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Wednesday, June 23, 2010
The 7-inning pythag
Somebody asked me about creating a pythag for a 7-inning game. Here’s how you can do it.
First, let’s look at this data, which shows that the home team in the 1980s win 54.2% of their games. I don’t have their runs scored and runs allowed (per 27 outs), but we can work backwards to figure that out.
If we give the home team 4.6 runs per 27 outs and the road team 4.2 runs per 27 outs, and we put it through PythagenPat (4.6 plus 4.2, raised to .283), we get exactly .5420. (Note: the .283 could be anywhere from .28 to .29… I just used .283 because it made the numbers work out cleanly.)
Now, how about for a 7-inning game? That’s easy enough: start the game tied in the third inning! (*) The home win% is .528. To match that, we need to set the pythagenPat exponent from .283 to .096, if we keep the runs as per 27 outs, or to .109 if we make the runs as per 21 outs. If you want a general rule, just make the exponent .100; and it won’t matter much if you put the runs as per 21 or 27 outs.
(*) Yes, this changes the lineup order, since if we start the game in the third inning, we are not guaranteeing that Rickey Henderson will lead off every game. I agree. But, you look for easy reaonable solutions where you can get them, and that’s what I’m doing here. If someone wants to try it another way, feel free.
Interestingly enough, if you start the game in the 4th inning, or the 8th inning, tied, you end up with the same home win%. This obviously makes no sense. The reason is because of the strategies employed, and personnel available. Meaning, bullpen usage. That, and sample size.
We can look at far more years here (that chart shows the win% for the batting team, not home team). Numbers make a bit more sense.
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