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Monday, January 18, 2010
Alan Nathan on the performance of bats
Here is da man:
Among people who have thought about this question, a consensus has emerged that a good working definition of performance is batted ball speed (or simply BBS).... I answer that by writing down the only formula you will find in this article:
BBS = q*(pitch speed) + (1+q)*(bat speed)
This “master formula” is remarkably simple in that it relates the BBS to the pitch speed, the bat speed, and a quantity q ... which I will call the “collision efficiency.” As the name suggests, q is a measure of how efficient the bat is at taking the incoming pitch, turning it around, and sending it along its merry way. It is an important property of a bat… q is approximately 0.2, so that the master formula can be written BBS = 0.2*(pitch speed) + 1.2*(bat speed). This simple but elegant result tells us something that anyone who has played the game knows very well, at least qualitatively. Namely, bat speed is much more important than pitch speed in determining BBS.
...
Indeed, the formula tells us that bat speed is six times more important than pitch speed, a fact that agrees with our observations from the game. For example, we know that a batter can hit a fungo a long way (with the pitch speed essentially zero) but cannot bunt the ball very far (with the bat speed zero). Plugging in some numbers, for a pitch speed of 85 mph (typical of a good MLB fastball as it crosses home plate) and a bat speed of 70 mph, we get BBS=101 mph, which is enough to carry the ball close to 400 ft if hit at the optimum launch angle. Each 1 mph additional pitch speed will lead to about another 1 ft, whereas an extra 1 mph of bat speed will result in another 6 ft. On the other hand, if the bat were a “hotter bat” with q=0.22, that would add 3 mph to BBS, adding a whopping 18 ft to a long fly ball.
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