Bayesian Prediction of Golfer Performance (Individual Tournament)

I’ve posted several studies attempting to predict golfer performance. This attempted to find the importance of the previous week when predicting the following week. The study was not particularly sophisticated (simple linear regression), but the results indicated that the previous week’s performance should be valued at around 10% of the projection for the golfer the following week (90% would be the two-year performance). This other study attempted to predict golfer performance for an entire season using prior season data. That study found that no matter how many years are used or whether those years are weighted for recency, the resulting correlation is ~70%. Doing better than that for full-season prediction would indicate an additional level of sophistication beyond aggregating prior seasons or weighted data for recency.

This post, however, concerns predicting individual tournament performance using my Bayesian rankings. These rankings are generated each week by combining prior performance and sample performance using the equation ((prior mean/prior variance)+(observed mean/observed variance))/((1/prior variance)+(1/observed variance)). In this way, each golfer’s prediction for a week is updated when new information is encountered. The prior mean for a week is the Bayesian mean generated the prior week. My rankings also slowly regress to a golfer’s two-year performance if they are inactive for a period of weeks. For each week, the prior mean is calculated using the equation  (((Divisor – (Weeks since competed)) / Divisor) * (Prior Mean)) + ((1 – ((Divisor – (Weeks since competed)) / Divisor)) * (Two-year Z-Score)). I use 50 as the Divisor, which weights two-year performance at 2% for 1 week off, 27% for 5 weeks off, and 69% for 10 weeks off.

To measure how predictive these rankings were, I gathered data for all golfers who had accumulated 100 rounds on the PGA, European, Web.com, or Challenge Tour between 1-2010 and 7-2013. My sample was 643 golfers. I then examined performance in all tournaments between the 3-28-2013 and 8-8-2013. My sample was 6246 tournaments played. I then generated Bayesian rankings predicting performance before each of these tournaments played. The mean of my predictions was +0.08, indicating I expected the sample to be slightly worse than PGA average. I then compared each prediction to the golfer’s actual performance.

The table below shows the performance of Bayesian and pure Two-year predictions by including all predictions within +/- 0.05 from the displayed prediction (ie, -0.50 includes all predictions between -0.45 and -0.55). The accompanying graph shows the same information with best-fit lines.

Obviously, the Bayesian and Two-year predictions perform similarly. To test which is better I tested the mean square error. This shows how closely the prediction matched actual performance. I also included “dumb” predictions which simply predict all rounds will perform to the mean of all predictions (+0.08 for Bayesian, +0.055 for Two-year). The “dumb” predictions are the baseline for judging any predictions. If a prediction can’t beat it, it’s worthless.

The mean square error for the Bayesian predictions was 0.381 and 0.446 for the “dumb” predictions. The mean square error for the Two-year predictions was 0.389 and 0.452 for the “dumb” predictions. So both sets of predictions provide value over the “dumb” predictions, but both perform fairly similarly when compared to the “dumb” predictions (-0.065 for Bayesian and -0.063 for Two-year).

This study indicates two things; first, using Bayesian methods to predict golfer performance doesn’t substantially improve accuracy relative to unweighted aggregation of the last two years of performance, and second, that predicting golfer performance in individual tournaments is very difficult. A mean square error of 0.38 indicates an average miss of 3.5 strokes for golfers playing four rounds and 2.5 strokes for golfers playing two rounds.