On May 9, 2010, Dallas Braden became one of just 21 (then 19) pitchers in the history of Major League Baseball to throw a perfect game, so-called because not a single member of the opposing team reached base. Braden recorded 27 straight outs, striking out nine. This was the first complete game of his career. By May of the next year, he was out of baseball, and has not pitched competitively since 2011.
On April 21, 2012, Phillip Humber, a 29 year old journeyman on his 5th major league team, recently signed after sporting a AAA ERA of 4.47 for the Royals affiliate, threw a perfect game, with 9 strikeouts. It was his first major league complete game. The rest of his career has been disastrous. His ERA since that single start lies at 7.52.
What is it, then about perfect games (and their lesser counterparts, the no-hitter)? Why is it that, among the Nolan Ryans (5 no-hitters) and Roy Halladays (1 PG, 2 N-H), there are the likes of Humber and Braden, not to mention Dennis Martinez, Tom Browning, and Len Barker who can claim to have had such a perfect day?
The answer, sadly, is in very simple statistics. Since the pitching mound was regulated in 1969 (34 years ago), there have been 14 perfect games and 98 no-hitters that were not perfect games. In this time, the league-wide on-base-percentage has hovered near .320, with a batting average near .260. Assuming that individual at-bats are uncoupled to one another, with 162 games per season, 2 teams per game, and 30 teams in the league, the expected number of perfect games in a given season is 162*2*30*(1-.325)^(27) ... near 1/4. The expected number of no-hitters is higher, 2.89, near 3.
34 years * 2.89 = 98
34 years * .25 is around 9.
Nice! This takes a bit of the magic away from what a no-hitter means. But what gives with the misfit to perfect games?
One theory: no-hitters are well-dispersed, but perfect games aren't coming against top competition. Of the six (six!) pitched since 2009, just one (Braden's) came against a team with a winning record, the then league-best Tampa Bay Rays. If the teams faced have a poorer OBP (say around .310 instead), the expected number of perfect games jumps to one every 2.5 years.
Second theory: Sample size error. We have plenty of no-hitters, but not many perfect games. In a couple hundred years, the numbers will refit to the mean.
Oceanographer, Mathemagician, and Interested Party