Friday, October 20, 2006

How much of a shot did the Mets have when Beltran went to bat?

My general feeling - or WAG, if you prefer - when Beltran came to the plate last night was that if you polled the people watching the game, or at least the ones I was watching it with, would have given the Mets a 50-50 shot of winning at that moment. Meanwhile, I was quickly trying to estimate the Mets win probability given the run/out situation, the pitcher, and the batter at the plate and those following him. Yeah, yeah, I'm a loser, whatever. I didn't get very far by the time Beltran watched strike 3, but I decided to run the numbers briefly today. There are many ways to go about this, and to do it with a methodology I would consider proper would take a long time and probably devolve into me creating a new PBP defensive metric. So to maintain sanity, in the exercise, I made the following flawed assumptions:

-'Chemistry', 'clutchiness', and the like are non-factors; Beltran's history of killing the Cards in the playoffs is a non-issue.
-The true talent of the Mets' hitters is equivalent to a 3-4-5 weighted average of 2004-6 regular season numbers. No regression. No sample error. No postseason numbers.
-The weather and time of year were non-factors. I have done absolutely no research on these, or postseason performances in general.
-The difference between the Cardinals' 9th inning defense (i.e., pitching + fielding) is exactly equal to the home-field advantage adjustment. That is to say, a thorough version would have a projection for Wainwright, would factor in the Cardinals' fielding, and would factor in the Mets' home-field advantage. This was not thorough. Wainwright had a good year, and the Cardinals have a pretty good defense. That having been said, Edmonds and Rolen were banged up, and Wainwright wasn't that good at Memphis and only threw 75 innings in 2006, so I'm arbitrarily pretending that a regressed projection for Wainwright + StL defense would magically be the same as the performance necessary to negate the homefield advantage of Shea. Off the top of my head, I can't say whether this is generous or not.
-Because of home-field advantage, the Mets will win 54% of the time if the game goes to the 10th. This completely ignores the question of the relative strength of the players still in the game and on the bench, as well as who would be coming up next, etc. Maybe they should win more because Wagner's still available, I don't know. I'm just calling them even for short.
-The only exception to the above is that any reached-on-errors we would expect will somehow disappear and simply become outs.
-Any single in the bottom of the 9th scores the runner at 2b, any double clears the bases, and there are no baserunner outs, pickoffs, SB or CS. And the Mets don't bunt.
-No adjustment need be made for situational hitting or pitching (other than excluding the possibility of an IBB or SH). The base-out situation is not considered germane in calculating the likelihood of a single, double, out, walk, etc. Everybody's approach is exactly equal to the average of the contexts in which the hitters involved have hit in 2004-2006.
-Fatigue is irrelevant.

In other words, what are the Mets' odds of winning if we take their hitters' basic stats from the past three seasons and pretend they exactly match what our expectations should be?

So under those conditions, you'd expect Beltran to make an out and immediately end the game 64% of the time. You'd expect him to win it (i.e., 2B, 3B, or HR) 11% of the time. He'll tie it up (1B) 12% of the time, and keep the Mets alive with a BB/HBP 13% of the time.

Next up is Delgado, and in a tie game he'd win it 38% and send it to the 10th the other 62%. If Beltran merely gets the Mets to 3-2, Delgado wins it 23%, ties it 14%, and makes the third out 62%. If Delgado ties it, Wright wins it 38% of the time and sends it to 10 the other 62%. And yes, the 38% for Delgado and Wright are, of course, simply their OBP's.

So, weighted, that means the Mets win it in the 9th 19.4% of the time, lose in the 9th 71.9% of the time, and send it to 10 8.7% of the time. With a .54 win% in extra innings, that means the Mets have a total win probability of 24.1%. If you go for the bizarre seasonal epistemology that's so predominant in baseball (i.e., use only 2006 regular season numbers), you can bump the Mets chances up to 25.0%. In any event, while the vast majority seemed surprised that it ended with a strikeout, that's nearly as likely an event as any, all things considered. Beltran and Wainwright both gets plenty of K's, and Beltran strikes out more often than he singles and more often than he walks. Beltran ending the game with a strikeout would have to be considered more likely than Beltran ending the game with an extra-base hit. A batted ball out would be a more likely event, but the chances of the Mets winning at all weren't much higher than the chances Beltran would strike out, at least if you assume a number of things that are likely but may not be accurate.

And if you think I only posted this so I could list the flawed assumptions that went into building such a model, you know my writing well.


At 6:10 PM, Blogger Studes said...

Only thing I might add is that a BB or HBP seems less likely in this situation. That would boost the odds of all the other events, I would think.

At 8:31 AM, Blogger benaiah said...

I would like to add that why don't you write more often since this type of stat heavy writing is not all that common on the web. You are too talented a writer to go on long vacations from blogging (because when you are gone no one really takes your place). If you were only a little more mediocre then you could do whatever you wanted. With great understanding of correlation comes great responsibility to post statistics on the internet.


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