Rare and Near Perfection - What are the Odds?

Prior to this season, in 134 seasons of Major League Baseball dating back to 1876, only 18 perfect games had been thrown. That’s one every seven or eight seasons. This year, we’ve had three in less than a month (though only two count).

Dallas Braden was on top of the pitching world with his perfect game on May 9. Not to be outdone, Roy Halladay matched his feat going 27-up, 27-down on May 29. Two days ago, on June 2nd, Armando Galarraga retired the first 26 batters followed by the umpire gaffe on the final play to deny him the official perfecto.

What are the odds of so many perfect games in such a short period of time?

With the advent of the 162-game schedule and gradual expansion from 16 to 30 teams, there is a greater chance of a perfect game happening in the modern era than there was previously; however, the odds still remain quite low.

The odds that a perfect game occurs in a season: 4-to-1

For two or three perfect games, the odds start getting quite remote:

The odds that there are two perfect games in a season: 43-to-1
The odds that there are three perfect games in a season: 580-to-1

But we had all two (three?) in a month. The odds on three perfect games in a month are astronomical at 16,033-to-1. Maybe Jim Joyce was thinking this subconsciously when he made the bogus safe call in Galarraga’s game.

The odds that there are two perfect games in a month during a season: 212-to-1
The odds that there are three perfect games in a month during a season: 16,033-to-1

You’ve seen history, folks.