## Quickie: Ryan Howard’s Choke IndexOctober 25, 2010

Posted by tomflesher in Baseball.
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The Choke Index is alive and well.

Previous to 2010, Ryan Howard of the Philadelphia Phillies hit home runs in three consecutive postseasons. He managed 7 in his 140 plate appearances, averaging out to .05 home runs per plate appearance. Not too shabby. It’s a bit below his regular season rate of about .067, but there are a bunch of things that could account for that.

This year, Ryan made 38 plate appearances and hit a grand total of 0 home runs in the postseason. What’s the likelihood of that happening? I use the Choke Index (one minus the probability of hitting 0 home runs in a given number of plate appearances) to measure that. As always, the closer a player gets to 1, the more unlikely his homer-free streak is.

The binomial probability can be calculated using the formula

$f(k;n,p) = \Pr(K = k) = {n\choose k}p^k(1-p)^{n-k}$

Or, since we’re looking for the probability of an event NOT occurring,

$(1-p)^k$

or $.95^{38}= .142$

using his career postseason numbers. That means that Ryan Howard’s 2010 postseason Choke Index is .858. Pretty impressive!