Keeping Score: Act of Perfection Remains Random – Bats Blog – NYTimes.com
Posted by Andy on June 4, 2010
Keeping Score: Act of Perfection Remains Random – Bats Blog – NYTimes.com
In the latest column by Sean (with a special pinch-hitting appearance by me!) we argue that perfect games require so many events to turn out just right that the overall likelihood of one occurring is quite random and has little to do with the average level of offense in the league at the time.
The number of near-perfect games isn't up this year, so the fact that there have been 2 (and nearly 3) perfect games so far isn't all that meaningful--just random luck.
June 4th, 2010 at 9:33 am
I don't disagree with the main point of the article, but I take issue with the notion "That translates to an average of about 1.5 fewer hits plus walks per game. In 2010 teams are averaging more than 12 hits plus walks per game, so reducing that number all the way to zero, as in a perfect game, is still a freak occurrence."
The change in the mean of 1.5 on a base of 12 is pretty significant. I don't know what the distribution of BB+H looks like (Poisson?), but I think the probability of 0 H+BB increases notably if you shift the mean from 12 to 10.5.
June 4th, 2010 at 9:35 am
It definitely increases, yes, but from one extremely small number to another. There are other factors, such as errors and bad ump calls, that are far more frequent and are the controlling factors.
June 4th, 2010 at 10:07 am
I just did the math for a Poisson process, where f(0,lambda) = e^(-lambda), where 0 = number of H+BB, lambda = the mean H+BB per game, f = probability.
f(0,10.5) / f(0,12) = 4.5, so a shift of 1.5 H+BB isn't inconsequential re: the odds of a perfect game- it's 4-5x more likely!
On the other had, the probability for 0 H+BB is really low either way- for an avg. of 10.5 H+BB per game, using this distribution the odds of 0 H+BB is 1 in 36,000 games!
June 4th, 2010 at 10:10 am
Thanks for doing the math. That speaks exactly to my point--errors and bad calls happen a lot more often than 1:36000 and therefore dominate the chances of a perfect game occurring.
June 7th, 2010 at 9:30 pm
As your data shows, there has been a significant increase, about 40%, in the rate of perfect games. Looking at total rate of hits/errors alone won't explain that. The key factor which increases perfect games is the higher K rate today. When pitchers strike out a lot of batters, the chance of a perfect game or no-hitter rises, even if total OBP stays the same. Strikeouts reduce the amount of luck a pitcher needs. If you have two .330 OBP pitchers, one with 4 Ks per game and one with 7, the latter pitcher is about 25% more likely to throw a perfecto. Now take that 7 K pitcher and add 3 Ks (10 K/9, .298 OBP) and his chance of a perfect game increases about 5 times, much more than the change in OBP alone can account for. There's a reason the average perfect game since 1960 has 10 Ks -- without Ks, the odds of a perfect game become vanishingly small.