Between 1952 and 2012 when is the best chance to see a HR? It happens to be on a 0-0 count in the 4th inning. Historically, 53.07% of all HR balls happen on an 0-0 count.
That number, to me, is surprisingly high.
The 4th inning holds a slight edge on most HRs in an inning with 12.623% of all HRs. In my opinion a couple explanations could be the pitcher is getting tired as the game progresses and/or the batter is having more success in second/third at bats against the pitcher. Again the margin is slight. Interesting note is that the 9th inning is relatively low related to the other innings at 7.89%. Perhaps explained by the dominance of closing pitchers. However when a closer gives up a jack we seem to remember it since typically the situations are high leverage situations with the game on the line.
The inning with the least chance to see a HR is the 25th inning with a .0005% chance. Of course if you make it to the 25th inning to see a HR you should get some kind of prize like a free ticket to a game or a free dozen donuts or something.
Looking at 3 recent HR sluggers you can see their success on the 0-0 count. The 0-2 count is incredible. Pitchers have the upper hand on 0-2 as far as the long ball is concerned.
Perhaps the batter switches plate approach to contact, but truly an amazing drop off in HR balls on 0-2. The HR numbers fall dramatically at 0-2 count. Of course 3-0 count is the lowest HR % count since typically you take that pitch.
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