Last week we talked about the validation of the Advanced NFL Stats WP model, and Brian Burke noted in his writeup that WP still failed to account for home field advantage. Now it does.

Although it’s clear that home teams perform better during a game, at least in terms of points scored, it’s not clear exactly how this translates into an increased chance of winning minute by minute. From simple win-loss records, all we know that at the outset of a game the home generally team ultimately has about a 56.5% chance of winning.

The problem, as should be fairly apparent, is that Burke only has WP available to test these win-loss probabilities. So what happens when you chart the home team win probability (go look!)? After extracting the results from the context from which they were derived (a model that learns over the course of the game), Burke found a WP curve with respect to HFA .

Starting with a 6.5% advantage at kickoff, and following the shape of the curve, we see the real, no kidding, actual HFA as the game goes on. This isn’t HFA in terms of yards per play, first downs, or points scored, or in terms of anything except the probability of winning.

The results are interesting in that HFA effect on WP decreases over the course of the game. Would you have expected this? Crowd intensity down the stretch of the game does continue to aid the winning team, but the marginal WP returns decrease. Why?

So there are (at least) two mechanisms at work. First is the decrease in performance advantage for the home team as the game goes on that I discussed above. Perhaps fatigue neutralizes the home team's edge, or perhaps it's visitor acclimation to a hostile, unfamiliar environment. Second, as the game clock ticks down, there is less time for the home team to capitalize on its advantage. By the end of the game the scoreboard doesn’t care which team is the home team and which is the visitor. A 1-point lead is good enough to win, period. So it’s a complicated thing to model. We just can’t add 6.5% to the win probability (WP) for the home team throughout the game.

The second point is the key from a WP standpoint. At the start of the game, the home team has 60 minutes of advantaged football ahead of them. As WP predicts the odds of winning the game from a given moment through the end of the game, you can't expect the same cumulative advantage at any point in the game. By the time a game has reached the final two-minute warning, home field advantage can only do so much.