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In the long-gone days of haphazard record-keeping, perfect games provided a special token of superiority, an important Hall of Fame credential unto themselves: you had to be pretty good to get 27 consecutive outs. Only three perfect games were thrown between 1904 and 1964. Almost every pitcher who threw one in the 20th century could safely be described as excellent. We have now had seven perfect games thrown in the 21st, with the roll of honour featuring such names as Dallas Braden, who is watching games from the stands at 30, and Philip Humber, who is currently toiling in long relief for the Houston Astros. For the non-fan, the last part of that sentence translates to “has the least important job on what is by far the crappiest team”.
plugging that rate into (what is called) a (Poisson) model
Is that the right way to do this? I would think it's 27 binomial events. So you would take the off-base percentage (1 - OBP) raised to the 27th power, to figure the chance of all 27 PA being outs.
But that gives results of quite a bit more infrequent than the article says. For year 2000 that's .655^27 = 1/91513 games. For year 2013 it's .688^27 = 1/30748 games. Both of those numbers are substantially scarcer than the observed real-world history of perfect games.
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