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Friday, June 10, 2011
How specific can we get in determining the true mean of a particular matchup?
Every matchup has a specific and true mean. God herself would establish that specific and true mean at that specific point in time-space with zero level of uncertainty. Pujols at Busch on July 3, 2011 against Doc and God knows that he can’t handle an outside cutter well, and the next pitch is going to be telegraphed by Doc as an outside cutter? God says that Pujols will contact that pitch 23% of the time (if allowed to replay in that time-space an infinite number of times) with 0 level of uncertainty.
But what about humans? If Pujols v Doc has an expected contact rate of 70% any time Pujols swings (with a certain level of uncertainty, say 10%), then how much a better mean estimate can we get in more specific situations (we find more data about Pujols and or Doc and or Busch and or the weather), and how much more can we reduce the uncertainty level?
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