Let’s play myth-busters, shall we?

Two outs. Bottom of the fourth inning at Wrigley in a 2-2 tie game. Strolling to the plate for the Cubs is Carlos Zambrano. He’s a good hitter-for a pitcher-with a lifetime .236/.243/.396 triple-slash line and 20 career home runs. In the American League, he’d be on the bench right now with a jacket draped over his right arm, but since this is the senior circuit, he’s out there hacking away.

This time, he gets a piece of an Ubaldo Jimenez off-speed pitch and beats it into the ground to the left side. It’s headed for the hole, but Troy Tulowitzki is ranging to his right and if anyone is going to get to that ball, it’s Troy Tulowitzki. Still, it’s going to be a tough play, and if Tulo has trouble with the transition to his throwing hand, maybe it’s an infield single. Zambrano’s gotta be asking himself, “Should I run this one out or just do one of those ‘couple of fake running steps down the first-base line’ things? Is it worth putting out the effort?”

Of course, these decisions are made within the space of milliseconds, and soon Zambrano is lumbering down the first-base line, huffing and puffing. He reaches first base just in time… to see the umpire raise an arm declaring him out. Tulowitzki sure plays a mean shortstop, Z allows himself the luxury of thinking for a moment, but he’s got other worries now. He’s a little gassed from the 90-foot dash he’s just done, and now he has to grab his glove and go out to pitch the top of the fifth.

Somewhere in the broadcast booth, an announcer tells the Cubs faithful gathered around their radios that, “The tough part about the pitcher batting is that after a close play like that, where you have to run, it’s got to affect him in the next inning.”


The way that broadcasters usually speak, the implication is usually that the pitcher is likely to fall apart in the next inning. If he gives up three runs, they might blame it on his having to bat the inning before. Is this true? Is a pitcher really more likely to falter after batting? Let’s take a look at what the data actually says. Start with a database of everything that happened in a National League park during the Oh-O’s (that would be the decade that ended a week and a half ago.) Next, figure out if the pitcher on the mound batted in the previous half-inning or not. Simple so far.

It’s tempting to say, “OK, show me an aggregated pitching line split by that factor.” The problem is that there are some hidden confounds that could influence those numbers. Consider for a moment two factors that no doubt influence a pitcher’s performance: his pitch count and the quality of the opposing batters. Why might these be confounds? A pitcher whose pitch count is up is more likely to be pinch-hit for when his turn comes up again, meaning that we are less likely to get to see him with a high pitch count and having batted the inning before. We also need to account for the fact that, particularly in a close game, a manager may allow his pitcher to bat if he knows that the bottom of the other team’s lineup is coming up, but not the heart of the order. If the middle of the order is coming up, it’s better to send out a fresh reliever, and if the pitcher’s not going back out, it’s better to send up a pinch-hitter.

Warning: Gory details. Viewer discretion is advised.

So, to control for these, let’s use a trick more fully explained elsewhere, that uses a binary logit regression to model the probability that a given plate appearance will end in a specific outcome (say, a strikeout), while controlling for various other factors. It first controls for the relative strengths of the batter and pitcher, using the odds ratio method. Because binary logit works by modeling the natural log of the odds ratio, the natural log of the expected odds ratio of the outcome between this batter and this pitcher was taken, out of a pool consisting only of plate appearances in which a batter with 250+ PA in the relevant season faced a pitcher with 250+ batters faced.

In this particular case, the pitcher’s pitch count and whether or not he and the batter were of the same hand were both controlled. The dichotomous variable of whether the pitcher had to bat in the half-inning before was then factored in which, after everything else has been controlled, is the variable most interesting to testing this theory.

This type of analysis requires that we make a few assumptions. We assumed that a league-average pitcher was facing a league-average hitter. You can plug in any numbers you want, but you have to plug something in, and league-average makes the most sense of anything. We assumed that the pitcher had thrown 25 pitches (there’s no particular reason for that number, we just have to put something in). Numbers were then run for the eight major outcomes of a plate appearance: walk, strikeout, single, double/triple, HR, HBP, reach on an error, and out in play.

So, was there a significant effect? Yes. A minuscule one.

The probabilities of the plate appearance ending in a strikeout went down by a matter of a few hundredths of a percentage point. Prorated out to 700 plate appearances, the effect was three strikeouts lost. Most of those percentage points seemed to go into the outs-in-play bin (about 2.5 of those strikeouts). That’s assuming that a pitcher had to pitch after having just batted all the time. There was also an even smaller effect in which the rate of singles went down and the rate of extra-base hits went up slightly. It appears that a pitcher does become a little bit easier to hit and to hit hard. However, the scale of these effects was so small as to be negligible to any decision-making process. Having to bat does not turn Carlos Zambrano into (Russell’s eleventh-cousin-once-removed) Celine Dion. (That’s true. Would we make something like that up?)

Just to make sure all T’s were crossed, a few variations on this method were applied. What if we only looked at situations where the pitcher had made contact with the ball? What about situations in which we knew he had to do some running because he got on base via a hit? Did it make a difference if he was the last batter in the inning? It turns out that the answer to each was an overwhelming “no.” The effects on game outcomes were still significant, but also very, very small.

PITCHf/x Checks In

Thus far, our efforts have focused on the results: Does performance data change after pitchers step to the dish relative to when they get to spend a half-inning munching on sunflower seeds and warming their throwing arm? From a technical standpoint, the outputs indicate that a delta does exist but is lacking in clinical significance despite its statistical significance-the differences are real, but matter very little. Shifting to the inputs drawing these outputs, what does PITCHf/x data have to say? We can theorize that the underlying pitch data should appear similar in both sets of data given the similar results. Using data from 2008-09 and across all pitchers with at least 30 plate appearances, four different tables were built: one including pitch data after innings in which they batted, another with pitch data in innings after not only batting but running as well, and the respective control groups-the pitch data in the other innings.

The rationale behind investigating the base-running aspect under this lens involves the idea of fatigue; while batting could certainly make a difference in the levels of energy and effectiveness of the pitcher, it makes even more sense that a pitcher forced to stay on the bases or hustle around the diamond might lose some energy and effectiveness. Looking at four-seam fastballs, curves, sliders, and changeups, the tables below house pitch percentages, velocities and both movement components. First, the batting vs. non-batting results:

Batting Results    %    velo     pfx     pfz
Fastball         56.2  90.47    5.89    8.74
Curveball        12.1  75.06    5.27   -5.69
Slider           16.7  83.31    2.69    2.55
Changeup         14.8  81.91    6.64    5.24

Non-Batting        %    velo     pfx     pfz
Fastball         58.8  90.58    5.95    8.84
Curveball        10.8  75.12    5.16   -5.58
Slider           16.0  83.35    2.68    2.62
Changeup         14.2  82.01    6.71    5.47

Holding aggregated analysis until the end, here is the running vs. non-running results:

Running            %    velo     pfx     pfz
Fastball         56.6  90.51    5.79    8.78
Curveball        11.9  75.11    5.39   -5.37
Slider           16.3  83.42    2.75    2.51
Changeup         15.0  81.94    6.55    5.18

Non-Running        %    velo     pfx     pfz
Fastball         58.3  90.56    5.94    8.82
Curveball        11.0  75.11    5.17   -5.62
Slider           16.2  83.34    2.68    2.61
Changeup         14.3  81.99    6.71    5.43

What do we see here? For starters, pitchers throw a lower percentage of fastballs after batting the half-inning prior, which is counterintuitive in the sense that it suggests pitchers vary their selections more when supposedly under more physical duress. The percentage shift is extremely small, however, made up by an increase in curveballs, with then numbers of sliders and changeups barely changing. Again, the clinical significance of the delta here is missing. After being on base, a similar drop in the heater rate is evident, with the differences accounted for by ever-so-slight upticks in curves and changeups. From a pitch selection standpoint, nothing here stands out for even a careful observer to spot. The idea of there being any fatigue evident might point towards more fastballs in innings after batting or running; here, we get the insignificant opposite of that expectation.

Moving on to velocity, a larger delta for fastballs is observed in the batting category than in that where baserunning’s an additional part of the pitcher’s duties, but how important is a drop of 0.11 miles per hour? Hitters may be well versed in identifying the tiniest of tells, but it’s far-fetched to suggest that Craig Counsell knows a pitch is thrown 90.27 mph instead of 90.38 mph. Then again, while he and others might be able to make this distinction, the bottom line remains that we do not yet know how hitters react and respond to such situations, or how their perceptions are affected by shifts of various magnitudes. The other three pitches experience even less of a change in velocity, registering reliably similar radar gun readings, though these off-speed offerings are not known for velocity and are more prone to changes in movement.

Movement is tricky to evaluate because a pitch is built upon both vertical and horizontal movement, yet the interaction is tough to quantify, leading to isolated analyses of both horizontal and vertical results. Looking at the fastballs, the change in movement occurs on both fronts, with a 0.05-inch drop horizontally and a 0.10-inch drop vertically. Alone, neither of these seems to matter much, but taken together the fastballs are thrown with less overall movement after batting. After running the bases, however, the shifts switch places, with a minuscule drop in vertical movement, but 0.15 inches of horizontal movement lost. This raises an interesting question for another day, in how a drop of 0.05 vertical and 0.10 horizontal inches compares to losing 0.15 horizontal and 0.05 vertical inches.

In both scenarios sliders feature deltas similar to those of fastballs, where the individual component changes do not seem very different but, taken together, can alter the shape of a pitch more than we think. The more interesting movement alterations occur with changeups in both groups and curveballs after running. The numbers speak for themselves: changeups are thrown with considerably less movement after batting or running, while curveballs after running move more horizontally than vertically relative to not batting or running at all.

While pitch selection, velocity, and even release points remain unchanged for the most part after hitting or running, the signs of fatigue surface in the form of movement, one of the areas of PITCHf/x data that remains relatively unexplored. We know about movement in general terms, in that decreases are considered suboptimal, but we do not know about the ramifications of a quarter-inch drop in one of the components. These results make sense when used in conjunction to prior research on similar subjects, which conclude that fatigue surfaces more in the movement of pitcher’s offerings than in their velocity or any other departments.

Wrapping Up

Having to bat or run in the top of the inning does change what we can expect from a pitcher in the bottom of the inning-slightly. Though the changes in movement could hold clinical significance in any portion of this study, it did not result in a huge downturn in performance, lending credence to the idea that these movement shifts, however different relative to the other inputs, might matter very little. Broadcasters who say that there will be an effect are correct, but when they imply that it will be a massive shift, they’re wrong. A pitcher might be a bit more tired in such circumstances, but he is unlikely to start throwing three miles per hour slower or from a much lower release point, just as he is unlikely to suddenly serve up gopherballs as if he were on Eric Milton-autopilot.

Myth busted, for now.

Russell A. Carleton, the writer formerly known as ‘Pizza Cutter,’ is a contributor to Baseball Prospectus. He can be reached here.

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Fantastic piece!
It's interesting, but it feels incomplete, and I'm sorry to say is poorly presented.

The most interesting and relevant data here are the batting results, but where are they? We get a text summary, but no table. The Pitch/FX data are the labor pains, not the baby.

One other point I would like to see addressed is, can you quantify and test the results of running hard, which you evoke so well in the intro? I.e., do pitchers perform worse after going first-to-third on a single, or scoring on a double?

Agreed, very nice piece of research and well presented. I like the lead-in and the take-away. Thank you also for leaving the gory details elsewhere!
I think an inning is too long to use as the independent variable. If you're controlling for the effect of the pitcher being winded after running around all over the place, it would make sense to see how many hitters it takes for him to catch his breath. It seems reasonable to suggest that the first hitter Zambrano faced in your example would be the one most likely to benefit from any significant fatigue effects.
Interesting hypothesis. If I have a moment, I'll go back and check that.
Sorry, but I can't appreciate the end result, when there were just too many variables, and so much conjecture. The premise was great, and the article was artfully done, but the specifics remind me of HOF ballot justifications.
A step by step derviation of the methodology would really help me out in understanding what you did. The paragraph form of the explanation just doesn't do the work justice. It's like trying to explain physics without ever writing F = ma on the board.

I know its not BP's job to teach people probability and statistics, but it sure would help me to better understand the methods used and be able to leave better comments. Maybe going through an step by step example once, and then linking to it when it's used?

Maybe some of the more quantitatively-oriented writers could consider having a Technical Appendix for their articles, in an effort to allow everyone to have their cake and eat it too. The people who want to be able see the gory details (with mathematical notation) would get what they want; the people who want to read a smooth-flowing article without getting bogged down in technical details would get what they want.
Not a bad idea. I don't know whether if it would work logistically on our end (it might!) but it is a good idea. I think in the mean time, I'll flag the "gory details" part so that if people want to read it or want to skip it, they can make up their own minds.
Rowen, stop making so much sense all the time. Gosh!
Did you control for home ballpark effects? Sure, they'd be weak but it seems that in a high offense environment, the pitcher will come to bat more often, the pitcher fares worse than average and (perhaps) the pitcher is left to face more opposition batters than in a low offense ballpark. If that's the case, then there's be some correlation not causation if we don't control for ballpark effects.
Guys, in the pitch f/x data, did you control for that quality of the batters and for pitch count? IOW, is the control group matched up, batter-wise and pitch count-wise, with the non-control group, in the pitch f/x data, as it is in the "outcome" data? As you said, pitchers will tend to hit when the bottom of the lineup is coming up the next half inning and when their pitch counts are not high, at least late in the game. Early in the game, pitchers will tend to hit in the same inning as the opposing pitcher will tend to hit. So it is really critical to control for the quality and even identity of the batters, as well as pitch count.
It seems that most of the 9 people who commented so far feel that this is an interesting/helpful piece. I have to say though that for most BP readers, including myself, most of this article went over our heads. Unfortunately, I'm finding myself adding another column to my mental "SKIP" list on BP (along with Prospectus Q&A). I hope that with the departure of Sheehan we're not going to see BP focus more on statistical analysis and move away from good commentary and writing altogether.
Pitchers strike out so much, and such a plate appearance I'm guessing involves less exertion than a ball in play, especially reaching base and having to run all-out, slide etc. I wonder whether an effect might be detected if their innings after striking out were set aside. If the data would support it, it would be interesting to see whether there is any difference among all the possibilities: innings after no at-bat, innings after a strikeout, innings after making an out in the field or reaching base and getting stranded there, and innings after reaching base and having to run the bases.
What about a similar study about AL pitchers who have to sit on the bench while their team has a long inning at the plate? That could be interesting as well. Maybe anytime 7 or more batters come to the plate, or a half-inning that lasts 20 or more minutes (if you have access to that kind of data).
A well-conditioned professional athlete ought to be able to sprint 30 yards without falling apart.