Prize Money and Sporting Performance

By John Considine

In 2018, Dustin Johnson finished 3rd in the US Open and 27th in the PGA.  Zack Johnson finished 12th and 19th in the same tournaments.  Who performed better across these two tournaments?  Adding the rankings we might make a case for either.  However, the distribution of prize money in these tournaments meant that Dustin's bank account increasing by a greater amount.  Dustin took home a combined total that was twice as much as Zack's.  It makes one wonder if prize money is a good measure of sporting performance.

Another illustration is the gap in prize money accumulated by Tiger Woods and Justin Rose in these two majors.  Tiger Woods missed the cut in the US Open and finished second in the PGA.  His second place was worth $1.188m.  Justin Rose collected about one-third of that for finishing 10th and 19th.  Sporting performance translates into prize money in a non-linear fashion as the picture below illustrates.

Sports economists have refined their view of the relationship between sporting performance in golf and financial rewards.  A good summary can be found in Super Golfonomics.  In the book, Stephen Shmanske presents a model linking skills to performance, and then performance to earnings.  Shmanske makes a statement in the book, supported by statistical evidence, that seems obvious on the surface.  Talking about skewness and variance in golfing scores, he says "this random variation is also rewarded generously by the nonlinearity of the tournament payouts".  Even a quick look at the picture above might suggest that it is better to have four consecutive low scoring rounds followed by four high scoring rounds than have eight average rounds.  And, the literature suggests that this can be a matter of luck

All this suggests that there is a need to be careful about the use of financial rewards as a measure of golfing ability.  This is particularly so for short periods of time.  However, over longer periods of time there should be a better relationship.