When Joe Maddon opted out of his contract with the Rays two weeks ago, there were immediately rumors that he would be joining up with all of the other 29 teams. (Yesterday, we found out that one of those rumors was true. He’s taking his talents and his back pocket card which drips with analytics to the North Side.) The rumors were understandable. After all, Joe Maddon is a certified genius. He’s gotta be better than that bum in our dugout. (Yes, Joe Maddon is a really smart guy, but so are the other 29 managers. All of them. Yes… even him.)

But then another conversation started that always pops up around this time of year, mostly because there are a lot of managers being fired (and hired) and there’s not much else going on. What is a good manager worth? What does a manager even do that produces value? We know that he makes the strategic decisions for his team, including making the lineup, putting the rotation together, and calling for the sac bunt. But we also know that most managers seem to manage out of the same “book” and while there are improvements over that “book” that could be made, the perfect Sabermetric manager probably clears a win or two more than a standard-issue manager. As Sabermetricians, we’ve spent a lot of time criticizing those strategic decisions, and while mathematically, we’re right, we’ve kinda missed the forest for the trees.

There’s an interesting paper that came out a few years ago in the field of clinical psychology (my home field) which looked at how well therapists did treating people who had panic disorder. The therapists were all conducting their therapy out of the same book. Literally. Panic disorder is one of those disorders that gives itself nicely to treating with a manual. There’s plenty of research saying that these types of treatments work great. Often, the manual specifies what happens in session 1, then session 2, and so on, specifies techniques, and gives standardized “homework” assignments for the client. There was a clinic that was evaluating one of these manuals, and so they recruited several therapists to follow this model in a specialty clinic that worked with people who have panic disorder. The researchers did careful measurement of panic symptoms over time and found that while most people got better, some therapists got better results than others. There was also no correlation between how well the therapists followed the manual and the treatment outcomes for their clients. If a good process is all you need, then it shouldn’t matter who’s administering it, but the researchers surmised (based on other research as well) that results were about much more than process. The relationship between the therapist and the client turns out to be rather important. Might the same thing be true for managers?

I’m fond of the thought that managers have three major jobs. They are in-game tacticians, PR spokesmen, and the guy in charge of wrangling 25 young millionaires who are on a six-month mission where they have to perform nightly. I’m sure the amount of amateur psychology that a manager has to do is staggering. Sabermetricians have focused mostly on the tactical aspect of management, because it’s easily visible and quantifiable. But let’s see if we can find evidence on some of the other work that a manager does. I don’t know that there’s a way to really get at how well a manager handles the media, but as far as his duties in managing the people who wear the uniforms, we might be able to learn a thing or two.

Warning! Gory Mathematical Details Ahead!

Let’s start with a reasonable assumption. Players don’t like losing and, even if in just some small way, it makes them sad. Not massively depressed, mind you. They’re big boys and they know that no one goes 162-0, but they also didn’t get to where they are by lacking in competiveness. We know that there’s even some evidence that being part of a team that loses a lot of games can stunt a player’s development, so losing must have some sort of effect.

I took all events from 2009-2013 (the 2014 Retrosheet file isn’t yet available) and coded everything, this time on a pitch-by-pitch level. I coded all pitches for whether the batter swung, and if he swung, for whether he made contact. I also looked to see, if he took, whether it was a called ball or strike. Once I had done that, I took the annual percentage for each of these for both the pitcher and batter (min 500 pitches faced/thrown). I converted these percentages into odds ratios, and created an odds ratio that expressed the chances of an individual pitch, given this batter and this pitcher, would involve the batter swinging. I have previously used this method in my work at the PA level.

Next I created a simple binary variable on whether the team at bat was losing during that at-bat. I wanted to see, once we’d controlled for the general tendencies of both the pitcher and hitter, whether players actually behaved differently when they were losing as opposed to winning (or being tied). I entered the control variable and the binary losing/not losing variable into a binary logistic regression. The results were interesting. When a hitter’s team is losing, he is less likely to swing, but when he does, he is more likely to make contact (and it’s more likely to go into fair territory). However, when he takes, it’s more likely to be a called strike. The effect sizes are a couple of percentage points, but that sort of change in approach can have big effects for some hitters.

We could make the argument that when a batting team is losing, it makes sense for them to swing less. Why take chances on iffy pitches when your team really needs baserunners. It pays to be more selective then. Plus, swinging less drives up the pitcher’s pitch count, and maybe it would be helpful to get him out of the game. Maybe we’re seeing a perfectly reasonable response to that situation.

But using the same approach, I looked at whether a batter’s behavior varied as a function of whether his team won or lost their last game. In this case, it makes absolutely no sense to change approaches based on what happened yesterday, and yet if a batter’s team lost yesterday, he is more likely to swing and less likely to make contact. Why the worse outcomes? One possibility is that even a slightly depressed mood—one that wouldn’t qualify as clinical depression, but is still mildly sad—can affect a person’s reaction time. I’ve previously argued that one of the most important things that a team can have is a way to deal with losses. Some sort of ritual, whether formal or silly, that says “That was yesterday” and allows players to move on. One might define that as one of the jobs of a manager. (The aforementioned Joe Maddon famously allows only 30 minutes after either a win or a loss for his players to revel or sulk. Tomorrow is a new game, guys.) You don’t want yesterday affecting today.

Well, now that we know that hitters swing and miss a bit more after a loss, we can ask whether that effect varies based on the identity of the man who put that hitter on the lineup card to begin with. To check this, I added new variables. I took the managers from that time period (2009-2013) and weeded out the interims and the bench coaches who managed a couple days while the regular manager was ill or on other business. I entered the manager into the equation (for the initiated, a categorical fixed effect), and the interaction between the binary “won/lost yesterday” variable and the manager. If the manager has some sort of impact on how well a team rebounds from its losses, then we would see that the manager by won/loss interaction would be significant. For swing rates, the overall multi-variate Wald on this variable was not significant, but for contact rate, it was. That means that for contact rate, once we’ve controlled for the batter and pitcher tendencies, we still see that hitters are less likely to make contact on the day after a loss, but that with the right manager, this effect can be blunted or even reversed.

The next thing to do is to look at which managers appear to be the best (and worst) at stunting this problem. We can tell this by looking at the regression coefficients on that interaction term. Because of the way that these analyses work, the coefficients themselves are actually read as “better or worse than Ned Yost.” Why Ned? His name was last alphabetically and the program needed a reference category. So, to list the coefficients would actually be a little misleading. But we can look at the coefficients relative to one another.

The best managers at preventing players from getting losing their contact mojo after a loss:

1) Bobby Valentine

2) Bobby Cox

3) Terry Francona

4) Tony LaRussa

5) Bud Black

Not a bad group of managers. Bobby V, for all his… quirks… apparently inspired his hitters to bounce back after losses in his one year at the helm in Boston. Cox and LaRussa are Hall of Famers.

The worst managers

1) Cecil Cooper

2) Bo Porter

3) Terry Collins

4) Mike Redmond

5) John Russell

Collins and Redmond still have jobs. Then again, if this list were to extend to 6 spots, no. 6 would be Joe Torre. Like Cox and LaRussa, he also recently capped off a Hall of Fame career.

(For those wondering, Maddon came in middle of the pack.)

The range between the top of the chart and the bottom is something on the order of five percentage points. The way to understand that goes something like this. Assuming an identical batter facing an identical pitcher, we expect the outcome of a swing (contact vs. no contact) to be different based on whether a batter’s team won or lost in their last game by some non-zero amount. Let’s say a contact rate of 85 percent after a win and 84.5% after a loss, for a spread of half a percent (numbers made up on the spot.) We’d expect the “loss penalty” to be bigger for Cooper than for Bobby V (or maybe we might even expect Bobby V’s guys to increase their contact after a loss.)

Fighting the Grind
I’m happy to be the first to say that this is an experimental stab in the dark on this topic. I don’t know whether these effects are stable. I don’t know that even if they are that we could credit everything to the manager. He might have just been sitting in his office and the veterans on the team were the ones really powering the effect. I’m also hesitant to speak too prescriptively about whether making more or less contact is a good or a bad thing. Not making contact on a swing is obviously a strike, but that can be correlated with other good things, such as power. Maybe after a loss, Cecil Cooper’s crew realized that they needed to get back to what they were good at and swing for the fences a little more.

But let’s assume for a moment that the extra swing-and-miss is even somewhat bad. If there’s one thing that we’ve learned from the discussions of catcher framing, it’s that anything that has a slight impact on the ball/strike outcomes of pitches can add up, because a) balls and strikes are worth real runs and b) there are a lot of pitches over the course of a season. If there really are differences between managers in something as simple as being able to keep the players from getting too down after a loss, that would be valuable, especially because managers don’t consume a roster spot and can manage 162 games per year. And yeah, more valuable than the guy who wouldn’t bleed away a little bit of value by bunting once in a while.

I have a theory that we’ve missed the most powerful force in the baseball universe: the grind. Baseball, like any job, can get boring if you do it day after day. Most days, you only get one chance for that validation that you crave, because you only play one game per day. Lose that game and you have to sit with that for 24 hours, plus do a lot of travel and live in close quarters with a bunch of guys whom you may or may not like. After a while it can get depressing, and if the wins aren’t coming, you need something else to lift your spirits. When we speak of managers, we often talk about how he must manage personalities and make sure everyone is working together, or at least tolerating one another. Here, I’d argue, we get some glimpse of an idea of how valuable that could be.

Thank you for reading

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I think Bill Veeck wrote half a century ago that that ideal way to hire a manager would be to get a really good psychologist and figure out a way to give him a plausible-enough baseball background that the players would pay attention.
In terms of your overall analysis of what a manager's whole job is, I think your "three parts" idea overstates one piece (notwithstanding the post-game press conference, the manager's PR job is nowhere near as important as on field strategy and psychologist-leader) and leaves out a fourth piece altogether: technical analysis and training. Is a player's slump related to a change in swing? Why is someone throwing the ball away to often? Can you teach someone who's been catching ground balls their whole life how to catch them better? Of course there's a whole staff involved in these activities, but the field manager manages that staff, and needs expertise in all of it.

From the moment I started paying attention to sabermetrics in 2011, I've hated the way writers treat the manager as principally an on field tactician, when that seems obviously less important than the leadership and operations aspects of the job. You are the main exception to that tendency: you always treat the leadership aspect of the job as at least as important as the tactical aspect. Add the technical analysis and staff training and you will have an actual picture of the job as it is experienced by the people who do it.
I've actually mused on that topic before, as well:
I'd argue that the technical aspects of which you speak are primarily handled by the hitting and pitching coaches, with the bench, and base-coaches handling fielding, baserunning, etc. Obviously it helps if the manager has the type of ability to help in this aspects, but expertise seems like overkill. I think as a requirement it's significantly behind the other three listed by Russell.

I also wouldn't be so quick to put the PR aspect behind the other two. Dealing with the media is a big deal. Managers with good relationships don't get browbeat or second-guessed as much as those who are inept with the press. There's also the matter of keeping things from the clubhouse relatively quiet. Some managers are better than others at this, and being able to keep small issues from blowing up into larger ones is key. Part of that is relationships with the players, of course, but another part is dealing with the media. Managers who can keep the focus on them, and off their guys are probably greatly appreciated within the clubhouse, and doing so in a tactful way with the press isn't the easiest thing to do.
I wonder if this analysis would change if you only used playoff data. After closely watching Bobby Cox over 20 years or so, it became obvious that his handling of "his boys" was a factor in the braves' success. But in the playoffs Bobby would let one of his boys who was at a disadvantage with the pitcher bat late in the game when a pinch hitter was obviously needed. His dependency on the status quo was settling to players who were sure that they would be in the lineup every day as starters, and used the same way as pitchers, but in the playoffs you have to go with the best person for the situation regardless. Bobby didn't. He stuck with his guys and the Braves only won one world series after all those division championships. There were plenty of other factors also but I believe this was definitely one that hurt us several times.
If I understand the analysis correctly, then the batter-pitcher outcome is a zero-sum game. If a manager can positively influence performance following losses, then he has exactly the off-setting influence following wins, correct?

If you created a list of managers whose players performed best following wins, would not the list be exactly flipped. Would Redmond not be the best active manager in contributing win streaks?

This is an interesting stab into how psychology might be measured in a manager, but it seems to me that the affect you find is neither positive nor negative.
That's in there. Maybe the guys to focus on would be the ones who statistically show no difference between win and loss, but as I pointed out in the last part, I'm hesitant to even speak prescriptively about whether the effect _should_ be positive or negative. If one of the reasons that teams have a bad day is because they fall out of tune in one direction or another, then a good corrective manager should put them back in the proper direction. It's all rather speculative at this point.
One of the things I had wondered about managers is if there is a measurable effect of them getting ejected. I've seen some managers that seemed so passive, almost never coming out of the dugout to argue, that I wondered if that might make a difference in his players in some way. What I'm getting at is if a managers willingness to get run from a game defending his players to the umps might engender some level of trust that bonds the players with their manager.
I actually have that in the "to do" queue.
As the husband of a cognitive behavioral clinical psychologist, continued thanks for letting me read baseball content that has the side benefit of being able to share the occasional interesting psych-related study (e.g. the importance of the therapist vs. the therapeuetic technique).

High leverage reading.
There are a lot of cofounding issues with the "game after loss" numbers. For instance, you'd often be still playing the same opponent. You might be more effected by the quality of your opponent team, the ballpark (when on the road), the opponent team's choices in how to pitch to you, the opponent team's choice of how to defend you (shifts and all), etc. So there are a lot of things other than just win/lose that might be involved. If I swing less against team A because they know how to defend and pitch to me and I don't like the sight lines at their ballpark, my team might be more likely to lose. Now I'm more likely to see team A following a loss because 2/3 to 3/4 of the time after we lose to team A we play them again.