The Market for Defense: An Application of Moneyball

Billy Beane

We all know the story. Financially strapped, the 2002 Oakland Athletics rose to prominence through the shrewd market analysis of General Manager Billy Beane and Co. This simple plotline, of course, is the premise of Moneyball: the theory, the book, the movie, and now culture, that has both revolutionized talent evaluation in Major League Baseball and permeated the vernacular of fans and nonfans alike.

The Moneyball hypothesis focuses primarily on the undervaluation of a player’s ability to get on base. Given its contribution to a team’s likelihood of winning, the statistic On-Base Percentage (OBP) was not adequately compensated on the open market. This inefficiency allowed for teams such as the A’s to purchase these critical statistics at affordable rates. However, it is a widely held conception that the Moneyball hypothesis has now dissipated, largely due to the dissemination of knowledge across MLB. Naturally, once other teams catch on, the market inefficiency can no longer exist.

But have market inefficiencies totally eroded?

Find out after the jump.

Not quite, according to our analysis.

If the market is efficient, we expect the correlation between team winning percentage and team payroll to be quite high. That is, teams pay players to win games, so if they are spending money wisely, these two figures will fall in line with one another. In 2011, the correlation coefficient between winning percentage and team salary was a modest .41. Clearly, this relationship is still far from perfect.

This insight opens the doors for future discussion. Even if Moneyball has largely dissipated, it is almost certain that other market inefficiencies are at play. One of the hallmarks of the Moneyball hypothesis is that defense does not matter. But perhaps this disregard for half the sport stems from a failure to objectively and accurately quantify baseball’s mysterious final frontier. After all, the best defensive metrics are still far from ubiquitous.

Though much more research still needs to be done with respect to the usefulness of defensive statistics, we can use the ones at hand to see if the market for defensive skill is functioning optimally. In the spirit of Billy Beane, we must evaluate this question analytically. To do so, we will compare the correlation between UZR/150, a sabermetric statistic that, according to FanGraphs, quantifies “the number of runs above or below average a fielder is, per 150 defensive games,” and team winning percentage, with the correlation between UZR/150 and team salary.

In 2011, the correlation coefficient between team UZR/150 and team winning percentage was a modest .349. This figure indicates that UZR/150 contributes to 12.2% of the variance in team winning percentage. To place this in figure into perspective, team OBP and team winning percentage feature a correlation coefficient of .551. As such, OBP accounts for 30.4% of the variance in team winning percentage. Pursuant to this somewhat crude analysis, Beane was correct in his assessment that offensive trumps defensive value.

Next, let us compare these correlations to the correlations with team payroll. We should expect that, in an efficient market, the correlations would be similar, since, as stated prior, the overarching goal of paying players is to win games. However, the correlation between UZR/150 and salary is just .04. Thus, less than 1% of the variance in salary is accounted for by UZR/150, a shockingly small figure. Interestingly, our results indicate that OBP is undervalued as well accounting for just 14.8% of the variation in salary with a correlation of .38. The results are encapsulated in the chart below:

R-Squared Values			Ratios
	Salary	WPCT	Sal/WPCT
OBP	14.80%	30.40%	48.70%
UZR/150	0.20%	12.20%	1.60%

What can we take away from this analysis? For one, though neither statistic is totally justifiably compensated, offense is more fairly remunerated than defense on the open market. But the scope of this difference is startling. The ratio of salary accounted for to win percentage accounted for by OBP is 48.7%, indicating the market is operating at less than 50% efficiency. Surprisingly, this would suggest that the Moneyball hypothesis is still relevant.

More shocking, however, is that same ratio for UZR/150 equals only 1.6%. Yes, 1.6%. In light of its contribution to winning percentage, UZR/150 is only accounted for by 1.6% of what it should be in salary determination. Granted, the validity of UZR/150 is not necessarily accepted, but this utter lack of relevance is still inexplicable. Though UZR/150 accounts for relatively little in a team’s variance in win percentage, it is still disproportionately undervalued.

Evidently (at least in 2011), the original Moneyball hypothesis is still alive, as is the possibility (or plausibility) for future Moneyball endeavors. Perhaps when front offices can more effectively operationalize the obscurity that is defense, we will see new small market teams rise to power through Beane-like market analysis.