When Is A Slump A Slump?

Good morning, Fackers. Yes, I just made a Geology picture "joke". Doc Nardacci would be so proud... Now get ready for some logarithms! WAKE UP!

Over at the Freakonomics blog at the NYT, they used some statistics to propose a more solid definition for what actually consititues a slump (or any streak with an absence of a certain event) using A-Rod as an example (h/t BBTF):

It occurred to me that it would be pretty easy to derive a statistical standard for determining when an athlete was having a “statistically significant slump.” For example, Alex Rodriguez recently went through a homerless drought of 72 at-bats. Over his career, A-Rod has averaged one homer for every 14.2 at bats — suggesting there is about a 93 percent chance that he will not homer on any individual at bat. It would be crazy to say that he was in a home-run slump after failing to homer after just a few at bats. But the question is how many homer-less at bats is enough to be a statistically significant drought?

The answer is 42. There is less than a 5 percent chance that Rodriguez would go homerless 42 times in a row — so we can reject the hypothesis (at a 5 percent level of statistical significance) that he is going homer-less merely as a matter of chance.

They are essentially drawing the line at a 95% confindence interval (2 standard deviations), but you can set your own parameters by altering the simple formula:

Total consecutive number of bad events > log(.05)/log(probability of single bad event)

It's a little more difficult because you have to play around with it to find the right number, but you can also figure out what the likelihood of A-Rod going on a 72 at bat homerless streak (beginning in his next at bat) would be. It's about one half of one percent.

Using this method, we can determining the (im)probability that Derek Jeter would go 113 plate appearances without working a walk like he did from July 28th to August 25th. In 9656 career PAs, Jeter has walked 863 times, giving him a walk rate about approximately 8.9%. This makes the odds of him going that long without a base on balls 0.0025% or 1 in 4,000.

Fun stuff, huh? No? Well at least it gives you a way, numerically, to prove that Tim McCarver is an idiot. You're welcome.