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Thursday, February 14, 2008
How to calculate Marcels, day-by-day
If you look at Pujols’ Marcels, his reliability (r) is .87. The league average PA that is added to all players is 1200 PA. This equation is true:
r = PA / (PA+1200)
Since we know r for Pujols, we solve for PA and we get 8031. That’s how we can infer Pujols’ weighted PA of 2005-2007. If you wanted to figure this out yourself, you take 5 times his PA in 2007, 4 times in 2006, and 3 times in 2005. You’ll get a number very close to 8031. (It should be exact, except for rounding.)
Instead of using weights of 5/4/3 (and 1200 PA for league average), let’s divide everything by 5, so we have weights of 1/0.8/0.6 (and 240 PA for league average). Instead of 8031 being Pujols’ weighted PA of his last 3 years, it’s now 1606.
His Marcel wOBA for 2008 is .421, and is based on 1606 of his PA and 240 of league average PA for a total of 1846 PA.
Now, all we have to do is, game-by-game, include his 2008 performance to these 1846 PA. If you remember, the weight is:
weight = .9994^daysAgo
In this case,
daysAgo = July 1, 2007 minus gameDate
So, a game played on Jul 1, 2008 will be weighted at 1.25. A game played on Apr 1, 2008 will be weighted at 1.18. A game played on Oct 1, 2008 will be weighted at 1.31.
That’s pretty much the process you can follow to get a running day-by-day Marcel. It won’t be exactly right, but it’ll be close enough.