Do Batters Swing Too Often in a Full Count?
A while ago iamawesomer wrote an interesting piece about the game theory of swinging at 3-2 pitches, and MGL often talks about how he thinks batters swing too often in a full count. The idea intrigued me and I wanted to examine it.
First off a little background, batters tend to swing more as they get more strikes. This makes sense, with no strikes they can be selective and wait for their pitch. But with two strikes letting a strike go by ends the at bat. Similarly batters tend to swing less when they have three balls compared to fewer. Again this is a good strategy. The benefit of going from 3 to 4 balls is more than going from 0 to 1 balls. So taking a pitch, that could be a ball or a strike, is better with three balls than with fewer.
It seems like this trend of breaks down when the count is full. Consider the two counts 2-2 and 3-2. In both counts the penalty for taking a strike is the same--a strikeout--but the benefit from taking a ball is greater at 3-2. Taking a ball at 3-2 results in a walk, while taking a ball at 2-2 just brings the count full. If a pitch is right on the border of a strike/ball a batter has more incentive to take that pitch at 3-2 than 2-2. But that is not what they do. Batters swing at more pitches at 3-2, the trend is true for pitches in the zone and pitches out of the zone. Also if you look at pitches in a given location batters swing at that pitch more often at 3-2 than 2-2. So batters are either swinging too often at 3-2 or too rarely at 2-2 or both. For this post I am going to look at the full count.
I am going to restrict my attention to RHB/RHP. I think the results would be similar in other cases, but I have not checked. Here is the swing rate by pitch location at 3-2.
In other at-bats batters swing at pitches inside more often than outside, but this preference breaks down when the count is full. Overall this is a huge area over which batters swing.
I took the run value by location of 3-2 pitches swung at (swinging strikeouts, fouled off and balls in play) and subtracted the run value of a 3-2 pitch taken (walks and called strikeouts). That value I plotted in colors with red negative (penalty for swinging) and blue positive (better to swing). On top I plotted the 50%, 75% and 90% swing contours.
The white is the break even. The average batters, if he knew the exact locatoin a pitch would end up and preformed optimally, would swing at pitches inside that white band and take outside.
In the blue region batters swing over 75% and for most of it over 90% of the time. So batters do a good job of swinging at pitches they need to. In the red region just outside the break even batters swing between 75 and 50% of the time. So they swing at a large number of pitches they should take, they do not do a good job of taking pitches they should take.
Generally a batter would want to swing inside the blue and always take inside the red. It is not possible to do this perfectly, the batter does not know where the ball will end up when he swings. Most likely if he tried to be more selective and take more balls (those in the red area), then he would also end up taking some additional strikes (those in the blue). Right now it looks like batters are too swing-happy, they should be more selective, and give up some called third strikes in exchange for more walks.