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Friday, March 13, 2009
Sample v True Talent
Boy, we’ve been giving Dewan a big platform these last two weeks! Here’s another. The writer, Geoff Baker (used to write for the Montreal Gazette) asked Dewan that since Dewan believes the Mariners upgraded their fielding by +2 wins, then…
Q: Could you qualify that? Does that mean that if they won 62 games last year, they’re going to win 64 this year? Dewan: “Yes. Yes.”
No. No.
No!
If you “show” you win 62 games in one season, this does not mean that you are a 62-win team. That is not the baseline you are working from. The actual baseline you are working from is whatever your talent base happens to be. And what that talent base did in their previous 162 games, as captured by the win-loss record, is not the true baseline. What that talent base did in their previous 162 games, as captured by OBP, SLG, PA, UZR, ERA, FIP, and alot of other component metrics is alot closer to the true baseline. And even then, it’s still not the true baseline.
Performance metrics are nothing more than samples. Just like when you run an experiment and you record what you see is just a sample of what the thing actually is. 162 games may sound like alot of trials, but it is not. And the reason that it is not is because all the teams are so close in talent anyway. If you have 30 coins, and each of them is weighted so that it will land heads a specific percentage of time, from a low of 45% to a high of 55%, do you really think that if you pick out one coin, and it lands on heads 40% of the time after 160 trials, that this means that the coin actually lands 40% of the time? Seeing that I’ve established that the minimum is 45% of the time (that’s your prior) then it becomes a simple Bayes problem to figure out the best estimate as to which of those 30 coins you’ve been flipping. There’s even a chance that you’ve been flipping the 55% coin!
So, no, no way, does it mean that if the Mariners stood pat that they’d win the same number of games, and no way does it mean that if the Mariners adds 2 wins in talent that they’d win 2 more games. That’s not how it works.
I don’t know if that quote captures the discussion between Geoff and John, and it’s not important for my purposes. What is important is that the answer quoted to the question quoted is 100% wrong.
(Hat tip: USSM)
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