from Amazon
Tuesday, June 08, 2010
Perfect Game calculation
Replying to Tommy:
Tommy, I think you might have a problem with your 40% or 38% figure. You are probably counting three one-third of innings as one inning, rather than three innings, to begin with.
As for the chance of a perfect inning, why not do it the even easier way, and take OBP (the real OBP, one where reaching on error is a good thing, etc). Chance of a perfect time at the plate for a pitcher is around 66%, so a perfect 1-2-3 is .66^3 = .287. A perfect 27 is .66^27 is around 1 in 75,000.
Presuming that perfect games occur in slightly more conducive settings, say a true OBP of .300, that makes the above calculation as 1 in 15,000.
With about 350,000 starts in MLB since 1900, that works out to 22 expected perfect starts.