Baseball Therapy: The 10th Man in the Lineup

“There are two things in the world that every man thinks he can do better than anyone else: cook a steak and manage a baseball team.” –former Cleveland Indians owner Dick Jacobs

When I was growing up, Bud Black had a couple of good years for some bad Indians teams. I’m sure that I saw a start or two of his back at Old Municipal Stadium. He arrived by trade in late 1988 and left by trade in 1990, and is now noteworthy for being part of the second longest active trade lineage in MLB. Cy Young Award winner Corey Kluber can trace his ancestry back through a series of trades that in which Bud Black is one link on the chain back to Jerry Dybzynski.

Now Bud Black is the manager of the San Diego Padres, and now is one of the 30 most criticized people in all of baseball. Every single fan in baseball who has access to a keyboard could do Black’s job (and all of the other 29 managers’ jobs) better than he can. Just ask them. Because, after all, what does Bud Black even do? He writes down the names on the lineup card. He walks to the mound, waves his arm to the bullpen, and smacks the starter on his backside when the starter has had enough. He stands there and looks forlorn as the camera focuses on him in a moment of intense concentration. I can write. I can walk and wave my arms. I can smack a grown man on the backside. I can look like I’m concentrating. I could totally rock this manager thing! Not that hard, right?

As fans, we have a far-too-narrow understanding of what a manager actually does on a day-to-day basis. A couple of months ago, I wrote about “The Grind.” Not the MTV dance show, but the fact that baseball is a game of intense concentration that happens every single day, punctuated by alternating moments of heartbreak and elation. After a while, the human body and mind are crying out for a break that won’t come. It’s the manager’s job, whether he wants to or not, to make sure that The Grind doesn’t overtake his 25 charges. What I found was that there appear to be certain managers who seem to have magical powers in combating The Grind and some guys who are bad at it. Today, we’re going to take a deeper look and put some value to that ability.

Warning! Gory Mathematical Details Ahead!

Let’s establish a few things first. We know that over the course of a season, plate discipline gets worse for hitters, in the aggregate at least. Previous research has strongly suggested the obvious. The season is long and the players are tired. The effects aren’t visible to the naked eye (we’re talking about an extra strike every couple of hundred pitches), but the nice thing about big data is that you can see these patterns over time.

I used data from 2010-2014. I started by looking at several ball/strike related outcomes. For example, swing rates, contact on swinging, strike calls on taken pitches, contact rates on two-strike pitches, and whether an at-bat went to a 1-0 count or an 0-1 count. I calculated the batter’s mean, the pitcher’s mean, and the league mean, and created a control variable based on the pitcher-batter matchup using the log-odds ratio method. This gives us an estimation of how often we would expect any of these events to happen, assuming that players always performed at their seasonal averages and that other factors had no impact. Of course, it’s silly to think that no other factors would be in play (that’s the whole point), but now we’ve taken away such counter-explanations as “Well, different players are on the field in April than in September.”

I calculated how many calendar days had passed since a team played its first game of the season. I created a series of binomial logistic regressions in which I modeled the chances that a batter would make contact on a particular swing. I used the control variable above and then added in the “days since Opening Day” variable. The results showed that over time, the same hitters and pitchers would produce slightly (but statistically significantly) different results as the year wore on. In general, a hitter was more likely to swing, more like to miss when he does swing, but more likely to end up with a ball if he takes. The actual effect sizes were rather small. Even late in the season, our expectations might be only a couple tenths of a percentage point or so (1 pitch in a few hundred) different, but seeing that in 2014, the average team saw 137 pitches per game, and changing a ball to a strike (or vice versa) has an average value of around .14 runs, things can add up quickly. On something like two strike contact, the stakes are higher because if you swing and miss at a two-strike pitch… I think you can figure the rest out. The calendar really does subtly and slowly bleed value out of hitters. That’s The Grind.

But, as we saw in my previous article, the players who play play play play play for some managers seem to lose their abilities more slowly. In fact, some managers even seem to have players who get better over the course of the year, and that a manager’s performance in one year was actually very predictive of his performance in the next year. Last time, I looked only at a single measure of whether a pitch resulted in a strike or not (my crude measure of plate discipline). This time I looked at several of these component measures (like contact rate, called strike rate, etc.)

I took all pitches at which the hitter swung from 2010-2014 and created a batter-pitcher matchup control variable for how often the batter was expected to make contact. I added in the number of days since Opening Day and a main effect for manager (for the super-initiated, this guards against the possibility that one manager may simply have better/worse contact-making hitters and assigns a manager credit for this) and then an interaction effect between the number of days and the manager. This interaction term is what we want to look at. When we looked above at the aggregate relationship between time elapsed and the probabilities of a hitter making contact, we saw that the line bent slightly downward. By adding this interaction term, we see how much we should “bend’ that line for each manager. Most of the time, that line slopes downward, but if a manager seems to have an ability to either level it off or even get it pointing upward, this will tell us.

At first, I treated each manager’s season as a separate entity. Bud Black’s 2010 season and his 2012 season and his 2014 season all got their own special interaction term in the regression. Once I had each one of Black’s regressions (along with all the other managers in the sample), I looked at how likely a hitter was to make contact under Black’s (or anyone else’s) tutelage given a standard set of circumstances to put everyone on the same footing, statistically. It’s all a mathematical abstraction, but it’s the only way to try to disentangle a manager from the personnel he has at his disposal.

I assumed that we had a batter and pitcher whom we would assume would produce a 50 percent likelihood of a swing making contact. (Note: The average contact rate on a swing in 2014 was much higher, 79.1 percent. I chose 50 percent for the reason that it was being put into a log odds ratio. The initiated will note that the log of the odds ratio for 50 percent is zero, which allowed me to simply zap that term from the regression, making the math a bit simpler.) I then adjusted that 50 percent chance for each manager-season at 90 days from Opening Day. That basically puts us at the half-way point in the season. In the land of this regression, this hypothetical 50/50 batter pitcher would be a 50/50 shot on Opening Day and slowly adjust itself upward or downward (or sideways) as the days go by. Real life is not so linear, but this gives us a reasonable bird’s eye approximation of what’s going on. For example, given these parameters, in 2012, we would expect this abstract standardized hitter to have a contact rate of 50.3 percent if Bud Black was his manager. In 2014, it would be 50.0 percent. For Ron Gardenhire, those numbers were 49.0 percent in 2012 and 49.4 in 2014. Black’s charges got a tiny bit better and Gardenhire’s hitters did a little worse at making contact over the course of the season.

I repeated the same process for all of the variables mentioned above (two strike contact, counts that go 1-0 rather than 0-1 – which is an antidote to strikeouts, called strike rates).

Once I had the projected numbers by year, I looked to see how well those numbers correlated year to year with specific managers. I used an AR(1) intra-class correlation (for the non-initiated, this is kinda like a year-to-year correlation, except that it can handle multiple data points) to look at how well the “manager effect” on each stat held up over time. For those familiar with DIPS theory, we know that strikeout rates correlate very well from year to year for pitchers, so we consider them to be a “real” skill, but BABIP does not. Using this method, I found the following correlations:

All of the numbers are pretty robust. It looks like that if a manager is good at keeping player’s contact rates up over the course of one season, he’ll be good at it the next year. Even better, it’s pretty good for all of these stats.

Now that we know that these numbers are pretty stable from year to year – and that we’re fairly sure that we’ve identified an actual talent (although more on that in a bit) – I went back to treating 2010-2014 as one giant undifferentiated whole. I calculated each manager’s effect on each of the stats mentioned, and looked to see whether managers who were good at one tended to be good at another. It turns out that the answer was… no.

Among the 29 managers who managed at least three out of the past five years, here’s the correlation matrix.

Not a lot of surprises in that contact correlates with contact and taking pitches for balls correlates with the count going 1-0, but there’s very little correlation between a manager being able to keep his players from drifting too far on making contact while swinging and on only letting the good pitches go by. A manager could be good at one or both (or neither), but success in one tells us nothing about ability in the other. (For the super-initiated, a quick little exploratory factor analysis told the same story.) Still, it all roughly correlates with our working definition of plate discipline. It means that there are different ways that managers can accomplish the same goal of making sure that the grind doesn’t eat away at the value that their hitters can provide, although ensuring that hitters are making contact when they swing is the best correlate for ensuring that managers will do well in helping their hitters in controlling the strike zone.

So, let’s take a look at the managers who over the past five years have done the best at stopping the grind from eating away at their players' plate discipline. To be on this list, a manager had to manage more than three years in the last five. You can read this table as “Given a batter-pitcher matchup that would result in an overall 50/50 chance on Opening Day of a pitch resulting in a not-strike, a player who had manager X would have this percentage of avoiding strikes by mid-season.”

It’s easy to look at those numbers and say “So what?” They’re all bunched together, but remember that over the sample size of 22,000 pitches per year that each team faces, a difference of a tenth of a percentage point affects 22 pitches that end in strikes that didn’t used to. Even if each is worth .10 runs (my best estimate is .097), then that is 2.2 runs of value bleeding away. Davey Johnson, who retired after the 2013 season, seems to be the best at fighting The Grind over the years, followed by active managers Bud Black and Joe Maddon. Jim Leyland is in the middle of that list, and is almost dead on even with holding the line at 50 percent (he’s at .4995), and so Black and Maddon are roughly half a win better than the average manager by virtue of their Grind fighting powers. However, if we take Fredi Gonzalez as replacement level, we suddenly see that Black and Maddon are worth almost 20 runs more than replacement level by virtue of their ability to fight The Grind, and we have already established that this is a real, consistent ability. Much was made of Joe Maddon’s reported $5 million salary. If the ever-popular $7 million per win conversion factor is still valid, the Cubs are getting a deal.

Manager of the Year?

Manager of the Year is one of those awards that’s really hard to figure out. It usually goes to the manager who skippered a team who had low expectations, but still made the playoffs. For a while it went to the manager whose team most out-performed its Pythagorean expectations. I think the assumption there was always “It must have been the manager” rather than “Everyone swung and missed on the players” or “He got really lucky.” In fact, what we know about Pythagorean residuals and about how well coaches and managers are able to influence breakouts in their players says that these sorts of measures are more likely lucky phantasms than manager skill.

Here we have something that is stable and predictable, strips out the conflating effects of whether a manager has good or bad players, and maps onto a manager’s job is to keep the clubhouse going in the face of The Grind, My standard definition for team chemistry is that it is the answer to the question “Why should I bother?” A good manager gives his team a reason to bother. Now, this doesn’t cover everything a manager does in that regard (this has nothing to do with the pitchers, who are half of his roster!), but it’s perhaps a better indicator than what’s been previously used. So, for 2014, here are the numbers.

For what it’s worth, Sandberg led the league in 2013 as well. He might have been given a team that was only good for a sub-.500 record, but they didn’t fade on his watch. (In case you don’t remember — and let’s be honest, no one does — Buck Showalter received the AL award last year, and Matt Williams took it home in the NL) Maybe Ryno deserves a second look. Maybe we all need to take a second look at how we think about managers.

From what we’ve learned today, there’s no one magic way to fight The Grind, but it can be done and it is very powerful when a manager does. A manager can add something on the order of 2 wins above “replacement level” on this one skill alone. We now know that being able to keep hitters from losing their contact abilities is important. It’s hard to do anything helpful when you swing and miss. Maybe that’s just as simple as some managers being able to keep players using a good, solid approach over the course of a season, even when they are worn out. Consistency. It all sounds a bit cliché, but it’s a cliché that might be worth millions of dollars if teams can figure out how to better promote it. So if you want your team to get better, you might study the sweet swing of Miguel Cabrera or the defensive wizardry of Andrelton Simmons, but spare a bit of time for the managerial methods of Bud Black.