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The Strike Zone and the Probability Density Function

A little over a decade ago, I did play-by-play announcing for the AA London Tigers, a London, Ontario, affiliate of the Detroit Tigers. One night, during a lengthy rain delay (and we had stopped broadcasting from the ballpark), we had one of the umpires up in the press box telling us war stories -- the usual macho stuff.

At one point I asked him about pitches over the black part of the plate -- how difficult is it to tell when a pitch is just over the black and when it is just off the black?

He angrily grabbed a piece paper. He put the paper on the counter and slammed an empty Coke can on the edge of the paper. Then he picked up another empty Coke can and slammed it down just off the edge of the paper. He glared at me [and here I'll use the standard Lenny Bruce substitution]:

You show me a guy who tell those two apart and I'll "blah" his "blah"!

When we resumed our broadcast, I decided not to relate that story on-air.

Instead, I launched into a monologue about how pitches in the middle of the strike zone are almost certain to be called strikes, how pitches near edge of the strike zone are much less likely to be called strikes, and how pitches outside the strike zone still have some probability of being called strikes.

I then looked at my co-broadcaster and said,

So you see, Joe, the strike zone is little bit like a probability density function. The probability that a pitch will be called a strike depends on where it is. When it is on the edge of the strike zone, we don't know for sure whether it is in or out of the strike zone, and the less certain an umpire is that the pitch is in the strike zone, the less likely that pitch will be called a strike.

It was this umpire's bold statement about how difficult it is to call balls and strikes that played a part in my earlier argument that we should use computer triangulation to call balls and strikes.

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