to use Brian Fremeau’s FEI, which is focused on drive efficiency. This is for two reasons. First, I want to vary my use of projection systems to broaden my experience. Second, Fremeau’s website has a page dedicated to game projections, which came in very handy for this piece.

Deriving the FEI Game Projections

To use Fremeau’s projections, I had to first derive the formulas he used. I started with the bowl game projections from 2021, removing whatever home field adjustment he uses from the equation. I was particularly interested in each game’s Team Advantage (TA), which is the projected favorite’s per possession advantage over the underdog. Because this was on a possession basis, I hypothesized that the Projected Margin (PM) would be equal to the TA multiplied by an average number of possessions. I settled on 19.5 possessions, which yielded the smallest error*.

*This is almost certainly not the formula Fremeau uses. For every game, there was a small discrepancy between his projected margin and mine. Still, the average error was 0.054 points, and the largest error was 0.165 points, so I think my results are close enough. My guess is that Fremeau uses a floating number of possessions depending on each team’s profile.

Now I had to calculate the home field advantage being used. To do this, I took one week’s worth of games from 2021 and followed the same process I did for the bowl games. This time, however, I added a home field adjustment and tinkered with it until it matched Fremeau’s data. In doing so, I got an adjustment of 2.5 points*.

*Again, my projections did not match Fremeau’s exactly. This time, there was an average error of 0.075 points and a maximum of 0.230 points.

But was this the best we could do? To answer that I looked at all data from 2021.

Checking Our Work

Now, instead of using one or two weeks of data, I used every game from 2021. For each game, there was a Projected Margin and a Team Advantage. I could use that to determine which team was hosting (or if a game was at a neutral site) for every game. Once I knew the site for each game, I took the error between the projected and final scores, gave it a positive or negative sign depending on which direction the error was in, and took the average.

What do I hope to see from the data? Ideally, the average signed error will be 0. If it is 0 (or close to it), that means that during the season, the home team outperformed the projections as frequently as the road team did. Furthermore, the magnitude of the error would be approximately equal either way. In short, an average signed error of 0 means that the home field adjustment is as accurate as can be expected. Here’s how the data did:

When I originally saw this, I thought it said the error was 0.19 points, and I thought “OK, that’s pretty good, so the 2.5 point home field adjustment has merit.” Then, I took a second look and realized that it was 0.019! That’s not just pretty good; it’s really good. And with it, I can confidently say that 2.5 is the best numerical adjustment you can make for home field advantage based on what we know.

How can this help us understand football better? Well, using the 2.5 point home field adjustment, we can make better game projection models that are (hopefully) more predictive of what will happen in the future. And if you ever find yourself as one of Brent Musburger’s proverbial “friends in the desert”, having good game projections could be very helpful.