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We are now a week and a half into the (interim) reign of George Brett as Royals hitting coach. Brett took over the task of straightening out Mike Moustakas and Eric Hosmer when tandem hitting coaches Jack Maloof and Andre David were re-assigned within the organization. There are surely plenty of theories circulating around Kansas City as to why the Royals made the switch, but at the end of the day, they probably all boil down to "the kids aren't hitting."

It's a common script. The hitters aren't hitting as well as we thought they would at the beginning of the year, and someone must be sacrificed. Since the problem is the hitters, it must be the fault of the hitting coach. And then the spin machine goes into high gear. The new guy will have a "better connection" with the young guys. He's more hands on or hands off or hands in the air and waving them like he just doesn't care. He worked with these guys in the minors. He was a Hall of Fame hitter himself. And then the next night, the team goes out, scores seven runs (huzzah!), and someone declares "mission accomplished!" In the same way that the best quarterback on the football team is the backup quarterback, the best hitting coach in the league is the new guy in his first week.

In fact, the most common rationale for firing the hitting coach that I've heard is that it will "send a message" to the hitters to "wake up." (This is also the function of an alarm clock.) The firing of a hitting coach is a signal that can't be missed by major league hitters, and like kicking a piece of electronic equipment when it isn't working, it can only do good things.

Does firing the hitting coach actually work? Does it make the hitters on the team better? We do have evidence that a hitting coach can have a strong effect on a team. If we assume that teams have some idea of what they're doing, they should be able to spot a bad hitting coach, and if they have a better one, to slot him in there. Right? Then again, maybe the hitting coach isn't the problem. Maybe he's working hard and the hitters just aren't as good as everyone thought they were.

If firing the hitting coach works, we ought to be able to see some effects, right?

Warning! Gory Mathematical Details Ahead!
Thanks to the fine folks at Retrosheet, we have a list of coaches who worked for teams during each season, and their start and end dates on the job. And sure enough, some teams have more than one hitting coach listed, and one seems to start right after the other one comes off shift.

I looked at all seasons from 1998 to 2012 ('98 because it was the first instance of Retrosheet recording a hitting coach change), isolated teams where there had been a change of the hitting coach, and coded all plate appearances for that team based on whether it took place under the team's Opening Day hitting coach or his replacement. A hitter must have had 250 PA overall in the season and at least 100 under each of the hitting coaches to qualify for the analysis. He also needed to be facing a pitcher who faced more than 250 batters (of any sort) in the season in question.

I used the log-odds ratio method to investigate rates of the seven principal outcomes of a plate appearance (strikeout, walk, HBP, single, double/triple, home run, or out on a ball in play), which I have explained in more detail elsewhere. This controls for batter and pitcher quality. We want to make sure that if the new hitting coaches, as a group, do better, it's not because the team simply gets better hitters or faces an easier stretch of schedule. The nice thing about looking at different hitting coaches within the same team is that we don't need to control for home stadium or league/year.

I ran a series of binary logit regressions predicting whether each plate appearance would end in each of the seven principal outcomes, controlling using the above log-odds ratio, a dummy variable for platoon advantage within the plate appearance, and of course, the variable that coded for whether this was pre-firing or post-firing. If firing the hitting coach really does work as a signal to "wake up," then the pre/post variable should show some effect.

And it did. (Surprise!)

Hitters, in general, performed better than expected under a new hitting coach. They made fewer outs on balls in play and hit more singles and home runs than would have otherwise been expected. The magnitude of the difference was in the area of about one percentage point, which is equal to 10 points in OBP, plus roughly 15 points of SLG. According to the model, firing the hitting coach made everyone on the team about 25 OPS points better.

Curious, I checked whether firing a pitching coach had the same effect. For the most part, I did a find-and-replace command and swapped "pitching" in for "hitting" using the same basic framework. The conclusion: It doesn't work for pitching coaches.

Brushing Up My Latin
Post hoc ergo propter hoc. ("After this, therefore, because of this.") It's an argument in formal logic that states that because one event (a team's offense getting better) follows another (firing the old hitting coach), it's not necessarily the case that one caused the other. It's also one of the few times that I get to use my four years of high school Latin (the other time was when they announced the new Pope.) One event might have caused the other, but we can't assume that without further evidence. Here we do have the evidence that this blanket improvement holds when looking at multiple cases (there were 27 cases of teams switching hitting coaches in my data set). But maybe there are other things at work.

One thing that baseball is famous for is over-reacting to small sample sizes. Often teams will go through slumps that are little more than random variation, and the poor hitting coach will take the blame. His successor gets to look like a hero when the team suddenly "improves" because of regression to the mean. This is known more broadly as the "punishment" fallacy. If you have a particularly good day, I might praise you, but the next day, you regress to the mean and it looks like my praise made you worse. If you have a particularly bad day, I might yell at you, and the next day, it looks like my yelling made you better.

But let's leave regression to the mean aside for a moment. It's probably involved, and that's worth noting, but I think there's another, less talked about issue that we need to discuss. The teams that fire their hitting coaches (and the hitting coaches who get fired) are a very selective sample. There are plenty of teams who don't perform to expectations or who are just downright awful, but who don't fire their hitting coach. Maybe he's a nice guy. Maybe the team understands that he's doing the best he can with a bad hand. Maybe he has naked pictures of someone in the front office. But he sticks around for a reason.

The hitting coaches who get fired are the ones who are not only shepherding under-performing hitters, but are also perceived to be the reason for the problem and to have no hope of being part of the solution. Maybe the hitters are reporting that they really can't connect with this guy. In some way, the hitting coach is so bad that a team is willing to disrupt the usual routine and grab whatever replacement-level hitting coach happens to be out there.

It's probably not the act of firing the hitting coach that makes the difference. It's not about sending a wake-up message. It likely has more to do with the "addition by subtraction" that comes with removing a guy who was so clearly, for one reason or another, bad at his job that it was worth firing him mid-season. So, if you read this and think, "I wish my team would fire their hitting coach, if only for the 10 points of OBP," you've got the wrong idea of how this all works.

But these findings do mean something interesting. There are apparently hitting coaches that are so horrid that firing them and replacing them with some interim guy (remember, the other 29 teams already have hitting coaches) can boost performance by a good amount. Even if some of that is regression to the mean, it's still worth mentioning. If a hitting coach can be that destructive, chances are that he could be somewhat equally constructive, and those soft factors like good rapport between a coach and his players, or a good match between the learning styles of the player and the teaching style of the coach can make a noticeable difference for a team. It might be hard to measure these, but a team that could do it, upgrading either its hitting coach or the hitting coach's approach, could draw a good deal of benefit from doing so.

Thank you for reading

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Post hoc ergo propter hoc just makes me think of The West Wing.
Same. Always struck me as far-fetched that Josh didn't know what it meant.
I've never watched the West Wing.
I'm sorry.
Seriously, Russell? If a team fires a hitting coach, the hitters have been underperforming. If they hire Mickey Mouse as his replacement, they will do better because of regression. You mention this and then essentially dismiss it.

How can you draw any conclusions whatsoever without controlling for regression, which is inevitable?
I do think regression to the mean is in there, and stated as much in the piece. I don't know how much of the improvement is due to regression to the mean (and I'm not immediately sure how to model that), but there may very well be more to it.
You know it's time to replace the hitting coach when the results of too many at-bats is "Habemus popup."