F/X Visualizations August 21, 2009
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.

Interesting study. Are there some hitters that are good at not swinging on 3-2?

Dave - For some information your graphs of percentages are very useful. In this instance it would also be informative to know how many pitches are being thrown in those red areas outside the strike zone where the batter is swinging more than 50% of the time. It makes a huge difference whether we are talking about batters making misjudgements on 5 out of 10 pitches a year or 5000 out of 10000.

I think that game theory would explain why hitters swing more on 3-2 pitches than they do 2-2. They know the pitcher knows the penalty for a ball 3-2 is far worse than 2-2, therefore they know they are far more likely to see a strike.

This is an interesting study, but I think it would be interesting to do a psychological study of the mindset of batters. I was raised in a house where strikeouts were unacceptable, so my natural inclination in a full count is to protect.

Another thought that enters my mind during a 3-2 count is not letting the umpire beat me. It is impossible to count the number of times an umpire has rung up a hitter on a pitch location he called a ball earlier in the same plate appearance. It happens frequently, and if I am going down, I'm not going to let that jerk have the satisfaction.

@Dan - that's what I was thinking. The analysis in the article assumes that the ratio of balls to strikes is the same for 2-2 and 3-2. For purposes of reducing the variables I understand the assumption. But empirically, is it correct? As a practical matter, since the pitcher (a) knows the batter can wait & (b) wants to avoid the 3-2 situation, it seems to me that he's more likely to throw a pitch more likely to be called a strike. But then, much depends on the batter's tendencies. Does he swing at that low curve? Would it be better to offer it on 2-2 or 3-2? WWMD? (what would Maddox do?)

It is difficult to determine whether batters swing too much at 3-2 counts or too little at 2-2 counts, and if the former, by how much, from the data. One would have to estimate at what level an average batter can discern a pitch in each location. And yes, since the pitcher does indeed throw more strikes at 3-2 (although not as much as he should if the batter swing less often), the batter is forced to swing more at marginal pitches.

That being said it is a given without looking at the data that batters will swing too often at 3-2 counts for the reason that Dan explains above and we all know from playing, coaching, or watching baseball. You get heat from the bench when you get called out on strikes even at a 3-2 count on a marginal pitch, and you are always taught to protect the plate with 2 strikes. That is, unless you played on my team when I coached baseball. I taught my players to swing more often at marginal pitches when they had more strikes and fewer balls. I specifically told them that at the 3-2 count, that they should NOT swing at a marginal pitch. I also told them that that depended on the game situation and how good a hitter they were and how good a pitcher was on the mound. For example, in Little League where you often have a batter/pitcher combo whereby the batter is like a .700 hitter including errors, it probably is NOT correct to take a close 3-2 pitch.

After coaching high school baseball for 28 years I will say that(I have no stats for this so it is purely anectdotal) it seems that HS hitters will take a close 2-2 pitch to run the count full then immediately swing at what would be ball four on the next pitch. It is a strange occurence, but happens quite a bit from what I observe.

Peter,

very good point. For RHB/RHP 70% of the pitches where in the area of blue area (batter should swing area), while just 16.5% were in the intersection of the red area and the >50% swing contour. So pitchers are throwing most of the balls in the zone. So that is probably a big reason batters swing so much, they are expecting a pitch in the zone, like Dan said.

Dave - From the numbers that you gave in your comment it appears that you have a certain number of batters that are plain guessing wrong on the pitch. Expecting a fast ball and getting off speed or vise versa. That would be the 5% of the pitches that are in the strike zone and don't get swung at plus the 8.25% of the pitches that are way out of the strike zone and do get swung at plus some unknown amount of the 33.5% of the pitches that are in the grey area at the edges of the strike zone. Did you include pitchers batting in your study? If so, they may have more trouble with pitch recognition than position players.

To discover if the idea that at 3-2 the batter swings more because he believes he is more likely to see a strike due to the consequences for the pitcher of throwing a ball, it would be interesting to look at situations where the impact of a walk are different -- bases loaded or bases empty for example -- and see if there are more swings in the bases loaded scenario.

What happens to this analysis if we don't assume that a hit and a walk have the same value? That is: aren't doubles and home runs better than walks? And as phineasb suggests, the context of the at-bat may make a big difference. I would guess that considering these things would make the value of the walk go down relative to the hit just a bit, and therefore the cost of a potential strikeout looking goes up a little; but how much? Intriguing stuff.