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Wednesday, February 17, 2010
Sending the runner home from 3B
Pizza Cutter has an article at ESPN and BPro, and, I wonder if he made a faux pas:
Without going into all the algebra, it says Perlozzo needs to be 73.2 percent sure that Rollins will make it before he sends him. So, if third-base coaches leaguewide are playing the game correctly, we should see that about 73 percent of the runners in this situation wind up scoring.
No, that is incorrect if “this situation” is man on 3B and less than 2 outs. The MINIMUM success rate has to be 73.2%, meaning that if the third base coach is 73.2% to 100% sure of making it, then you send him. So, the average will be more than 73.2%. How much more? Well, there are tons of gimmes here. Let’s say that one-fourth of the time you have a gimme (say 96-100% success rate), one-fourth of the time you have a great chance of scoring (say 83-87% success rate), one-fourth of the time are the borderline plays (say 70-76.4% success), and one-fourth you have a less than 50/50 chance (say 0-50% success rate).
So, if this is true, then this is what happens:
98% success x 25% frequency x 100% attempt
85% success x 25% frequency x 100% attempt
73.2% success x 25% frequency x 50% attempt
25% success x 25% frequency x 0% attempt
The average is 87.8% for this illustration. For that third case, you can argue that you should run 0% or 100% of the time, and it won’t matter because it’s so close that it’s borderline. And therefore, the success rate if you never run on the borderline plays will now become 91.5%, and if you always run on the borderline plays, it’s 85.4%. That is, under this illustration, your run expectancy is maximized when your overall success rate is anywhere from 85.4% to 91.5%.
On the other hand, if he means “this situation” that includes the distance of flyball and speed of runner, such that these parameters would lead to a 73.2% success rate for these subset of plays (my third line in the 4-line illustration), then okay. That’s not how I read the line the first time, which is all well, because it gave me a chance to make the point. Re-reading it, I guess Pizza could have meant it the right way.
The rest of the article doesn’t go back to Pizza’s quoted line above, and is an otherwise good piece of trying to show that the thirdbase coach is too conservative. The knockout is this line:
Here’s an interesting one: What would happen if third-base coaches just sent everyone, playground-style, on these potential sac flies, regardless of whether it was a good idea? It turns out that teams probably would score more runs than they do now.
Indeed, it was rare that it was a bad idea to send the runner, even after controlling for the distance of the fly ball and the speed of the runner. It was almost always the case that the chances of the runner succeeding were above the break-even point.
The article audience doesn’t lend itself to Pizza presenting his evidence here. Maybe he’ll show it to us, though I have a vague recollection that we talked about this when he was at statspeak.