By The Numbers: Perfect Games

Nathaniel Stoltz takes a closer look at the statistical odds Dallas Braden had to overcome to earn throw his historical perfect game.

I'd like to offer my congratulations to A's left-hander Dallas Braden on his perfect game on Mother's Day. I watched the game, and I realized he had a perfect game through three innings, and gradually got closer to the edge of my seat as the game wore on. It was quite the experience—I've never watched a no-hitter or perfect game on TV before (other than ESPN cuts to the last couple of outs), so it was enthralling.

Fangraphs' Jack Moore broke down Braden's odds of accomplishing the feat, and came up with .001517%, which translates to about 15 in a million, or 1 in 66,000.

Moore's estimation is pretty accurate, of course, assuming that Braden would be allowed to get all 27 outs every time. As it is, he threw nearly 110 pitches in the game—15 or 20 more would have left Bob Geren with a mighty difficult decision. Braden isn't the biggest guy in the world, and he had arm issues in the minors. He also had never even thrown eight innings in a big league game. Therefore, the odds of Braden actually getting through the entire outing are probably even lower than the 1 in 66,000 Moore outlines in his article.

Due to this strict pitch counts of modern baseball, even complete games are rare nowadays. In the 4,860 games of 2009, only 152 were complete games—just 3.1 percent. Sixty-three of those 152 were shutouts—41.4 percent of the complete games, and just 1.3 percent of the total games. Just two of the A's games were complete games last year, as Brett Anderson and Brett Tomko tossed complete game shutouts.

What's interesting about Braden is that he is a control pitcher who rarely walks hitters, which means that if he manages a no-hitter, he also is fairly likely to manage a perfect game. If Braden does not allow a hit to 27 straight batters, he has a 43.7% chance of managing to not walk or allow an error to any one of those 27 batters as well (using Moore's numbers), which is a fairly staggering rate.

Another way to look at Braden's odds is to consider the likelihood that one of the 21 balls in play off of him would go for a hit. The average batting average on a ball in play is typically around .300, and Braden's career BABIP is .308. If we say that each ball in play had a .308 chance of falling in, the odds that all 21 would not be a hit (this doesn't account for errors) are .0004387, or .04387%, or 1 in 2,279.

Braden allowed four liners in the game, and line drives have average BABIPs around .720, so just the odds that all four would be caught are about 1 in 163—that is, if Braden took his turn in the rotation every start for five seasons, and allowed four liners every game, he would have one game in those five seasons in which all four were converted into outs. And that's just four batters!

Given that he's not a huge strikeout pitcher (minor league numbers aside), and he's not the most durable pitcher ever, Braden had a ton of obstacles to overcome to pull this off. It took an incredible amount of luck to happen, and he should obviously savor the moment—the odds of Braden ever throwing a perfect game again are, of course, unbelievably slim.

To read more from Nathaniel, visit his blog at The Bleacher Report.

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