Comments on: 2 HR vs 1 HR games http://www.baseball-reference.com/blog/archives/701 This and that about baseball stats. Mon, 21 Dec 2009 15:41:25 -0500 http://wordpress.org/?v=2.8.4 hourly 1 By: whiz http://www.baseball-reference.com/blog/archives/701/comment-page-1#comment-4960 whiz Tue, 01 Jul 2008 19:45:53 +0000 http://www.baseball-reference.com/sotd/?p=701#comment-4960 Very interesting. You can crudely estimate what this ratio should be by assuming Poisson statistics, which says that the number of 1-HR games to the number of 2-HR games is 2/x, where x is the average number of HR per game for a player. Assuming 9 batters in the AL and 8 in the NL (don't count the pitchers), in 2007 there were 4957 HR hit in 20,752 player-games, so x = 0.1204 and the 1-HR/2-HR ratio is predicted to be 16.6 -- not too bad! In the peak year of 1992 the prediction is 23.7 and in the low year of 1987 it is 16.1 -- also not too bad. The Poisson model ignores the fact that there are substitutions, different numbers of PA per game, and many other factors that might affect HRs per game, but it does seem to get a result in the right ballpark (so to speak). Eliminating pitchers ABs can be motivated by the fact that they don't hit many HRs, and they are often pinch-hit for anyway. It predicts that the 1-HR/2-HR ratio should always decrease as the HR rate increases, as expected. Very interesting. You can crudely estimate what this ratio should be by assuming Poisson statistics, which says that the number of 1-HR games to the number of 2-HR games is 2/x, where x is the average number of HR per game for a player. Assuming 9 batters in the AL and 8 in the NL (don't count the pitchers), in 2007 there were 4957 HR hit in 20,752 player-games, so x = 0.1204 and the 1-HR/2-HR ratio is predicted to be 16.6 -- not too bad! In the peak year of 1992 the prediction is 23.7 and in the low year of 1987 it is 16.1 -- also not too bad.

The Poisson model ignores the fact that there are substitutions, different numbers of PA per game, and many other factors that might affect HRs per game, but it does seem to get a result in the right ballpark (so to speak). Eliminating pitchers ABs can be motivated by the fact that they don't hit many HRs, and they are often pinch-hit for anyway. It predicts that the 1-HR/2-HR ratio should always decrease as the HR rate increases, as expected.

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