Randomness and Lean and Perfect Games

One of the rarest feats in sports is the perfect game. For those non-sports fans among you who don’t know what that is, it simply means that no batters were able to reach first base. In short, 27 people in a row failed to do their job properly.

In fact, the feat is so rare, that until last night, only 18 perfect games had been recorded in Major League Baseball’s hundred plus year history. Then on Mother’s Day of 2010, Dallas Braden threw the 19th.

For some reason, I got the urge to dive into the statistics behind what is generally touted as a historic event. I wanted to see if it actually happens more or less often than we’d expect. Here’s my back-of-the-envelope analysis…

• There are 30 teams playing a 162 game schedule, resulting in 2,430 games a year. That yields 4,860 chances a year to have a perfect game, since there are two pitchers battling it out.
• The average baseball player gets on base about three out of ten times, meaning that the pitcher wins the duel seventy percent of the time.
• A pitcher has to retire 27 batters in a row to get that perfect game. So…
• There’s a .700 to the 27^th power chance of any game being perfect, or .00657% chance of having one happen for any given pitcher in any given game.
• Multiply that by the 4,860 chances a year, and you’d expect to see 0.32 perfect games each season.

In the last 30 years, guess how many perfect games there have been…10. Less than half of a perfect game more than the numbers say we should see (30 x 0.32=9.6). (For reference, there have been 72,900 regular season games over that span.)

In Lean, the lesson is not to jump to conclusions. Don’t immediately assume that something changed or that there is a special cause of a problem just because there is an outlier. Normal randomness built into non-standardized processes is just as likely to be the culprit as something exotic.

Of course, despite the math saying otherwise, I still think it’s a pretty great feat, and congratulate Braden on his accomplishment.