# Managers and the Pythagorean Theorem

It’s been a while since I actually played around with some Retrosheet files.  Time for some good old-fashioned research, this time on a question that has bugged Sabermetricians (and some mainstream folks) for a while.  Do Pythagorean residuals tell us much of anything about a manager?
A little bit of set up: a little while ago, I published an article here in which I mathematically showed that pretty much all of the variance in Pythagorean residuals can be explained by three factors: a bias in the formula (about which we can’t really do anything), a team’s average margin of victory (teams which won a lot of close games outperformed) and a team’s average margin of defeat (teams which got blown out a lot also outperformed).  This wasn’t anything new.  Anyone who has stared at the formula for more than five minutes could have figured that one out.  But, I did find that a team’s average margin of victory (calculated only in the games it wins) was largely uncorrelated (r = .2) with it’s average margin of defeat.  This means that in order to explain Pythagorean residuals, we need to look into why teams win (or lose) close games and why they win (or lose) blowouts.  It’s been said that it’s the manager who makes the difference in a close game, presumably because he’s the one “pushing the buttons.”  So, a good manager would be good at winning one run games which would translate into a bump in outperforming Pythagorean residuals.  Right?
The problem is that it has never really been established whether a manager really has any skill at winning (or losing) one-run games.  Or blowouts.  Ah, but through the magic of Retrosheet’s game logs, that information is only a few calculations away.  I took all of Retrosheet’s game logs from 1871-2006 (the day after I compiled that database, the 2007 one came out…)  That represents just about every regular season major league game ever played, and the database has manager information for almost all the games!
Well, do managers have a repeatable skill for winning one-run games?  Well, if they do, it ought to show up in a split-half reliability.  I coded all games as even or odd, depending on what game number it was for the team during that season.  (i.e., Opening Day is Game 1, an odd number.)  I took a manager’s record over his career is games decided by one run that were even-numbered and those that were odd-numbered.  What that does is control for team quality… well, sorta.  More on that in a minute.  If the manager is good at winning one-run games in odd-numbered games, he would be good at winning one-run games which are even-numbered.  Assuming that there is some sort of skill involved, there should be a correlation.
Split-half correlation for one run games: .004
Two-run games: .172
Blowouts (difference of 6+ runs): .508
But, that includes all managers, from Connie Mack down to the interim managers who hung out on the bench for 20 games and were never heard from again.  I restricted the sample to only those managers with at least 500 games managed (223 managers).
Split-half correlation for one run games: .342
Two-run games: .323
Blowouts: .756
So, there’s a much more consistent skill in managers winning or losing blowouts?  Well, if there’s one type of game where a manager probably doesn’t have much control over the outcome, it’s a blowout.  Introducing the Buddy Bell corollary.  When you manage a team that’s awful year after year, you usually get fired and never re-hired to manage anything other than other lousy teams.  So, you end up in charge of a lot of really consistently awful teams.  And when you’re running a bad team, you get blown out a lot.  There’s a lot of managers who fit Buddy Bell’s profile.  On the other side of the fence, good managers on good teams stick around for a while.  It’s hard to disentangle the manager from the types of teams he gets to manage.
Still, one-run and two-run games have a split half reliability in the .3 range, which is pretty low.  Taking a look at it from a variance explained framework, a manager’s performance in one and two run games is about 10% repeatable skill and 90% other things, like luck and… the players?
But let’s see if we can take a look at the issue in another way.  I counted each game that a manager managed in sequential order.  His first game ever as a manager was game 1, the next game was 2… I think you can figure it out from there.  Managers with more experience might be better at winning one-run games.  The experience might serve them well in knowing how to “push the right buttons.”  I coded all one-run games for whether the manager won or lost that game.  I ran a binary logistic regression to see whether manager experience (in games managed) mattered in a one-run game.  The answer is… no.  The coefficient on manager experience was not significant.  For two-run games, there was a significant finding, although it was 2/100ths of 1 percent (that’s .0002).  For blowouts, there was again significance, but this time with an r-squared of .002.  Hmmmm… looks like manager experience, in relation to other factors, doesn’t have a lot to do with whether a team will win close games.  Or blowouts for that matter.
But maybe the important thing isn’t how much managerial experience a man has.  After all, if I’ve managed 2000 games, and you’ve managed 2000 games, then there isn’t an experience advantage to either one of us.  So, I caluclated how many games the opposing manager had managed and took the difference between the two.  This “experience advantage” did significantly predict victory in one-run games, but the R-squared again was very small: in this case .00005.   Same basic findings for 2 run games.  Blowouts had an R-squared value of .004.  Wow.
Maybe there’s a learning curve, and after a few years, a manager has learned all he can and the curve would flatten out.  Let’s take a look only at the first 500 games of a manager’s career to see whether number of games managed had a more pronounced effect there.  Nope.  I tried a few other numbers.  Nothing.
Maybe it’s the number of one-run games previously managed?  Still almost a nil effect.
When a team finishes above or below it’s Pythagorean record, should we blame (or congratulate) the manager?  It doesn’t look like we should.  A manager’s experience and even his edge in experience is a relatively minor contributor to the odds that his team will be victorious in a close game.  Why?  Well, think about this rationally:  If I look at this only from the perspective of the moves that one manager makes, it doesn’t allow for the fact that there’s another manager in the other dugout attempting to counteract those moves.  Managing seems to be a game of holding serve.  Then there’s this other matter: when baseball returns (please… soon!), sit down and watch a game between two teams you don’t follow regularly.  As you’re watching the game, call some of the managerial decisions from your couch.  You’ll probably call many of the same things that the manager actually does.  Why?  Because most managers use similar strategies.  The manager may not matter because most managers follow “The Book.”  Not this “The Book”, but the one that most managers follow.
These findings also call into question the old saw that “a good manager might win you (1, 2, 3) games per year.”  Taking a look at one-run games again, where we might expect a manager to have the greatest influence, about 30% of all major league games have ended as 1-run games.  Figure a team over a season is involved in 48.6 one-run games (.30 * 162, but let’s say 50, just to keep round numbers).  Using the regression equation I got above, despite the fact that it’s not significant nor is the R-squared significant, how many games experience would it take for a team that was a true 25-25 in those games with a replacement level manager at the helm to 26-24?  9843 games, or about 2000 more than Connie Mack managed in his career.
Sure, a manager has other jobs.  He’s the team’s chief psychologist, babysitter, media relations guy, and liaison to team corporate management, and maybe all of that has a part in winning.  It just doesn’t look like being able to influence close games is one of those jobs.  There are just too many other factors involved, and in large part, the manager is just along for the ride.  Perhaps the better saying is “good players make a good manager.”  Either way, seems like it’s time to retire the logic that Manager of the Year voting should be based on outperforming the Pythagorean projection.  Come to think of it, maybe “Manager of the Year” should just be re-named “Luckiest Ex-Catcher of the Year.”  Pythagorean residuals are driven by winning one-run games and blowouts, and it looks like the amount of skill involved is, while not trivial, minimal.