Perfect Problem

Yu Darvish nearly pitched a perfect game last night. Here's the evidence that he wasn't perfect:

Perfect games haven't quite become common place, but they are more common now than ever before. There had never been more than one perfect game in a season before 2010. Last year, there were three. For some perspective there weren't any perfect games from 1968 to 1981, a stretch of over a decade. Yu Darvish nearly pitched the sixth perfect game in the last two seasons, plus two games (and that total doesn't count the one Armando Galarraga lost on a blown call at first base).

On some level, perfect games are fluky. They are extreme outliers by definition, with them being perfect and all. Looking for patterns in extremes is a bit destined for failure for a number of reasons (sample size being one of the biggest). Still, it certainly seems like there is something about the modern game that allows for more perfect games. I decided to look for an explanation.

I developed a new metric I call "critical batters," which is utterly useless for anything but perfect games. The premise behind critical batters is simple - a pitcher needs to retire 27 batters in a row in a perfect game, so I developed a statistic that attempts to measure how many of those batters are the difference between a normal game and a perfect game. Here's how the stat works:

1. Start with 27 (the number of batters in a 9 inning perfect game)
2. Subtract a pitcher's K/9 rate (the number of batters they would strike out in 9 innings)
3. Multiply the remaining number by (1 - defensive efficiency). Defensive efficiency is simply the percentage of balls in a play a defense turns into outs.
4. The result is what I call "critical batters." It represents, out of every 27 batters, the ones that would be expected to reach base out of 27 batters. The major shortcoming of the statistic is that it does not consider walks or home runs, both of which must also be 0 in a perfect game.

Essentially the critical batters are the ones, in any string of 27, that would make contact and be expected to reach base. The higher the number of critical batters, the more extreme/unlikely a perfect game would be in theory, because all of the critical batters can't reach base.

I looked up MLB K/9 rates and defensive efficiencies for 1960 through 1912 to calculate critical batter rates for all of baseball the past 53 seasons. The chart below summarizes results, with perfect games in red:

Critical batters passes the eye test as a meaningful statistic. 1968, the famed "year of the pitcher," sticks out on the chart, as might be expected. The dead decade for perfect games featured a rapid rise in critical batters, which makes some sense too. However, the most stunning part of the graph is at the tail end, where the number of critical batters plummets.

The modern game is a perfect storm for perfect games. Critical batters are at a minimum, mostly thanks to all-time highs in strikeout rates. There are also more games played now than in the 1970s and 1980s, thanks to expansion in 1993 (Marlins and Rockies) and 1998 (Diamondbacks and Rays). The number of games does not alter the graph above, but it does provide more opportunities for perfect games. More games + fewer critical batters = more perfect games, or so it seems.

However, just because current conditions are more favorable for perfect games doesn't mean they should be as common as they've been. Maybe we have reached some sort of perfect game tipping point (and that would be fun to investigate) but I doubt it. It is more likely that the recent glut of perfect games is an anomaly, assisted by more favorable conditions but hardly explained by them. Baseball may never see another run of perfect games like this.