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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 Insider.

Related Content:  Chase Utley

32 comments have been left for this article. (Click to hide comments)

BP Comment Quick Links

Richie

Understand what you're saying here, but I'm not sure many non-Economics majors will.

Also to be factored in is the wear-and-tear of base stealing. If you only go a couple of times a week (factoring in foul balls, balls hit in play, ball four), how much that amounts to, I don't know. But I'm sure it pushes the real break-even point up some.

Feb 03, 2010 10:12 AM
rating: 0
 
Peter Hood

The other aspect is that with a RHP on the mound the cost of being caught goes up significantly with Howard at the plate. I wonder how many of those SB attempts were made after Howard was retired?

Feb 03, 2010 10:56 AM
rating: 0
 
CRP13

In 451 PA vs RHP in 2009, Ryan Howard hit 39 HR, or 8.65% of the time.

In 138 times standing on base (H-2B-3B-HR+BB+HBP) while an RHP was on the mound in 2009, Chase Utley had 12 SB, or 8.70% of the time.

Eerie how even those two percentages are.

Given that Howard was at bat close to 100% of the time that Utley was standing on first at some point during the inning and that Utley was standing on first in roughly 30% of Howard's AB vs RHPs, (I wouldn't know where to find the data saying exactly who was hitting when Utley actually succeeded in stealing) I would postulate ($5 word?) that Utley's success rate at SB goes up when Howard is at bat vs RHPs. Especially because neither Jayson Werth nor Raul Ibanez hit RHP as well as they do LHP (despite their HR splits, which is weird), and certainly neither hit RHP as well as Howard.

If true, then the "cost" of being caught in that situation would likely be offset or marginalized by the increased likelihood that Utley will be successful stealing.

Feb 03, 2010 12:18 PM
rating: 0
 
CRP13

That's discounting, of course, Utley Stealing 3rd or Home, which I have no idea if he did when Howard was at bat. Irrelevant to my logic I think, but it does screw with the numbers.

Feb 03, 2010 12:19 PM
rating: 0
 
mtofias

If only there was a systematic way to study strategic interaction. I bet we could use such analyses to ditch Econ 101 and build a whole theory of games.

Feb 03, 2010 11:19 AM
rating: 2
 
ddrezner

Some discussion of the marginal benefit of stealing might have been worth including -- particularly if/when it leads to an IBB.

Feb 03, 2010 11:24 AM
rating: 0
 
mtofias

What? No Robinson Crusoe fallacy citation?

Feb 03, 2010 14:03 PM
rating: 0
 
Tommy Bennett

This is worth noting. Certainly the marginal benefit is not static, and depends not only on the possibility of an IBB but also on the count, inning, number of outs, handedness of the batter, shape of batter's offensive production, location of other base runners (especially on third base) and fielding ability of the fielder who will field a throw from the catcher.

Feb 03, 2010 14:50 PM
rating: 0
 
mtofias

Now all you need to do is renounce the decision theory, admit the mixed-strategy equilibrium, and then we'll be cool.

Feb 03, 2010 15:31 PM
rating: 0
 
Tommy Bennett

I'm not sure the two aren't reconcilable in this context (as you seem to be alluding with the invocation of the Crusoe fallacy). Consider that, even if the relevant costs and benefits are situation-specific and depend on the choices of the rational opponent, it is still possible to rank all possible stolen base opportunities by perceived likelihood of success (weighted by the payoffs and costs).

As long as that is the case, we can still identify a threshold beyond which it would be inadvisable to steal. Individual actors may be mistaken in identifying where the threshold is located, and in cases near the threshold a mixed strategy will still be optimal, but the other team can only do so much to deter base running and in most cases their attempts to do so are patent (pitcher repeatedly throwing over, predominantly fastball pitch selection, etc.).

Feb 03, 2010 15:48 PM
rating: 0
 
mtofias

Okay, I'll be more charitable. The stealing game, if you will, only has a mixed strategy equilibrium, but the runner has a prior choice to the stealing game, he gets to choose whether that game will be played at all. Therefore, the rational runner is only going to play that game if the expected value of entering into the stealing game is higher than the value of waiting to be advanced. That's the end of the marginal analysis.

But if you buy that setup, the runner's mixed strategy is based only on the payoffs of the defensive team, not his own team's marginal benefit. And more importantly, the resulting interactions that we get to witness may produce any pattern including Utley's 23-0 performance (however unlikely). If you buy this though, it's crucial to note that Utley played the stealing game more than 23 times. Sometimes by strategic chance he didn't attempt to steal.

I have to assume that someone (perhaps in the Journal of Sports Economics?) has produced a more thorough treatment of this game. What I really object to is the idea that a 100% success rate demonstrates that Utley and the Phillies left something on the table or that a 70% rate demonstrates a well-optimized team because it simply doesn't.

Feb 03, 2010 16:40 PM
rating: -1
 
Tommy Bennett

"What I really object to is the idea that a 100% success rate demonstrates that Utley and the Phillies left something on the table or that a 70% rate demonstrates a well-optimized team because it simply doesn't."

I'm not sure if I was unclear or if you misread the article, but exactly the opposite of the claim you ascribe to me is the thesis of this article.

Feb 03, 2010 17:44 PM
rating: 0
 
mtofias

I just re-read the article. I am an idiot for not seeing what you were trying to say, but you've got to throw me a bone with your key point buried in the last sentence of the second to last paragraph.

Feb 03, 2010 20:09 PM
rating: 0
 
taustin660

Yawn. Nice explanation of marginal utility, but you failed to apply it to Utley's specific case in anything but the vaguest of fashions.



Utley steals at 88 percent. How many more situations would he have to steal in to lower his rate to 70 percent? The author of the article does not know, and makes no attempt to determine the answer to this question.


If Utley attempted 40 steals a season instead of 23, what would his (typical) success rate be? 88%? 85%? 80%? 70%? His next marginal steal attempt would result in a success rate near his 88% maximum. If he kept stealing until his MOST UNFAVORABLE situation still yielded a 70% success rate, he would still (in general) be helping the Phillies' offense on every steal attempt, and his overall success rate would be somewhere between 70 and 88 percent. How many more times could he attempt to steal before he started hurting the Phillies? I don't know, but I'm pretty sure the answer is not "zero".



Utley could certainly try to steal more bases, and would be very likely to help the Phillies by doing so.


Feb 03, 2010 11:27 AM
rating: 2
 
Kampfer

Agreed. The author is assuming that Utley is stealing until the overall successful rate falls to 70%,instead of when the next steal attempt successful rate is 70%

Feb 03, 2010 11:41 AM
rating: 0
 
Tommy Bennett

I don't think this is a fair characterization. However, if you were given that impression, I apologize.

Feb 03, 2010 12:17 PM
rating: 0
 
CRP13

Wow. Way to miss the point. Just because he didn't come to the conclusion that you wanted to read, doesn't mean that he missed the conclusions that he wanted to reach.

Unnecessary and pointless criticism. He never even insinuated that the answer to "how many more times..." was "zero". Re-Read the Conclusions paragraph and beg/raise/provoke/prompt/stimulate for forgiveness.

Feb 03, 2010 14:40 PM
rating: 1
 
TGisriel

Wow. Marginal economic analysis in two articles on one day. Let's break out our economic textbooks!

Feb 03, 2010 12:38 PM
rating: 0
 
eighteen

Utley being perfect in SB attempts might "raise" the question of why he didn't try to steal more. It might even "prompt" or "provoke" or "stimulate" the question.

BUT IT DOES NOT BEG THE QUESTION.

Feb 03, 2010 12:53 PM
rating: 5
 
Tommy Bennett

You are correct. I regret the error.

Feb 03, 2010 12:57 PM
rating: 0
 
CRP13

Utley's Fantasy owners disagree with you.

Feb 03, 2010 13:00 PM
rating: 0
 
jtratz

Then Utley's fantasy owners don't know what "begs the question" means.

Feb 03, 2010 16:34 PM
rating: 3
 
TheRealNeal

Actually, language use defines the definition, not the reverse. If people are using the phrase "begs the question" to mean "can't help but make one think to ask the question", then that is what the phrase means.

Feb 03, 2010 19:20 PM
rating: 1
 
John Collins
(110)

Not really. That's too simplistic a thesis about how semantics works.

Feb 15, 2010 14:03 PM
rating: 0
 
BrewersTT

Unfortunately I don't think the section headed "The Proof" is proof of much. The question of whether Utley should attempt more steals is not settled, and in fact the conclusion begs off, saying that the answer would "depend on variables that change from game to game and inning to inning". That's true of everything sabermetricians study, but it doesn't mean that general truths can't be teased out of large enough datasets by well designed studies. Maybe someone will follow up on the tease title given to this piece.

Feb 03, 2010 13:43 PM
rating: 2
 
BrewersTT

Trying to remember - has anyone studied whether the opportunity for the first baseman to cover more field instead of holding a runner detracts significantly from the value of a successful steal? Thanks.

Feb 03, 2010 13:46 PM
rating: 2
 
kmbart

Context note: Utley was coming off of off-season hip surgery and I would expect that he and Lopes would have babied the hip earlier on, and with more confidence later in the season, perhaps run more frequently. Do the numbers back this up?

Feb 03, 2010 13:58 PM
rating: 1
 
deckholm

It would seem so

Utley stolen bases by month:

Apr: 2
May: 3
Jun: 2
Jul: 5
Aug: 4
Sep/Oct: 7

Utley was also 3-3 in stolen bases during the postseason.

Feb 04, 2010 13:59 PM
rating: 0
 
CRP13

"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. "

I love this line. It calls to mind a mental picture of Utley sitting in the on-deck circle with a calculator figuring the effect of SB or CS on the Phillies' chance of winning. Good writing.

Feb 03, 2010 14:44 PM
rating: 0
 
TheRealNeal

One key to a high success rate is never being put into a hit and run situation. When you're running ahead of wind farmers like the Howard and Ibanez there's probably not a lot of those being called.

Feb 03, 2010 19:28 PM
rating: 2
 
BillJohnson

Wow. An observation that actually has something to do with baseball. Thank you.

It is easy to forget that for the overwhelming majority of players, Utley included, the decision whether or not to steal in any particular situation is largely tactical, informed at a top level by strategy and long-term personal success rate, but dominated by the question of whether it will be beneficial THIS TIME. Factors like the contact rate of following hitters, who's on the mound and behind the plate (does anyone think that Utley's performance would have been 23/23 if he'd played more games with Yadier Molina's cannon behind the plate?), etc., must dominate the abstract analytical approach in practice. If Utley and Lopeshad guessed wrong even once, we wouldn't even be having this article and conversation -- but Utley would still be an excellent base stealer.

Feb 04, 2010 08:04 AM
rating: 0
 
prs130

"whether it will be beneficial THIS TIME" - quite true. He might have been 21/21 if he'd played more games against Yadier... As a Phillies fan, I start with the assumption that Utley is godlike and omniscient, and conclude that he just so happened to get precisely 23 opportunities to successfully steal a base last year, no more and no less.

Feb 04, 2010 11:54 AM
rating: 3
 
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