The root (part 3)
In part 1 we discussed the methods of salary evaluation. In part 2 we discussed a specific model for player salaries. I promised an evaluation of how well our salary model explains actual salaries, and I will get to that … next week.
But first, there’s one point I want to swing back around to and cover again, just to make sure I’ve given it the treatment it deserves. It is, after all, where my model differs the most from those built by academic economists, and so I really do owe it to the reader to make sure that I put the most emphasis on this point.
In short, I believe in replacement level. We can and should argue over where to put that replacement level, how to adjust between positions, etc. But the general concept seems to answer a lot of questions that otherwise go overlooked.
In academia, baseline chooses you
Economists, as a group, do not seem to believe in replacement level. They believe in measuring absolute production, or how many runs a baseball player produces in comparison to the lack of a baseball player. Or they will measure production based upon average (with the caveat that this doesn’t tell us anything about the worth of an average baseball player).
This works (to some extent) for run scoring, because with runs you start from zero and work up. In essence, what you are doing is comparing a player’s production to a batter that hits .000/.000/.000.
How the concept is supposed to work for run prevention is a mystery that frankly I’ve never seen tackled headon. In short, nobody ever actually advocates evaluating defense from the perspective of preventing all runs—the equivalent of a .000 hitter is not a 0.00 ERA pitcher but a pitcher with an infinite ER. This is simply impractical—Excel doesn’t respond well if you try to subtract the 257 runs Livan Hernandez allowed last year from infinity. (This approach also undervalues playing time.)
If you do not explicitly come up with a baseline, you will implicitly come up with a baseline. And here’s how it typically works:
 Offense and defense are equally valuable to team wins.
 One run scored on offense is equal to one run prevented on defense.
 Therefore, an average team team scores and prevents an equal number of runs.
Nobody ever comes out and says this. They may not even think this. But this is the way a lot of regression models seem to work. Now, if this is true, then that’s fine. But I haven’t seen anyone advocate for that point of view, and to simply assert that this measures absolute production without making an arguement for it strikes me as flawed at best.
Considering defense
And what’s the point of having flaws if you’re not going to compound them? I am greatly willing to be corrected here, but for the most part published MRP models of baseball seem to attribute all of the credit of run prevention to pitching, such that hitters produce half of all wins (and revenue) and pitchers produce half of all wins (and revenues). This is fine, if you want to simply ignore the impact of eight fielders on defense. (There’s very little to suggest this is correct, but you’ll have that sometimes.)
An alternate approach is to give a player credit for his defense in addition to his hitting. Of course, most defensive ratings are relative to average at the position (and if you’ve come up with an absolute measure of fielding value, I’d love to see it). In other words, if a player is worth 100 absolute runs on offense, but 10 relative to position on defense, you put him at 90 absolute runs.
You can easily go astray here: for starters, you can ignore position. Some people will consider that perfectly appropriate—after all, a run saved by a shortstop and a run saved by a first baseman are both a run, aren’t they? So what’s the big deal?
The problem is that you can only have one shortstop and one first baseman, and you must have a shortstop and a first baseman. And so if you need one of each, and instead go out and acquire two first basemen, one of them is going to have to play shortstop. So if you have two players with offensive runs above zero and defensive runs above average equal to zero at position, they aren’t equal if they play different positions; if we make our 90run first baseman play shortstop he’s no longer a 90run player, because the average defensive talent at each position is different.
Let’s take a look at the average hitting production, by wOBA, of freeagent players at each position, along with average salary:
POS

Num

wOBA

Salary

C

44

0.288

$4,528,547

CF

25

0.307

$8,336,848

2B

24

0.315

$4,071,422

SS

30

0.315

$7,183,764

LF

38

0.329

$7,325,970

3B

34

0.335

$8,127,860

RF

30

0.341

$8,813,600

DH

22

0.344

$7,462,316

1B

47

0.345

$6,088,575

There are what I would term sampling issues with this chart (as well as the second baseman/catcher issue—I think that’s due to the disproportionate amount of bench players who are primarily second basemen or catchers), but it should serve as a rough illustration of the point. First basemen are the best hitters among the positions, and yet they make less than shortstops and outfielders. Center fielders are very highly paid despite being poor hitters overall.
This makes sense to baseball fans, of course, but point this out to an economist and you’re likely to get a response that’s essentially “defense was not statistically significant at the fivepercent level in my regression.” I would consider this evidence of a misspecified regression, but that’s me.
What if we shift to considering a player’s offense relative to positional average as well? This approach allows us to trade out problems. If you’ll recall, the problem with using an average baseline in a salary model is that we’re left wondering what an average player is worth. Multiply that difficulty by eight. You could, of course, simply declare that the average player at each fielding position is equally valuable. And you probably wouldn’t be very wrong very often, as teams will probably shift players in order to achieve some measure of equilibrium in the long run .
There’s also the matter of the designated hitter. He is, of course, an average fielder for his position. But even a mediocre defensive first baseman is providing some defensive value in the abstract—he’s fielding some ground balls and making some putouts at the bag. The DH isn’t providing that value at all.
In academia, baseline chooses you
The point to this is that not that replacement level is necessarily the best or only solution to these myriad issues. But it is a solution, and these are issues worth solving. There is, in my opinion, little point in developing a salary model for baseball that ignores the fact that as free agents, two players who are identical hitters (and identical in all other respects, such as age and health) will get paid differently if one is a shortstop and one is a left fielder. There could well be other ways to address these (and other) issues with current MRP models that I’ve seen. (And I do not read everything—if you are aware of such work, please let me know.)
Our models of baseball are only as good as we let them be—they’re determined by how we construct them, what data we feed them and how we use them. I’d rather have them than not, to be sure, but that doesn’t constitute an abdication of responsibility in being careful with them. (John Beamer has a great discussion of this topic.) But it’s instructive to ask, why do regression models miss the boat on the value of fielding?
For the most part, the measure of fielding value used has been fielding percentage. Of course, fielding is even in the name of the thing, innit? Why wouldn’t you use fielding percentage? Well, it’s simply a very poor measure of fielding. The correlation between FP and team runs allowed (looking at 19932008) is only .18, a weak correlation at best. A better measure of defense at the team level is DER, which has a .55 correlation with runs allowed. (There is also remarkably little variance between players in fielding percentage: only .006, compared to .025 for OBP; and the average fielding percentage is essentially constant among positions.)
So instead of looking at these results and concluding that fielding percentage is not a significant measure of fielding performance, a lot of very smart people instead decided that fielding is not a significant part of playing baseball. This is not a consequence of regression, this is a consequence of not doing it correctly.
“This is what my regression says” is not a defense of the assumptions made when creating the regression. You are responsible for what goes into your regression, and so you’re accountable for what comes out of your regression. It’s as simple as that. If advanced econometric techniques are capable of the role they’ve played in our current economic downturn, they can certainly make mistakes on how much baseball players should be paid.
Next up
Next time we really do look at how the model shakes out, and we look at the two most common objections to a linear salary model: largemarket teams and superstar players. Promise.
References & Resources
Data used in this article courtesty of the Baseball Databank.
Service time data courtesy of Tango and Cot’s Baseball Contracts.
JC Bradbury points out an interesting study on baseball player salaries. I haven’t read the paper itself yet, but this discussion makes it seem interesting.
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