from Amazon
Friday, October 28, 2011
Make the sure out at first, or try for a play at home?
Here’s the situation. It’s the bottom of the 10th, the defense is up by 2 runs, there’s runners on 2B, 3B, and there’s 1 out.
There’s a GB to third base, and a decent chance for a play at the plate, or a sure out to first base. What do you do?
You need to know the chance of winning in those situations. Let’s start off with the win probability before the ball is put in play (and average batters following, which is NOT the case anyway, with Pujols and Berkman due up): Markov says .301 chance for the home team. You don’t really need to know this, but it just sets it up for you.
You get the sure out, let the runner on third score, and now you have a runner on 3B, up by 1, and 2 outs. Home team has a .172 chance of winning.
If instead you go home, you have these two outcomes:
everyone is safe: up by 1, ONE out, runners on the corners, chance of home team winning is .478
runner out at the plate: up by 2, two outs, runners on the corners, home team is .107
So, that’s the choice facing Beltre: go for the sure out for a .172 chance of losing the game, against try for home, and get into either a .478 chance of losing if he doesn’t make the play (.306 change in win probability) or get into a .107 chance of losing if he does (.065 change in win probability).
The breakeven point is 82%. He has to make the out at home 82% of the time in order for that play to breakeven. If he thinks he can make that play 90% of the time (chance of losing for Rangers goes down to .144), then he should go home. If he thinks he can make that play 75% of the time (chance of losing goes up to .200), then he should get the sure out at first. If it’s somewhere in-between, then it’s pretty much a gray area.
Things get more complicated with Pujols on deck. Going for the sure out at 1B allows Pujols to be placed at first base. According to page 306 of The Book, with the defense up by 1 in the bottom of the last inning, and runner on 2B and 2 outs, the defense BENEFITS by walking the batter, if his true talent wOBA is 120% that of the guy on deck. In his last three years, Pujols has a .418 wOBA, while Berkman is at .380, or Pujols is 110% of the guy on deck. When you include the platoon disadvantage for Pujols, it becomes even more of a reason to not walk Pujols. But, let’s just say there’s enough uncertainty in our estimate of Pujols’ true talent and Berkman’s true talent in a Game 6 do-or-die situation that maybe Pujols was at least 120% the hitter that Berkman was, and so, it’s a net benefit to the defense for not wanting to face Pujols.
I’d love to hear Beltre’s (and Washington’s I suppose) reasoning in wanting to go to first on that play.