A hierarchical approach to modeling golf hole scores with Hardy distributions

The Hardy distribution, derived by van der Ven (2012. The Hardy distribution for golf hole scores. Math. Gaz. 96: 428–438) and named after an idea by Hardy (1945. A mathematical theorem about golf. Math. Gaz. 29: 226–227), is a discrete probability distribution for modeling golf hole scores. According to the Hardy distribution, a golfer’s score on a hole is determined by the par of the hole, the golfer’s probability of hitting a good shot, and the golfer’s probability of hitting a bad shot. To fit a Hardy distribution to golf scores on a hole, an analyst needs only the scores and a value for the par of the hole. We present four different hierarchical modeling strategies to jointly model the scores of multiple golfers on multiple holes during one golf tournament round using Hardy distributions. We then apply our new modeling strategies to golf hole scores from two very different golfer populations: male professional golfers on the PGA Tour and female high school golfers from the state of Iowa, USA. Probabilities of good and bad shots vary across holes for both the male professional golfers on the PGA Tour and the female high school golfers. We find little variation among the male professional golfers but substantial variation among the female high school golfers.