Mathenaging: What Underlying Batting Trends Influence the Decision to Pull a Starting Pitcher

St. Louis Cardinals manager Mike Matheny is tasked with making the tough personnel decisions. When to pinch run. When to pinch hit. When to pull the starter in favor of a reliever. These choices are informed by a myriad of factors such as how the pitcher is throwing, who is available on the bench, which relievers are available in the bullpen, and more.

Another factor that comes into play is how opposing batters fare against a pitcher after having faced him multiple times in a game. Typically, a batter sees better results the more times he faces a starter. This is why it's important for starters to have a repertoire that allows them to show batters different looks. It's difficult to survive in the majors as a two-pitch starter because it doesn't take the opposition as much time to figure him out. But even pitchers with multiple pitches in their repertoire have the opposition experience more success as the game goes on.

Using the splits available at Baseball-Reference, the following graph shows the batting average (BA), on-base percentage (OBP), and slugging percentage (SLG) for MLB batters when facing a starting pitcher for the first time, for the second time, for the third time, and for the fourth time or more in a game.

BA, OBP, and SLG all go up between the first and second time a batter faces a starter, and between the second and third times. But batters experience a slight downtick when facing a starter for the fourth time (or more) in a game. This could be due to survivor bias (in the smallest sense of the term). The better a pitcher, the more likely he is to work deep enough into a game to face a batter four or more times. Nonetheless, it's still an interesting development.

The following graph shows MLB batters' 2013 OPS vs. starting pitchers based on the number of times they have faced one another in a given game.

This chart shows a bit more clearly the increase in production that batters enjoy when facing a pitcher for the second and third time in a game. It also illustrates the downtick in production when facing a pitcher for the fourth, fifth, or sixth time in a game.

Now compare how batters perform against a reliever when facing him for the first time in a game.

As you can see, overall, a reliever facing a batter for the first time is the most effective at holding down batting production. A reliever faces a batter twice in a game far less often than once, and three times even fewer. (I included the 3rd+ PA just for the novelty and to cause you consternation the next time the Cards play an innings total in the teens.) If a manager has seven relief arms to summon in the later innings, why leave one of them in long enough to face a batter twice?

The third time through the order is often where a manager has to make a decision. The manager has the choice of leaving the starter in to face a batter for perhaps the third or fourth time in the game. But he must also consider fatigue. Baseball-Reference also has splits based on pitch total. While somewhat arbitrarily grouped, they nonetheless offer a window into how fatigue might also play a role in a pitcher's effectiveness.

The danger zone, so to speak, appears to fall in the 75-100 pitch range. I was surprised that the 100+ range saw pitchers about as effective as during their first 25 pitches. This is clearly shown if we look solely at OPS.

When faced with the decision of whether or not to remove a starting pitcher from the game, the manager must consider these underlying trends in performance against how the pitcher looks on the mound. These are decisions that I don't envy Matheny having to make. With so few experienced starters likely to fill the 2014 Cardinals rotation, it will be interesting to see how quick the manager's hook is during the regular season.