Pitch Quality 4: Solving the Times Through the Order Penalty

Written by: Ethan Moore (@Moore_Stats)

This post is the fourth part of my Pitch Quality Series. The previous articles in the series can be found here: Measuring Pitch Quality, Pitch Quality 2: Estimating WAR, Pitch Quality 3: Times Through the Order.

Hitters do better the more they face a pitcher in a game. This is the Times Through the Order (TTO) Penalty with which we are likely all familiar by now. For a refresher, there are two main hypotheses for why we see this trend which are:

Theory Number 1: Starting pitchers get tired as the game goes on and throw worse pitches as a result of fatigue. These pitches get hit more than their pitches earlier in the game, so hitters’ stats are generally better the more they face the same pitcher in a game.
Theory Number 2: Hitters adapt to the pitcher each PA, increasing their chances of hitting a pitch of the same quality later in the game than earlier in the game, so hitters’ stats are generally better the more they face the same pitcher in a game.

In my previous article, I showed there was insufficient evidence to believe that this effect is a result of Theory Number 1. This leaves only Theory Number 2 (or some other theory I haven’t considered, of course).

Logically, I think Theory Number 2 makes sense. But on a deeper level, it’s pretty radical. If this theory is true, it would have sweeping implications about how hitters hit. For example, if we say that hitters’ inherent ability to hit a certain pitcher improves throughout the game, can’t we then say that a hitter’s “true talent level” isn’t really ever a constant?

Also, shouldn’t we be able to measure which hitters are best (and worst) at making these in-game adjustments and fold that information into our player evaluation, player development, and player projection systems? As far as I know, this attribute of a hitter’s offensive profile is not measured anywhere in the public sphere of baseball research.

I believe all of these implications (and more) are only possible if it can be shown that Theory Number Two, that hitters improve over the course of the game due to increased familiarity with the pitcher, is supported by the data.

In this post, I will lay out what I believe to be the necessary evidence to support the likelihood of Theory Number Two.

Methodology

In order to support Theory Number Two, we have to establish that hitters generally do better when they are more familiar with a pitcher than when they are less familiar with the pitcher. Currently, there is no way of quantifying how familiar a hitter is with a pitcher. If there was, this project would be a lot easier! So that’s a dead end right? Wrong!

We’ll do our best to estimate how familiar each hitter was with the pitcher for every PA in 2019. Since it follows that a hitter would get more familiar with a pitcher the more they face each other, we can use Times Through the Order as a proxy for familiarity.

If hitters tend to do better in High Familiarity Situations than Low Familiarity Situations, Theory Number 2 will be supported. An example of a High Familiarity Situation is a Plate Appearance where the hitter has already faced the pitcher twice in the game. An example of a Low Familiarity Situation is a Plate Appearance where the hitter is facing a reliever who was just brought into the game.

Case Study:

To make this more concrete, here is an example of a High and a Low Familiarity Situation as I’ve defined them.

High Familiarity Situation: Christian Yelich faces Jack Flaherty in the 5th inning. It is their third matchup of the day.

Low Familiarity Situation: Christian Yelich faces Archie Bradley in the 5th inning. It is their first matchup of the day.

Batter success in this case will be measured with the following formula:

Or, more scientifically:

Note: Expected Pitch Run Value is my Pitch Quality score for that pitch

Doing this adjusts our evaluation of the batter for the quality of the pitch. In other words, the hitter only gets credit if the result of the pitch was better than expected by pitch quality. This is good!

Results

Here’s what you’ve been waiting for.

Here are my results. Don’t panic! I’ll interpret below.

The top axis is how many times through the order the pitcher is in the game. The side axis is how many times the hitter has hit in the game.

In the top left box, when hitters and pitchers are in their 1st time through the order, hitters generally perform as expected. But take a look at the row in which hitters are in their third plate appearance of the day.

Hitters outperformed the quality of the pitches they saw by 8.59 runs per 1000 pitches when facing a starter for the 3rd time in a game (Hitter TTO = 3, Pitcher TTO = 3). In contrast, hitters only outperformed the quality of the pitches they saw by 3.85 runs per 1000 pitches when facing a fresh reliever in their 3rd PA of a game (Hitter TTO =3, Pitcher TTO = 1).

This is why MLB teams have increasingly suppressed their starters’ opportunities to face the order a 3rd time! Because relievers do so much better in this situation!

Now let’s take a look at the far left column.

Here, we can see that hitters’ output above expected when facing a pitcher for the first time increases throughout the game as the number of plate appearances per hitter increases. To me, this is evidence that hitters ‘warm up’ throughout the game. Perhaps this contributes to why hitters tend to do better later in games than earlier in games.

Here’s the final row of interest in this piece:

Generally speaking, this is a pretty grim chart for pitchers—except for this row. Here, we see that when facing hitters for the first time, pitchers tend to dominate if they have already gone through the order once or twice. To me this indicates that, all else being equal, starting pitchers fare worst the first time through the order, do best the second time through the order, and still do pretty well the third time through, all else being equal. This fact was corroborated by the graph at the end of my last article.

Case Study, Revisited

For the visual learners, let’s revisit our case study.

Here’s the entire video of Christian Yelich in a High Familiarity Situation, having seen Flaherty twice already in this game before this plate appearance. Here is where this pitch falls on our chart.

So what does he do?

He singles on a damn good pitch. This is a 96 mph fastball painted away thrown by a really good pitcher. But Yelich had seen Flaherty twice already in the game.

Advantage: Yelich

Now let’s see the entire video of Yelich in a Low Familiarity Situation, having not seen Bradley at all in this game before this PA. Here’s where this pitch falls on our chart:

What does he do?

He misses a completely hittable pitch. Fastball. Center cut. He’s frustrated. If the starter is still in, he may crush this pitch. But the starter isn’t still in and hitting a pitcher for the first time in a game is hard!

Advantage: Bradley

Note: This was a completely cherry picked example in order to bring the results of the table to life.

Takeaways

If you recall, we needed to show that hitters do better when they are more familiar with the pitcher than when they are less familiar with the pitcher in order for our Theory Number 2 to be supported.

The chart above shows that in 2019, hitters in their second plate appearance of the game facing the starter for a second time did 44% better than hitters in their second plate appearance who faced a fresh arm for the first time in that game. Additionally, hitters in their third plate appearance of the game facing the starter for a third time did 123% better than hitters in their third plate appearance of the game facing a fresh arm for the first time that game.

After all of this, I can confidently say that there is much more evidence for Theory Number 2 than Theory Number 1. In other words, the evidence suggests that the Times Through the Order Penalty is more so a result of hitters getting more familiar with a pitcher the more they face each other in a game than a result of pitchers getting tired and throwing lower quality pitches as the game goes on.

As I mentioned in the intro, this finding is more wide-reaching than just solving the mystery of what causes the TTO Penalty. It gives us a window into how hitters think in the box and how hitters’ abilities are constantly changing based on previous events (something that is not currently baked into any public baseball analyses). Going forward, there is more work to be done about hitter perception, which hitters are particularly good or bad at making these in-game adjustments, how this skill changes over time for hitters and whether that change may predict future on-field results, and whether this skill can be improved by targeted training.

But for now, let’s just be happy we cracked a baseball mystery!

Thanks for reading. Feel free to reach out with questions or comments on Twitter: @Moore_Stats

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