Intent

There is a very fair question asked in the comments to last night’s suspension post.

How does anyone know intent? Fulmer had been missing to the arm side most of the night. You need to pitch Sanchez inside. He gets hit at the waist. Happens all the time. Looks bad when its a guy who had hit a HR in his previous AB but to blame Fulmer for what ensued seems silly.

There was a time when I agreed with this line of reasoning. I went the other way after Cole Hamels intentionally plunked Bryce Harper for no other reason than Bryce was a rookie off to a good start. When it happened, I assumed it was a purpose pitch that got away, and praised Harper for this reaction to the pitch. When Hamels admitted that he intentionally hit Harper, my mind changed on such matters. A Baysian might say I updated my prior.

What Bayes rule does tell us is that being hit by a pitch is a poor test for predicting if the person plunked homered in the game. I looked at all games started by players since 1998 in which they had at last one PA.

Using HBP as a test for having hit a home run in the same game.

	HR in Game	No HR in Game
Games	91274	770232
Games HBP	2964	26946

It is very clear from the data that players are hit by pitches more frequently in games in which they do not homer. Bayes rule makes this even clearer. The probability of hitting a home run given that if the only thing you know is that the batter was hit by a pitch in the game is 10%. The probability of hitting a home run given that you were not hit by a pitch is 10.5%. So being hit by a pitch is a very poor test for a player having homered in the game. That’s a good argument in favor of not knowing intent.

The counter argument is that the intent is hidden by waiting for another game, or hitting a different batter. It’s possible that a temporal test, only looking at HBP after a home run, might change the probabilities. My guess, however, is that players have a very different Baysian view of this as they probably know when their pitcher intentionally hits a batter, so they know the conditions that lead to the situation. It’s not obvious in the basic statistics, however.

from baseballmusings.com http://ift.tt/2vqk0Ap