Baseball Therapy: What is a Good Hitting Coach Worth?

Two weeks ago in this space, I asked what a good pitching coach—someone like noted magician Leo Mazzone—is worth to a major-league team. I came up with an estimate that Mazzone might have been worth four wins to the Braves (and Orioles) per year during his tenure.

Well, what about a hitting coach?

Warning! Gory Mathematical Details Ahead!
The nice part about this article is that I took my syntax for the pitching coach one and did a find-and-replace for the word "pitching" and replaced it with "hitting."

I used the same basic method as before, but to recap:

• I studied the 1993-2012 seasons.
• The hitter played for the same team all year, and that team had the same hitting coach all year. If he was traded, or the team changed hitting coaches in the middle of the season, the hitter was assigned to a blank hitting coach. Also, the hitter needs to have operated under more than one hitting coach in his career.
• Only hitting coaches who had 10 qualified batter-seasons were included (hitter needed a minimum of 250 PA)
• Figures are park-neutralized to the best that I was able and era-adjusted to 2012 levels. I calculated rates of seven outcomes: strikeouts, walks, hits-by-pitch, singles, doubles/triples, home runs, and outs on balls in play.
• AR(1) covariance matrix for player results pegged to the calendar year
• Fixed effect for age (to set a general aging curve)
• Fixed effect for hitting coaches (which is what we will look at).
• Through all this, we create a model that controls for what the hitting coach had to work with (the model knows that certain hitting coaches had a team full of good/bad hitters), park, era, and age.

The Results

Something that I noticed right away was that a lot of the same guys kept showing up near the top (and bottom) of the list for strikeouts, walks, and home runs. Perhaps some coaches encourage a three-true-outcome approach?

To look, I ran a correlation matrix among the 101 qualifying coaches to see whether there were inter-relationships between the effects that different coaches had. The correlations weren't as strong as I thought they'd be. Strikeout and walk effects correlated at .29, and strikeouts and home runs were at .137. Walks and home runs were at .101. The three true outcomes don't seem to vary together very closely.

The clearest dividing line was along an axis that split singles and outs in play from walks and strikeouts (and to some extent, home runs). The effect that a hitting coach had on singles and the effect on strikeouts correlated at -.409, and singles and walks were at -.441. Outs in play correlated with strikeouts at -.730, and outs in play and walks checked in at -.535. Outs in play also lined up with home runs at -.426. Singles and outs in play are usually the domain of guys who make a lot of contact and take less risky swings. So, if there is an axis on which hitting coaches fall, it is those who preach a conservative approach vs. those who preach swinging away.

That's an interesting finding. I've done some work on plate discipline in these sorts of terms. In fact, I once created a couple of measures of plate discipline in terms of signal detection theory. There's the ability of a batter to pick out good pitches from bad (sensitivity), and there's his tendency to swing or not swing (response bias) when a pitch is borderline. (If you want the gory mathematical details of how that's calculated, read that article). Of course, a hitter should swing at the good ones and lay off the bad ones, but that's harder to teach than just saying, "Larry, you should swing more."

In fact, there are a lot of questions that can be conceptualized through signal detection theory ("How should I handle my investment portfolio?") that usually elicit advice along the lines of changing one's response bias ("Be more aggressive!") or the always unhelpful (even if true), "You need to find a balance." No one ever gives advice on how to tell the difference between a good investment (into which you should pour money) or a bad one, mostly because they probably have no idea. Perhaps hitting coaches are doing the same thing?

I got to wondering whether hitting coaches really are helpful in teaching plate discipline. This chart shows the coaches who were best (and worst) at teaching pitch selectivity. Someone once asked me to sum up this stat in plain vocabulary. I responded, "Strikes are bad." For this stat, higher is always better, although the numbers don't correspond to some specific event. (If you have a background in signal detection, you know what I mean. If you don't, just trust me. I know what I'm doing.)

Some frame of reference for scaling is important here. The range among hitters in 2012 with at least 250 PA was from .92 (Carlos Quentin) to .23 (Cody Ransom), and the standard deviation was .118. So, the best hitting coach might buy you half a standard deviation in pitch selectivity. And that's the best one.

I then looked at the hitting coaches who had the greatest effect on response bias (whether a hitter is more likely to swing at that borderline pitch or not). In this case, you want to see a good balance, and the perfect balance point is 1.00. A hitter who has a high response bias will swing (and miss) a lot, but he will also put a few more balls into play. A hitter with a low response bias will take many more pitches and have a lot of extra called strikes, but will also earn some extra balls. For a hitter who is below 1.00, you want him to swing more. For a hitter above 1.00, you want him to swing less.

Again, to give some sense of perspective, the standard deviation is .08, so again we're talking half a standard deviation at the extreme outliers. But that doesn't tell the whole story. The thing about response bias is that when a player has a response bias around 1.00, a small move in either direction actually can have a pretty big effect in the raw number of extra strikes he has. And a good chunk of MLB hitters in 2012 (44.2 percent) were between .95 and 1.05. So, an extreme coach on one end or the other will have some pretty big effects on a good number of his hitters.

Finally, for all seven outcomes of a plate appearance, I prorated the change in outcomes that we might expect from the model for each hitting coach over the course of 6000 plate appearances (roughly what an average team sends to the plate in a year). I assigned a linear weights value to the events and expressed this in runs.

By this measure, the best (and worst) hitting coaches were:

Okay, time for the smell test: 91 runs per year over the average hitting coach is a lot. Hurdle was the hitting coach in Colorado before the humidor (1997-2001), and then with the Rangers in 2009. Perhaps the model is crediting him too much with inflated numbers that came from his hitters playing in Coors Field. Lenny Harris and Tim Wallach were both hitting coaches for two years, and Chili Davis was a rookie last year, so we may have some small sample size issues. Kevin Seitzer, who has five years as a hitting coach under his belt (2007 Diamondbacks, 2009-12 Royals), checked in with 58.32 runs above average. Jim Presley has logged a decade as a hitting coach and rates at 50.43 runs. If we compare these marks to the 31st-best mark in the data set (Ken Griffey at 13.90), we see that Seitzer appears to be worth about 4.5 wins above "replacement" level, which is roughly on par with what we found for Leo Mazzone.

A Few Conclusions

• Just like with pitching coaches, hitting coaches can have a very big impact on a team, and at a very small cost. Even if the results I'm finding here are twice as big as they really are, the best hitting coach can be worth two wins. Not bad.
• Hitting coaches appear to have much more effect on whether or not hitters take a more aggressive or more passive approach at the plate than teaching them actual pitch selectivity.
• Hitting coaches also seem to be divided into those who teach hitters to put the ball into play and those who encourage a three-true-outcomes approach, although which one of the three true outcomes the hitter will see more of is something of a crapshoot.