At Homeplate - The Steal & the Bunt

The Steal & the Bunt

By Bjoern Hartig

Friday, 18 May 2007

I do not know what someone who has been living baseball his or her whole life is thinking about when I speak of “THE STEAL”, but for someone like me, who has been watching American baseball for only four years now (thanks to the wonders of the internet), it can only mean Dave Roberts' steal against the Yankees in game four of the 2004 ALCS.

For those two readers that do not remember it, here is a quick recap:

Trailing New York 3-4 in the bottom of the ninth with Mariano Rivera on the mound, Kevin Millar drew a lead-off walk and was replaced by pinch-runner Dave Roberts. When everyone knew he was going and after a very close pick-off play, Roberts then stole second and scored on Bill Mueller's RBI single to tie the game. The Red Sox later won the game in the 12th inning on David Ortiz' two-run home run.

Sending Roberts was a gutsy move by Boston manager Terry Francona and it paid off big time. Obviously, Francona felt confident that Roberts would be able to successfully steal second. But just exactly how confident was he?

Before trying to answer that, I would like to say a few words on decision theory. (Prescriptive) decision theory tries to provide means to make rational and practical decisions, for example in gambling situations. Now every manager's decision is essentially a gamble and while not every gamble pays off, some are more sensible than others, regardless of the final outcome. If, let’s say, Cleveland's manager Eric Wedge in a bases loaded, two out situation in the ninth inning of a tie game with a southpaw on the mound would pinch hit for Trot Nixon (career .649 OPS vs. LHB) with Jason Michaels (career .851 OPS vs. LHB), this was the right decision even if Michaels made an out. On the other hand, if Joe Torre let Mike Myers (career .865 OPSA vs. RHB) pitch against Manny Ramirez in a crucial situation, it was a mistake no matter who else is still available in the pen.

Those kinds of situations are rather easily assessable, because we can compare two options by looking at two numbers and take the better one. We can make it a little more subtle by including pitcher vs. batter data, considering sample size and so on, but it is still pretty much a straightforward decision. Things get a little more interesting when we look at decisions like “to bunt or not to bunt” or “to steal or not to steal“. I'm not talking about giving outs away early in the game, but rather late inning game deciding plays. So let’s get back to Dave Roberts' stolen base and analyze the situation a little more closely. Or maybe not just yet.

Before we start, allow me a few words on risk preferences. If someone weights a gamble only by its expected outcome, he is considered risk neutral. For example, a risk neutral person is going to accept a coin-toss game when he wins $1000 on heads and loses $999 on tails. Most people (including me) however, would not accept such a gamble because they are risk averse. They prefer a secure payoff over a lottery with equal outcome and are willing to pay a risk premium to avoid taking risks, e.g., in the example above, you would pay a risk premium of 50 cents (the expected outcome of the gamble) to avoid the risk. The third risk preference is risk lovingness, which means that you are willing to take risks just for the kicks even if the gamble nets an expected loss. Most people only display such a behavior if the losses are small compared to their wealth.

You often hear that one manager is not afraid to take risks or while another likes to play it safe, but which risk preference is the preferred one in a baseball manager? Since a season is 162 games long, luck and bad luck are supposed to cancel out in the long run. That is not entirely true because 162 is still a bit small for the law of large numbers to kick in, but it is a good approximation. Therefore, risk aversion is not a desirable trait for a major league manager, because, in the long run, being overly cautious will cost the team. By playing it safe, for example, by always sacrificing runners over, the team will have less no-run-innings than their competitors, but also less big innings and overall less total runs in the long run (i.e. the manager pays for the lower risk with a premium in form of total runs). On the other hand, while you often hear that a good manager sometimes has to be willing to take risks, that does not mean he should be risk-loving, because that would mean he might pinch hit with Neifi Perez just for the kicks of it and that will also cost the team in the long run, obviously. The best managers (just like the best asset managers by the way) are risk-neutral, i.e. they choose the strategy with the highest expected outcome to maximize the expected production of their team in the long run.

To evaluate a game situation, I decided to rate it by its win-probability according to Tangotiger's Win Expectancy List, because the W is the most important statistic in baseball at the end of the day (and the season). This method is obviously flawed since it does not take into account the quality of the upcoming hitters or the pitcher on the mound, but it is the best I can think of that does not require (really) complex calculations. Ok, I think we are ready to get back to Dave Roberts' steal now. Thanks to Millar's walk, the Red Sox have a runner on first with no outs and they are one behind in the ninth. Their win expectancy stands at 33.1% (Millar's walk was worth +13.7%, by the way) now. If pinch runner Roberts stays at first base, the win expectancy does not change, obviously, so 33.1% is the secure payoff that Francona gets if he does nothing. If he sends Roberts, there are two possible outcomes: Runner on second and no outs or no runners on and one out. For the sake of simplicity, we ignore the possibility of a throwing error by the catcher or any other freak play. A successful steal raises the WP to 43.7% (+10.6%), while a caught stealing lowers it to 10.8% (-22.3%).

Are you still with me?

Let’s call the probability of a successful steal attempt P, and then we can calculate the P that makes the expected outcome of the steal attempt at least as good as the decision not to steal. Or mathematically: P * 0.437 + (1-P) * (0.108) = 0.331
P is only 67.8% (please check that yourself), which means that if Francona thought that Roberts' chances to be successful were at least 67.8%, sending him was the right decision. Now, at that point in his career, Roberts had been successful in 80.8% of his attempts and just came off a 38/41 (92.7%) 2004 season. So all other things considered (Posada's arm, the probability of a pitch-out etc.) Terry Francona's decision does not appear overly risky or gutsy, but rather sound and very sensible.

Ok, here is a second, less spectacular case: A few weeks ago, Angels' infielder Erick Aybar made the news by twice making the last out of a game trying to steal second (something that Babe Ruth himself has done, in game seven of the 1926 World Series no less). Interestingly though, we have a comment from Angels manager Mike Scioscia about the situation in one of those games:

“With that combination -- the time we had for the pitcher [coming to the plate] and throwing time [for the catcher] -- I thought we had a better than 75 percent chance of making it, “ … “Erick got a decent jump. It took a perfect throw to get him -- and they got it. If it was a 50-50 proposition, obviously we're not going to do it.”

It is debatable whether Aybar, a 64% base stealer in the minors in 2006, really had a better than 75% percent chance of making it, but let’s just assume that is correct. Was Scioscia’s decision the right one? In that game, the Angels were one run behind and at home.

What would you have done?

Have you made your choice? Good, then let the calculations begin:
One run down and with two outs, the Angels WE stood at 9.3% and would have risen to 14.3% with a successful steal, while a caught stealing would have immediately lost the game.
    P * 0.143 + (1-P) * 0 = 0.093
The break even point is at 65%, which means that Scioscia’s reasoning was indeed pretty sensible and sending Aybar the right decision, even if the outcome was not the desired one.

I find it interesting that sending a good base stealer in late and close situations is something we do not see that often, at least when compared to sacrificing runners over, even though it appears as if sending a runner with a solid success rate leads to a positive outcome on average. Managers seem to go to the bunt much more often. So I wondered if bunting gives higher expected outcomes and so I analyzed three situations to check this. To make it a bit more entertaining, I will first put you in the dugout:

Situations:
1. Your team plays at home and the game is tied in the bottom of the ninth inning. Your lead-off man has just doubled and you have to decide whether to bunt him over to third or not. You have a pretty good bunter at the plate, who gets 90% of his bunts down successfully. For the sake of simplicity, let’s say there are only two possible outcomes of a bunt attempt: Runner on third with one down or runner on first with one down. What do you do intuitively?

2. Your team again plays at home and you are one run behind in the bottom of the ninth. However, a single and a walk have put runners on first and second with no outs. Again, the same player is at-bat. Do you bunt the two runners over when an unsuccessful bunt erases the lead runner?

3. For a change, your team plays away and bats in the eight inning of a tie game. Your lead-off man has drawn a walk and you have to decide whether to bunt him over to second or not. An unsuccessful bunt erases the lead runner.

Solutions:
1. The WP on the initial situation is 80.7%. With a man on third and one out, it increases to 83.0 %, while an unsuccessful bunt reduces it to 63.7%.
    0.830 * 0.9 + 0.637 * 0.1 = 0.81 ≈ 0.807
In this case, bunting is the right decision, but only narrowly so. The out has about the same value as the additional scoring possibilities of a passed ball, a sacrifice fly and so on.

2. Trailing by a run with two men on first and second in the ninth with no outs, the home team's WP stands at 51.7%. Bunting them over increases it to 54.0%, while giving up the outs for nothing brings it down rather dramatically to 33.7%.
    0.54 * 0.9 + 0.337 * 0.1 = 0.519 ≈ 0.517
Again, bunting the runner over is not really helping much, the WP only increases marginally.

3. The lead-off walk gives your team a win expectancy of 57.2 %. It decreases to 55.0% with a runner on second and one out. In other words, it is never a good idea to bunt in this situation.

I find it very interesting, that bunts have to be executed with a very high success rate to actually help your team, while steals are usually more worthy gambles if you have someone with speed on first base. However, it also shows that really good bunters (i.e. the ones that hardly ever miss execute a sacrifice) do indeed help a team and that good fundamentals and doing the small things can have a significant value to a ball club. Also, and I have to admit the evidence is not exactly overwhelming and I should look into that more closely, it appears that bunting makes only sense in absolutely crucial situations in the last inning, but not earlier in the game because your outs are just too valuable.
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