The Correlated Gaussian: Can it be applied to soccer?

Remaining on the subject of applying quantitative metrics from other sports, I’ll mention one from basketball — the Correlated Gaussian method.

The Correlated Gaussian method was developed by Dean Oliver, who wrote Basketball on Paper and is currently head of Production Analytics at ESPN.  This metric is similar to the Pythagorean in that it relates winning percentage to scoring statistics, but it expands the variables to points scored/allowed, their respective standard deviations, and the covariance between points scored and allowed.  (You can use any team-level offensive or defensive rating that you choose, but points work well and that’s the object of the game, anyway.)

All of those variables are calculated in such a way that it produces a z-score, which is a standard score that relates how far a quantity is from its mean.  In this case, the quantity is point differential.  Winning percentage is calculated as the probability that any standard score would exceed that z-score value in a standard normal distribution.

I’ve written before that the variance of goal statistics can tell a lot about which teams are likely to win league championships.  The Correlated Gaussian incorporates those parameters unlike the Pythagorean, so it’s an appealing metric to me.  But like the baseball Pythagorean, it’s written for a sport with no draws in its league competitions.  How can this metric be adapted to soccer competitions?  I’ll post some thoughts on that soon.