Consistency or Heroics: Skewness, Performance, and Earnings on the PGA TOUR
Shmanske, Stephen, Atlantic Economic Journal
PGA TOUR professional golfers play in tournaments where the payment structure to the winners is decidedly nonlinear. This payment structure disproportionately rewards superlative performance and brings forth more effort as predicted in the tournament compensation model of Lazear and Rosen (1981) and statistically verified in a couple of papers by Ehrenberg and Bognanno (1990a, 1990b). It also brings about the possibility that some of the hallmarks of the game of golf, namely, consistency and steady play, will be eclipsed by one-time heroics or flash-in-the-pan, "hot hand" performances. (1)
Although it is not immediately clear what PGA TOUR officials can do to affect consistency or heroics, the issue is important to the marketing of professional golf. On the one hand, for example, if mean performance were the only thing that mattered (that is, if the variance of individual golfer's scores approached zero), then the outcome of a tournament would essentially be a foregone conclusion. While some fans would still pay to see what amounted to a display or exhibition of exceptional skill, there would be no interest in the sport through the avenue of uncertainty of outcome. There would be no value created for fans wishing to root for their favorites and gambling markets would largely disappear. On the other hand, if a large variance in golfer's individual performances (or a large negative skewness) was of predominant importance, then different golfers would win each week and a different set of golfers would be among the leaders in each tournament. Such "competitive balance" might be desirable for team sports organized in leagues, but the issue is an unsettled one (Schmidt and Berri 2001; Szymanski 2001; Zimbalist 2002; Humphreys 2002; Sanderson and Siegfried 2003; Fort 2003; Kahane 2003). In golf, however, it might be detrimental. Name recognition would suffer and the lack of one or a few superstars might cause fan interest to wane (Rosen 1981). Indeed, it has often been documented how television ratings suffer when Tiger Woods is not in contention (Fitzgerald 2006). Is it consistency in the sense of low mean scores, low variances, and insignificant skewness that matters in professional golf? Or is it heroics in the sense of a high variance and a large negative skewness in the distribution of a golfer's scores that golfers cash in on? Or is it both?
In one sense we know the answers to these questions. Tiger Woods is a household name because of his superstar status and there have always been superstars from Bobby Jones and Walter Hagen through Ben Hogan to Arnold Palmer, Jack Nicklaus, and Tom Watson, to today's stars, Woods, Phil Mickelson, Ernie Els, and Vijay Singh. However, the extent to which golfers achieve stardom (and earnings) through steady play and low mean scores, versus through mediocre play with a large variance that allows one to contend for first prize roughly half of the time, versus relatively poor play on average with a large negative skewness that leads to a small number of exceptional performances with large paydays, is still an empirical question. Ultimately, there need not be one path to financial success. Which golfers achieve success through which of the above paths can be identified by an examination of the data.
I use the performances of the top 100 money winners on the official PGA TOUR money list for the year 2002 as the basis for the research. The raw data, summary statistics, and some interesting lists of leaders in each category are described in the next section. The next section also describes an important transformation of each golfer's scores to account for the difficulty of each tournament's golf course and the strength of the field of competitors. The third section reports the results of regression analyses that confirm the importance of the measurement protocol adopted with respect to each golfer's scores, and show the independent effects of mean, variance, and skewness on the golfer's earnings. …