Perfect Pair

Perfect games are amazing. They are never expected, and to me, arguably the most perfect feat in all of sports (mild pun perhaps intended). That's not to say that a perfect game is the hardest or greatest spectacle to accomplish. However, how many other things in sports are so staggeringly unlikely, yet approachable by just about anyone if it is their lucky day?

One perfect game in a year is amazing enough. After Roy Halladay's gem last night, we have witnessed two this month. With only 20 perfect games thrown in the last 120 years of Major League Baseball, I find that stunning.

What are the odds of that?

Actually, not too hard to figure out.

The odds on a perfect game are pretty simple to calculate, assuming a game goes nine innings. It is simply the chance that a pitcher retires 27 batters in a row. On-base percentage measures exactly how likely a pitcher is to get a hitter out, and how likely a hitter is to record an out. It is the only statistic we need. For our purposes, we will assume the defense never makes an error, which is rather reasonable, because reaching base on error is included in on-base percentage.

I looked up the box scores for both Dallas Braden's and Roy Halladay's perfect games, to figure out their odds of throwing perfect games against the hitters they faced. I compared each pitcher's opponents on-base percentages (essentially WHIP, but in OBP form), to the league average to figure out how above or below average both pitcher was, compared to the league average. Not surprisingly, both are well below league average. I then took the factor I had created through the comparison, and multiplied each hitter's on-base percentage by it. In theory, the resulting number was the expected on-base percentage in the matchup between the pitcher and hitter.

Since I was digging this deep into the calculations, I decided to go a step further. Both of these games were pitched early in the season, particularly Braden's. So, instead of using each hitter and pitcher's numbers at the time of the perfect game, I decided to go on their projection for the full season at this point, according to ZiPS. This brought regression into play, and should capture the true talent levels in the games better than the limited numbers accumulated had.

Bringing regression into play passes the eye test. It made Halladay's perfect game more likely than the raw numbers suggested, and Braden's four times less likely than the raw data implied.

Without further ado, the numbers:

  • Odds of Dallas Braden throwing his perfect game: 11,402 to 1
  • Odds of Roy Halladay throwing his perfect game: 5,938 to 1
  • The Rays lineup Braden faced would have to play 373 seasons before it would be expected to have 1 perfect game thrown against it by an average pitcher
  • The Marlins lineup Halladay faced would have to play 306 seasons before it would be expected to have 1 perfect game thrown against it by an average pitcher
  • Odds of Braden throwing a perfect game this year: 296 to 1
  • Odds of Halladay throwing a perfect game this year: 182 to 1
  • Odds of Halladay and Braden both throwing perfect games this year: 53,936 to 1
  • Odds of Halladay and Braden both throwing perfect games this year, within three weeks of each other: 3,545,976 to 1
I think the numbers illustrate why this hasn't happened before. Thanks to expansion, increasing strikeout rates, and better defenses, perfect games are more likely than ever before. Perhaps putting a more concrete number on how much more likely is a good topic for another post. How counterintuitive is it to think that perfect pitching is easier in an era where baseball offenses are understood better than ever before?

Still, perfect games in today's baseball world, however more likely they may be, are not that likely. A couple in a month, when it historically takes 15 or 20 years for a couple to get tossed, is beyond something we will never see again. It is something we never should have seen in the first place.