In which Nate provides a simpleish way of updating your expectations.
Binomial Distribution (or What the Heck is Up with Miguel Tejada and Alex Gonzalez?)
May 7, 2003
Abstract: A month into the season, Nate tries to fashion a sort of PECOTA update using binomial distributions. Basic premise: If PECOTA thinks Miguel Tejada is a .270 hitter, but he’s hitting .370, and binomial distribution estimates a very low likelihood that a .270 hitter could hit .370 over a month, then it’s very unlikely that Tejada is a .270 hitter, after all. If I correctly understand what he was doing, he basically charted two probability lines, like this,
and where the two lines met he declared a new truth existed.
Key quote: “Ichiro has the capacity to change his approach, but seems uninterested in doing so; as he continues to age, his slap-hitting ways will seem ever more gradually out of place, until one day he's Larry Eustachy at a sorority party.”
Results: Nate gave 12 “corrected” projections. Imagine that all 12 players were projected to hit .270, but the new projections said they’d hit .280, and all 12 had hit below .270. We’d fairly conclude that the binomial distribution patch was overestimating players’ new developments. If they all hit over .280, we’d conclude that PECOTA was overweighting the past, or was overweighted in Nate’s new math. In fact, though: According to Clay Davenport’s historical EqAs, six of the projected hitters hit the under*, five hit the over, and one was spot on the new projection. The thing worked!
If you’re smart, you can probably use this, somehow.
*under, in this case, means the final result was closer to the previous projection than the new projection was. Because Nate looked at players who had hot starts and players who had cold starts, “under” might mean that the batter hitter better than his projections. Under=over, sometimes. Make sense?
Broken Links/Total Links: 3/5
On the Nate Silver Must-Read Scale: 1
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