February 3, 2010

Hot Stove U.

Maximizing Stolen Base Profits

by Tommy Bennett

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The Setup

Last year, Chase Utley stole 23 bases. That is a good number. In fact, it was a career high for the Philadelphia Phillies' All-Star second baseman. Even more remarkable was that Utley was not caught stealing once all season. A perfect season on the basepaths is a rare accomplishment, but it practically begs the question: "Why didn't Utley try to steal more bases?"

The Proof

The explanation consists of two interlocking parts: First, Utley caught some breaks, and second, he was demonstrating one of the basic truths of corporate economics.

Why would I try to take away from Utley's tremendous success by claiming he was lucky on the basepaths? And how, exactly, is luck involved with a feat that is so obviously related to pure physical skills like speed and instinct?

First, let's consult history. Since caught stealing statistics were first consistently recorded in the National League in 1951, there have been three major leaguers who have stolen at least 20 bases in a season without being caught once. Kevin McReynolds did it in 1988 with the New York Mets, and Paul Molitor matched the feat in 1994 with the Toronto Blue Jays.

Molitor was a consistently successful base stealer, and followed his 20-for-20 performance by going 12-for-12 in 1995. McReynolds, on the other hand, followed his 21-for-21 season with a pedestrian 15-for-22 one. If this limited history is a guide, Utley has, at best, an even-odds chance of another perfect season on the base paths in 2010.

Even that rough calculation overstates the case. Rather, it is much more likely that Utley's true base stealing talent is closer to his career success rate of 88 percent, which is, of course, still excellent. Maintaining perfection is terribly difficult, and it's more likely than not that some catcher will throw Utley out this year. The sheer rarity of the feat makes it nearly unrealizable twice in a row.

But let's assume Utley can expect to be successful between 85-90 percent of the time. Shouldn't he still steal more bases? While fans and fantasy players might appreciate the extra attempts, it's not clear doing so would help the Phillies win more games.

Imagine the easiest base-stealing opportunity Utley faces all season. He's got a right-hander on the mound. The pitcher has a slow, deliberate move toward first base. The catcher has a noodle arm. The dirt is packed just right to give Utley the best possible grip in his cleats. Under these circumstances, Utley is very likely to be successful, so he should absolutely steal. Now imagine the second-easiest situation, and the third. He should still attempt to steal, right? The question we want to answer is how unfavorable the circumstances have to get before Utley should stay put.

Introductory economics textbooks usually contain a case study that helps students differentiate between thinking in terms of average costs and benefits and thinking in terms of marginal costs and benefits. Using marginal thinking, the textbook invariably explains, is what helped, for example, Continental Airlines increase its profits during the 1960s. Utley, as well as his wise and experienced first base coach, Davey Lopes, is more like Continental than you might think.

The theory Continental applied was one of the first maxims of profit maximization. They realized that if they had empty seats on their planes, it would cost them very little to fill: essentially just the cost of the extra gas to accommodate the extra weight. As long as the marginal revenue they earned from selling another ticket exceeded the extra costs of carrying another passenger, they should sell more tickets. In economic jargon, firms should supply their product until the costs of making one more unit exceed the amount they can sell it for, the revenue they earn.

The Conclusion

By analogy, Utley should attempt to steal bases until the extra chance of winning is outweighed by the decreased chance of winning in the event he is caught. If Utley attempted to steal in any situation with a less favorable chance of success, he would be hurting his team because the marginal costs would outweigh the marginal benefits.

That exact break-even point is going to depend on variables that change from game to game and inning to inning. But let's assume that Utley, a smart base runner with a great first base coach, has found that point. Because each situation easier than the point at which Utley should stay put was by definition easier, Utley's average success rate would be quite high, much higher than the 70 percent success rate needed to break even. If he were to keep attempting stolen bases until his average season total matched the 70 percent point, he'd have been stealing in situations where he was hurting his team's chances of winning.

If the Phillies, Lopes, and manager Charlie Manuel consider analysis at the margins, Utley might not run more at all next season. And there is ample evidence that the Phillies do understand this analysis. Last year, the Phillies had four players steal at least 20 bases, and none of them was less than 75 percent successful. During Lopes' first season in Philadelphia in 2007, the team set the record for stolen base percentage at 87.9. In each of the subsequent years, the Phillies have led the league in the category. With Utley and Lopes, the perfect is not necessarily the enemy of the good.

A version of this story originally appeared on ESPN Insider .