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Monday, July 17, 2006
The Book at the All-Star Game
Scott Soshnick at Bloomberg looks into The Book
Let’s see what he says, and what should have been done.
Carlos Beltran, in the bottom of the 3rd, with the two outs, and tie game, is on second base. He tries for third base. Their chance of winning with him on second base is .537. If he gets to third base, it’s .542. If he goes home on an error, it’s .628. If he’s out, it’s .500
So, let’s work it out. Let’s say that when Beltran is safe, he makes it to third base 90% of the time, and 10% of the time, he’ll score on a wild throw. In that case, if he’s safe, his team’s chance of winning is .542 * .90 + .628 * .10 = .551. If he’s out, it’s .500.
So, on a safe play, he goes from .537 to .551, or +.014 wins. If he’s out, that’s .537 to .500, or minus .037 wins. The breakeven point is 73%. That is, 73% of +.014 is equal to 27% of -.037. So, The Book says “Way to go, Beltran!”.
However, are we being too optimistic about the chance for errors? In this specific case of Beltran, Halladay, curve balls, non-Jay catcher? 10% may seem right. If you think it’s something lower like only a 5% chance of something bad going to happen, then the breakeven point shoots up all the way to 80%. That makes it a tougher play to accept. But Beltran is 12/15 this year (80%) and 221/253 (87%) for his career.
The Book would say: if you are one of the greatest percentage stealers of your time, go for it. Beltran fits the bill.
Now, the other play that Soshnick talks about is With his team leading 2-1 in the top of the ninth inning Hoffman, of the San Diego Padres, had two outs and nobody on.
The chance of the home team (NL) winning here is .961. A single brings this down to .918, a double brings it down to .884, and a triple to .869. An out means that the NL wins (1.000). What to do?
Let’s say that, when you cover the hole, that in 660 plate appearances, you get 110 singles, 30 doubles, and 3 triples (and 440 outs). But, if you guard the line, let’s make that 130 singles, 18 doubles, 1 triples (and 434 outs). That is, you give up more singles, get fewer outs, but much fewer extrabase hits. What happens?
So, .918 x 110 + .884 x 30 + .869 x 3 + 1.000 x 440 = 570 wins.
And, .918 x 130 + .884 x 18 + .869 x 1 + 1.000 x 434 = 570 wins.
(Note that in both cases, since the HR and walks would cancel out, they are not included in the calculation.)
A wash. Whether you play to cover the line or not, the overall result is the same. So, you take your chances either way.
Of course, if you think that guarding the line produces numbers different than what I have (not 18 double, but say 8 doubles, or not 130 singles, but 160 singles, etc, etc), then that’s something you have to work out, with just a little bit of research.
Scott is right that the manager should throw out the old book. The Book may say something else.