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06-12-2009, 06:53 PM   #71
pahster
Something clever

Join Date: Feb 2005
Location: Columbia, MO
Posts: 1,902
Re: Willy Taveras or Chris Dickerson in CF?

Quote:
 Originally Posted by RedsManRick Say you're rolling a die and you've gone 30 throws without throwing a 6. You know that since there's a 1/6 chance of throwing a 6 on any given roll. Thus, in that time period you expected to have seen 5 6's, on average. So you surmise that you're "due" and expect a run of 6's sometime in the near future to "balance things out"... right? This is called the gambler's fallacy. Probability simply doesn't work that way. In reality, what's likely to happen is that from this point forward, you'll see 1/6 of your rolls showing up as 6's. So, if Willy Taveras is truly a .330 OBP hitter, we would expect him to put up a .330 OBP moving forward, regardless of what he's done in the last few weeks. "Due" is true, but only to the extent that we should expect a player to perform as his true level of ability moving forward rather than to continue to slump. There should be no expectation of a hot streak to balance things out. The mistake is made because we forget our assumptions. The most likely result of future events is based on the player's skill level. The player's skill level doesn't change because of what he did yesterday, or last month. Taveras won't be a better hitter tomorrow because he struggled yesterday. So if we want to know what is likely to happen moving forward, if he's the same player he was on April 1st, we expect a .330 OBP moving forward. If want to know what to expect by the end of year, we simply take the sample we've observed and add it to our best guess about what's likely to happen moving forward. So, given that we know that his OBP through 218 PA is .294, and we would predict a .330 OBP over the remainder of his PA (say 350), we would expect his final OBP to be around .316.
You deserve 10,000 imaginary probabilistic rep points for this post.