Still random after all these years?

When Philip Humber of the Chicago White Sox pitched a perfect game against the Seattle Mariners back in April, I wrote that the frequency of these exceedingly rare feats had ramped up dramatically over the last three decades.

Mathematicians argued that speedup was more apparent than real, a classic example of a Poisson distribution. This is the natural tendency for exceptionally rare but random events to bunch up in ways that appear non-random.

Humber’s flawless game was the 19th in modern baseball’s 112-year* history. Since April, there have been two more, including the 1-0 gem Félix Hernández of the Seattle Mariners pitched against the Tampa Bay Rays last night.

Here’s the latest chart:

True, there are more ballgames per year than there were 60 years ago—almost twice as many.

Still, from 1901 to 1960, there was only one perfect game every 15 years. From 1980 to Wednesday night, there was one every 2.36 years.

Random or not, there’s one thing I’m sure Félix Hernández can agree on:

Bayesian ball’s been bery bery good to me.

* Baseball is older than 112, but the rules were so different in the Nineteenth Century, most scholars date the modern era from 1900.

What’s up with all the perfect games lately?

Philip Humber of the Chicago White Sox pitched a perfect game against the Seattle Mariners yesterday. He faced only 27 batters, and got them all out. It’s an exceedingly rare feat—Humber’s was only the 19th in modern Major League Baseball history—but not as rare as it used to be. Or is it?

Click to view full-sized image.

(Click on the chart to view a full-sized version.)

In the first 60 years after the turn of the 20th Century, only four major-leaguers  managed to pitch perfect games; 15 have done it in the 62 years since. It sure looks as if pitching a perfect game got easier around 1980, but mathematicians argue that this is just an example of a Poisson distribution, which could be crudely stated as the tendency for rare events to appear non-random.

Writing in the Journal of Statistics Education, Michael Huber of Muhlenberg College and Andrew Glen of the United States Military Academy at West Point examined three other rare baseball feats: no-hitters; triple plays; and hitting for the cycle. None of these is nearly so unusual as a perfect game, but all three:

offer excellent examples of events whose occurrence may be modeled as Poisson processes. That is, the time of occurrence of one of these events doesn’t affect when we see the next occurrence of such.

When two perfect games occurred in 2010, statistician Martin Monkman of British Columbia took a similar view in his aptly named Bayes Blog.

As for Humber, his pristine performance at the Mariners’ Safeco Field took just two hours and 17 minutes.

“My wife is nine months pregnant,” he explained, “and I was making sure she didn’t give birth when I was pitching,”