I just had a student complete a thesis on issues regarding the first pitch in a plate appearance in baseball. One question she didn’t address is: **Should a player swing at the first pitch**? Here I’ll do a quick exploratory study to partially answer this question.

### Initial Thoughts

As we will see below, there is a lot of variability in the proportion of first pitch swings among regular players. It would see that a moderate value of this swinging proportion would be optimal. If a batter always will take the first pitch, then the pitch can just throw a fastball down the middle of the plate. On the other hand, if the pitcher knows that the batter will swing at a high proportion of first pitches, then the pitcher likely would throw a pitch outside of the strike zone that the batter would chase. To keep the pitcher guessing, it would seem advantageous (from the batter’s perspective) to swing at a “middle” proportion of first pitches.

### Swinging at the First Pitch is a Batter “Ability”

Using Retrosheet play-by-play data for the 2015 and 2016 seasons, I collected the fraction of first pitch swings for all players with at least 400 plate appearances. Here’s a scatterplot of the swing fractions for the two seasons — since there is a high positive association in the graph, this indicates that swinging at the first pitch is really an attribute that differs between players.

### Swinging at the First Pitch and Runs Value

Using 2015 season data, we collected (1) the first swing fraction and (2) the average runs value of the player’s PA’s. We want to see if there is any relationship between the two variables. Is there any evidence to indicate that the best players (from a runs value perspective) are the ones whose swing fraction is moderate? Below I construct a scatterplot using the players with at least 400 PA and add a smoothing curve to find the general pattern.

Looking at the pattern in the blue smooth, this graph supports my hypothesis. It seems that players generally peak in runs value for swing fractions about 0.25, and swing fractions between .3 and .4 have lower runs values. By the way, I notice two runs values outliers who were both free swingers — adding labels to the graph we see these players are Bryce Harper and Mike Zunino (remember I am looking at Harper’s 2015, not 2016 season).

### Advantage of Swinging at First Pitch?

How can we measure the advantage of swinging at the first pitch? One simple way is break the PA’s into the “first pitch swings” and “first pitch non-swings” and look at the difference in average runs value of the two groups.

Advantage = RUNS_swing – RUNS_no_swing

Here I graph the Advantage against the fraction of first swings for all players. Several interesting features pop out:

- The smoother falls below 0 for all swing types. This indicates for this season (2015) that it was generally advantageous not to swing.
- The Advantage of swinging appears to be maximized (on average), for first pitch swing rates between .25 and .30. In contrast, the Advantage is smallest for swing rates about .40.

Of course, we like looking at the outliers in this plot. Jimmy Rollins, Khris Davis, and Billy Burns really do better on the PA when they swing at the first pitch, and Omar Infante has the smallest (that is, most negative) value of Advantage.

### Summing up …

This brief analysis confirms a few things:

- There are sizeable differences in the fractions of first pitch swings among modern players — swinging at the first pitch is really an attribute of a batter that defines his batting ability.
- There seems to be some evidence to support the idea that hitters perform best (on average) when the fraction of first pitch swings is a moderate values.
- For a single season, particular batters seem to be more successful when they swing on the first pitch. It would be interesting to see if a batter, say Jimmy Rollins, always did between on first pitch swings throughout his career.