Wednesday, August 21, 2013
Leverage Index by Inning
Pizza provides some empirical-based results on what Leverage Index looks like, if you base it on half-inning by half-inning, rather than PA by PA.
As an example, the PA by PA approach for top of the 9th, tied game, the LI is 2.4. For the half-inning approach, the LI is 2.05. If up by 1, the PA-by-PA LI is 2.9, while by the half-inning approach, it's 2.35. And up by 2, it's 1.6 in either case. It's likely that the ordinal rankings remain the same, but the magnitude changes.
Indeed, in The Book, I focused on the approach that Pizza wrote about, since he is correct that in the case of relievers (at least in the situations we care about), it's more of a case of "to the end of the inning", rather than a single batter.
Anyway, there are multiple approaches to solving multiple problems, and Pizza gives us a good set of charts to work with. I'd like to see him generate a set of tables similar to what I did here, but just at the half-inning level.
But, I suppose we (read: enterprusing Straight Arrow reader) can come up with a reasonable simply by using this chart, and applying the Tango Distribution to it.
Note to Pizza: your chart has two rows for "Top of 9th, up by 2". I didn't verify the others.
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