We already talked about Cliff Lee and Matt Cain‘s pitcher’s duel for the ages last night, but that wasn’t even the most remarkable thing that took place last night. Over in Anaheim, Bartolo Colon was doing something that we might not see done again in our lifetime.
In the fifth inning of last night’s game, Colon threw a first pitch ball to Maicer Izturis. He wouldn’t throw another pitch that was called a ball until he faced Bobby Abreu in the eighth inning. Between Izturis and Abreu, he faced 11 batters and didn’t throw a single ball to any of them. His all-strikes, all-the-time approach lasted a remarkable 38 pitches. You can see all 38 of them in this video compiled by MLB.com.
How unlikely is that? Well, we can estimate the chances of an event occurring 38 times in a row using a mathematical tool called binomial distribution. Essentially, binomial distribution takes the probability of an event occurring and then extrapolates how often you’d expect that event to happen a certain number of times given a number of opportunities. In this case, the probability of Bartolo Colon throwing a strike on any given pitch is roughly 67% percent. In other words, out of every three pitches Colon throws, we’d expect two strikes and one ball.
Last night, we got 38 consecutive strikes without a ball. Binomial distribution tells us that the odds of that occurring, given what we know about Colon’s career strike percentage, is about 0.000000246. In other words, you’d expect to find one string of 38 consecutive strikes if you had a population of approximately 4.1 million strings of pitches thrown by Bartolo Colon. One in 4.1 million.
Yeah. What Lee and Cain did was downright ordinary compared to what Colon did.
Update: As pointed out in the comments, I should have clarified that the binomial distribution assumes independence of events, where the results of one test do not affect the probability of the next test. It is not clear that balls and strikes are independent from the previous pitch, as batters are more likely to chase pitches out of the zone when they are behind in the count. Of course, pitchers are also less likely to groove one down the middle when they’re ahead in the count, so these effects may cancel out to some degree, but it’s not clear that the probability of balls and strikes on each of those 38 pitches was indeed .67. So, consider this more of a rough estimate based on one model’s assumptions, which may or may not hold precisely true in an MLB game scenario.