# Fouls with Two Strikes

In recent posts, I have looked at pitch count transitions for hitters and pitchers. Here I will focus on one particular pitch count transition that looks interesting and may be helpful for measuring batter ability.

Here are the counts of the different transitions for the 2015 Mike Trout (recall the state X refers to the end of the plate appearance which could be a SO, BB, or a ball in play.)

```    0-0 0-1 1-0 0-2 1-1 2-0 1-2 2-1 3-0 2-2 3-1 3-2   X
0-0   0 361 294   0   0   0   0   0   0   0   0   0  27
0-1   0   0   0 139 162   0   0   0   0   0   0   0  60
1-0   0   0   0   0 130 125   0   0   0   0   0   0  39
0-2   0   0   0  29   0   0  96   0   0   0   0   0  43
1-1   0   0   0   0   0   0 133 115   0   0   0   0  44
2-0   0   0   0   0   0   0   0  57  55   0   0   0  13
1-2   0   0   0   0   0   0  53   0   0 139   0   0  90
2-1   0   0   0   0   0   0   0   0   0  79  50   0  43
3-0   0   0   0   0   0   0   0   0   0   0  26   0  29
2-2   0   0   0   0   0   0   0   0   0  64   0 108 110
3-1   0   0   0   0   0   0   0   0   0   0   0  33  43
3-2   0   0   0   0   0   0   0   0   0   0   0  49 141
X     0   0   0   0   0   0   0   0   0   0   0   0   0
```

When one watches a plate appearance, one notes the tendency of a batter to extend the PA by fouling off pitches. Down by two strikes, the batter will sometimes foul off a number of pitches. This seems to be desirable from a batter’s perspective. It lengthens the pitch count, the batter sees more pitches and is more likely to make good contact on the next pitch, etc. Looking at Trout’s table, let’s focus on the foul balls with two strikes which correspond to the transitions from “0-2” to “0-2”, “1-2” to “1-2”, “2-2” to “2-2”, and “3-2” to “3-2”. We see that Trout had 29 + 53 + 64 + 49 = 195 of these two-strike foul balls in 2015.

Creating a useful statistic, Trout had 195 2-strike foul balls in 682 plate appearances, so his average number of 2-strike foul balls (per plate appearance) was 195 / 682 = 0.286.

To see if Trout’s foul average is unusually low or high, we computed this statistic for all 2015 players with at least 400 PA. Below, I show the hitters where this foul average was .3 or higher, and the hitters who had a foul average of .2 or lower.

Some comments from looking at these high and low graphs:

• We see that Victor Martinez was the foul average leader in 2015 and Andrelton Simmons was at the bottom with respect to this statistic.
• Being a Phillies fan, it is a bit remarkable to find a statistic where two of the top six are Phillies — Odubel Herrera and Freddy Galvis.  Actually, I did see a recent Phillies game where the commentator commented on Herrara’s ability to stay in the count with a foul hit.
• Looking at the list of low foul averages, it seems that many light-hitting players are on this list such as Andrelton Simmons, Ben Revere and Billy Hamilton.  I am a bit surprised that Buster Posey is on this low foul average list.
• Note that I am computing the average number of fouls on two-strike counts.  Other statistics could be computed; for example, I also looked at the fraction of PA’s where there was at least one foul on a two-strike count.  My sense is that you would have a similar list of top and bottom batters using this fraction statistic.
• From a statistical perspective, I guess I am more interested in the significance of these values.  Is a foul average a batting skill which is related to other batting measures?  Can one accurately predict one’s 2-strike foul average in the next season using this season’s data?  Given that the length of a PA is considered to be a batter skill, I would think that a 2-strike foul average would behave in a similar fashion.  This recent fangraphs article asks if foul balls are a skill.
•  Generally, it would be interesting to look more carefully about usefulness of foul data to learn more about the abilities of batters and pitchers.