The Perfect Perfect Game in Baseball

Bill_James_BostonBaseball statistician Bill James, the inventor of sabermetrics, devised what he called a “game score” to measure pitching performance in a baseball game. The larger the game score, the stronger the pitching performance. James’s game score is calculated as follows, with points added or subtracted for every out that the pitcher records:

1. Begin with 50 points.
2. Add 1 point for each out (3 per inning pitched).
3. Add 2 points for completing the fifth inning and for each inning thereafter.
4. Add 1 point for each strikeout.
5. Subtract 2 points for each hit.
6. Subtract 4 points for each earned run.
7. Subtract 2 points for each unearned run.
8. Subtract 1 point for each walk.

These numbers make good intuitive sense: walks count negatively, any runs count negatively, every strikeout counts positively, etc. But this game score measure also has some quirky features. For instance, so long as the pitcher doesn’t allow any runs or walks, the game score will go up. Thus for a pitcher to get the maximal possible addition to his game score in a given inning, he should strike out six batters, with three getting on base, even though struck out, because of a dropped ball by the catcher, the other three getting struck out and called out, with three runners being left on base. Also, if the game can be prolonged for more than 9 innings without allowing a run or walk, that will increase the pitcher’s game score. This last feature of game score speaks to the pitcher’s endurance, and indeed, the highest game score ever recorded for a game is 153 and comes from a 26-inning pitching performance by Joe Oeschger back in 1920 (pitchers back then tended to pitch lots more games and innings).

When it comes to 9 full innings pitched (no more, no less), however, the highest game score ever recorded is 105. Cubs pitcher Kerry Wood got this game score against the Houston Astros on May 6, 1998. In that game, he struck out 20, allowed no walks but one hit. It was therefore neither a perfect game nor a no hitter but a shutout. The full game of Wood against the Astros can be seen here:

If Wood had struck out the Houston batter who got that one hit against him, Wood’s game score would have been 108, and it would have been a perfect game. So that raises the question, how high could the game score possibly get in a perfect game? Such a game would require 27 strikeouts. Doing the calculation according to the rules above yields a maximal possible game score for a perfect game at 50 + 27 + 10 + 27 = 114.

So, would a game score of 114 for a perfect game be what might be called a perfect perfect game? In such a game, every batter would strike out. Obviously, no perfect game ever pitched has seen every batter strike out. The most strike outs recorded in any perfect game have been 14 (Sandy Koufax for the Dodgers against the Cubs in 1965 and Matt Cain for the Giants against the Astros in 2012). One perfect game in recent times has even had as few as 5 strike outs (Dennis Martinez for the Expos against the Dodgers in 1992). And going back almost a hundred years, there was a perfect game with just 3 strikeouts (Addie Joss for the Cleveland Naps in 1908 against the White Sox).

Still, it seems that a game score of 114 for a perfect game, with 27 batters each striking out, might still indicate less than a perfect perfect game. If we think of a perfect perfect game as one in which the pitching performance could not be improved, then even in a game where at each at bat each batter strikes out, the best possible performance would be one where the pitcher throws no balls and the batter never even makes contact with the ball (in other words, the batter swings and misses or doesn’t even swing — this requirement for a perfect perfect game is justified because if the batter makes contact, it has a probability of getting into play and thus turning into a hit).

A perfect perfect game would therefore be a game with 81 pitches, each a strike, and each with the batter never laying bat on the ball.