The Win Probability Value of a Point

By Max Mulitz



This article about hockey analytics which explains that 94% of team wins can be explained by goal differential, got me thinking about the value of a point in football. I grabbed the Team point differential data from SportingCharts for each NFL team from 2011-2015 and ran a simple linear regression to predict wins.

The model had an adjusted R-Squared of .87. That means 87% of an NFL teams’ wins in a given season can be explained by their point differential. The remaining 13% of the game can be explained by luck relating to when a team scores their points as well as certain game management strategies that may distort point differentials (playing prevent defense up 3 scores in the 4th Quarter may increase your opponent’s chance of scoring while decreasing their chance to win the game if they take a long time to score, as one simple example.) Notice this isn’t the same as saying 87% of the game is skill, it is certainly the case that elements of luck (having a high fumble recovery rate, for example) can influence a teams point differential.

The equation for the model was as follows:

Wins = 8.0000 + .0.0278988 * Point differential.

It makes sense that our intercept is 8, since a team with 0 point differential would expect to win half their games. What’s more interesting is we now have a strong estimate for the marginal value of a point in the NFL. For each addition point a team scores (or prevents) in a season, they can expect to win .028 extra games. Using this estimate to value kickers, we see our hypothetical uber kicker (worth 9.6 points a season) is worth .27 wins a season, almost equal to our earlier estimate of .3 and a top 10 kicker is worth .13 wins a season, similar to our earlier estimate of .1.

Football Outsiders FAQ actually shows us that point differential predicts next seasons wins better than previous year wins, which is probably strong evidence that point differential is a purer measure measure of team quality relative to luck than previous years wins is.

Anyway, one thing that the hockey, basketball and baseball analytics communities have figured out that football doesn’t seem to have yet is that we ultimately want to be optimizing for wins, not points added. Some Win Probability Added models exist in football but those are based on fitting a model to specific game situations and then measuring the changes in Win Probability over time.

Because Point Differential is an extremely strong linear predictor of team wins, Expected Points Added can easily and meaningfully be converted to a Wins Added value, which is meaningful since our goal in measuring player quality is ultimately to optimize for number of wins.



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