#### Introduction

I just finished reading The Arm by Jeff Passan — it is an interesting description of the billion-dollar industry of pitching arms in baseball. It is remarkable that teams pay millions of dollars for pitchers on the free-agent market, but we don’t seem to have a good handle on what is causing the high number of elbow injures and Tommy John surgeries.

One specific thing discussed in the book is about limits on pitch counts. There is a general feeling that all pitchers (young and old) should limit the number of pitches they throw. At the major league level, one is familiar with the 100-pitch limit for starters. I don’t know why 100 pitches is the magic pitch limit (why not 95 or 105?), but this suggests several explorations.

- Do MLB teams generally stay within this 100-pitch limit for starters? Has there been any change in pitch counts for starters in, say, the last 20 seasons?
- Is there much variability in the pitch counts for starters between teams?
- One thing we noticed in an earlier post was that plate appearances are getting longer — that is, the average number of pitches per plate appearance has been increasing over recent seasons. Pitchers want to be efficient — that is, throw only a few pitches per batter. Can we identify some of the most efficient pitchers in the last 20 seasons?

#### The Data

Using Retrosheet play-by-play files, I collected the number of pitches thrown for each starter in each game for all games played in the seasons 2000 through 2019. In addition, I collected the player’s team, the number of batters faced, and the final inning for each of these starts.

#### Starter Pitch Counts in 2010

Let’s look at the number of pitches thrown by starters in 2010. I construct bar graphs of the individual pitch counts below broken down by team. I have added a blue vertical line reference value of 100 pitches to each graph. Obviously, some of the pitch counts are small due to poor starter outings. But the general impression is that the starters for the 2010 teams appear to average about 100 pitches with some variability. For most teams, the percentage of pitch counts between 90 and 110 is 50 – 70 %.

#### Starter Pitch Counts in 2019

Let’s fast forward to the recent 2019 season — I have constructed a similar display of starter pitch counts in this season. There are several changes that I see:

- Some teams (such as TBA and TOR) seem to have a large number of small pitch counts. This reflects the new strategy of opening the game with a reliever.
- Although some teams seem to still average 100 pitches, I see a general tendency for teams to have smaller than 100 pitches for their starters.

#### Focus on the Starters Who Make it to the 5th Inning

There are several types of starts including “rough starts” that last only a couple of innings and starts by relievers that we see in current seasons. During a game, a manager has to decide when to take out a starter — that appears to be when the magical 100 pitches comes into play. To get a handle of this decision making, I decided to focus only on the games where the starter makes it into the 5th inning. For this subset of starting pitchers, what are their pitch counts? I collect the mean number of pitches for these starters (the ones who made it into the 5th inning) for each team for each of the past twenty seasons. I plot these values below — I add a smoothing curve and a red horizontal line at 100 pitches.

We see some interesting things.

- First, the “average” team seemed to average 100 pitches for the seasons 2000 through 2014, but this “average” team is averaging fewer than 100 pitches in the last five seasons.
- There is remarkable variability between teams which seems to reflect different opinions about the 100-pitch limit. For example, the 2012 Colorado team only averaged 87.2 pitches per start and the 2012 Tampa team averaged 105 pitches per start.

Another way to look at this is to focus on the mean number of batters faced by a starter that makes it into the 5th inning. How has that varied across teams and seasons? Since you hear a lot about “3 times through the batting lineup”, I have added a red horizontal line at 3 x 9 = 27 batters. We’re seeing a similar pattern across seasons — the number of batters faced for this starter has dropped from 27 in 2010 to about 24.5 in 2019. Again, we see sizeable variation between teams.

Suppose we consider the starters who make it to the 5th inning — what fraction of these starters make it to the 7th inning? We show the graph with a red line at 50%. In 2012, roughly half of these starters made it to the 7th inning, but things are different now. This fraction tends to be only 30% (on average) in 2019, although teams again vary a lot on this measure.

#### Pitcher Efficiency

Since there are more pitches in a game in current baseball, one should value the pitcher who can are efficient — throwing a small number of pitches per batter. One can measure a pitcher’s efficiency by the number of pitches divided by the number of batters faced. Suppose I consider only the pitchers who have 20 or more starts in a season. Below I construct parallel boxplots of the pitcher efficiencies for all players and seasons from 2000 through 2019. Of course we see a general trend of increase of these efficiencies in this 20-year period. I’m interested in identifying the outliers on the low end — these are the most efficient pitchers in these 20 seasons. I’ve identified eight unusual pitchers whose points are labelled with a unique color. Who are these pitchers?

- Greg Maddux (red dot) is clearly the efficiency star — he was the most efficient pitcher for eight of the nine seasons pictured here.
- Bartolo Colon (green dot) had some of the smallest values in the seasons 2012 through 2018. What is interesting is that Colon wasn’t always efficient. His values in the 2000 through 2005 seasons were average.
- Ivan Nova (orange dot) is one of the current efficiency starts in the last few seasons.

#### Takeways and Future Explorations

Here are some takeaways from this brief exploration.

- In a game, each manager has to make a decision about the number of pitches for the starter. What we see is that 100 used to be an average number of pitches, but starting with 2015, this average has been falling. Also there is a tendency for the starter to face fewer batters, on average, and the proportion of starters going deep in games is falling.
- The mean number of pitches for starters seems to vary substantially across teams.
- Teams should value the starting pitchers who are efficient — they are the ones who have the potential to throw complete games.

A followup exploration would explore the factors that affect pitch counts. Here are some factors that might weigh into a manager’s decision when to relieve the starter.

**Injury?**The possibility of a pitcher injury is definitely a factor, but it is unclear how the pitch count or frequencies of starts affects the likelihood of, say, an elbow injury.**Effectiveness?**There is a general feeling that the effectiveness of a starter deteriorates as the pitch count increases. For example, I think one could demonstrate that that a starter tends to get less effective as he faces a batter for the 2nd time and the 3rd time. I probably have done this type of exploration in the past.**Individual effects?**Although there are some general “times through the order” effects, there are pitchers who seem to get more effective late in a game. Also there are pitchers who tend to weaken early in the game. So any managerial strategy about pitch-counts would likely depend on the specific starter involved.