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Book Review: The Baseball Economist (special guest reviewer!)
2007-04-18 04:00
by Bob Timmermann

Note: I'll be running some book reviews here from time to time (mostly after I read the books, but I thought I'd start with a review of a book by someone who knows a lot more about the subject matter than I do) so here we go.

By Phil Birnbaum

Books like The Baseball Economist are rare these days. Most sabermetrically-oriented baseball books out there are concerned with player predictions and such. This book, on the other hand, is interested in all kinds of subjects over its many chapters, and throws lots of interesting ideas at us. You could probably best compare it to last year's Baseball Between the Numbers.

Its author, economist J. C. Bradbury, writes pretty well, too, and the book is a entertaining read. I finished it within 24 hours of it arriving in the mail. I can't say I agree with everything Bradbury says, but I still wish there were more books like this, which suggest new ways of approaching some of the most interesting baseball questions.

The Baseball Economist walks a line between economics and sabermetrics (in fact, the author's website is called ""). Bradbury's brand of sabermetrics is pretty much indistinguishable from the regular stuff – the difference is more in the subject matter than the methods. Economics deals with the choices and behavior of human beings, and how they respond to incentives. And so Bradbury concentrates on those kinds of topics: how much should a team decide to pay a player? Are NL pitchers more afraid to hit batters knowing they'll later be coming up to bat themselves? Are some managers better at influencing umpires? And so forth.


As an economist, Bradbury is less interested in many of the traditional sabermetric topics, the ones more about the structure of the game. Which version of Pythagorean Projection is the most accurate? Which fielding stat is best? Does clutch hitting exist? This book doesn't care much. That's not a criticism – to my mind, the topics Bradbury deals with are more interesting, because they're new.

Take, for instance, my favorite chapter, the one on managers influencing the umpires. When they disagree with the home plate umpire's ball/strike call, managers are quick to make their displeasure known from the dugout. If some managers are more persuasive than others, both their batters and pitchers should outperform.

But how can you find out? Bradbury hit on an ingenious method.

MLB has installed the Questec system in several major-league parks. In those parks, a sophisticated imaging system figures out, after the game is over, which pitches should have been called what. Those decisions are compared to what the umpires actually called, and umps who vary significantly from Questec are presumably called on the carpet to explain themselves. And so, umpires have a stronger incentive to ignore both managers in Questec parks, and to instead concentrated extra hard on calling them correctly (or, more accurately, on calling them the way Questec does).

Therefore, Bradbury reasons, any variation between strikeout-to-walk ratios in non-Questec parks, compared to strikeout-to-walk ratios in non-Questec parks, perhaps can be attributed to the managers.

So which managers are the best at influencing umpires? The short answer: none – the results came out roughly as you would expect if they were just random. Of the sixty samples – 30 teams on offense, and 30 teams on defense – three came out statistically significant at the 5% level. That's dead on what you'd expect by chance. And, furthermore, there didn't seem to be a connection between the best-yelling managers on offense and the best on defense, which again suggests that the differences are random.


The biggest study in the book is the one that's most traditionally associated with economics – trying to figure out what a player is worth, in dollars. A huge portion of the book is devoted to his calculations; there's a 50 page appendix devoted to listing every player over the last two seasons and his salary value, as calculated by Bradbury. Alas, I don't agree with his methods or his numbers – for economic reasons, mostly, rather than sabermetric ones.

Specifically, Bradbury notes the accepted economic theorem that, in the real world (think McDonald's or Wal-Mart), the productivity of the marginal employee ("marginal" in the sense of "last hired") is exactly equal to his salary. The reason is easily explained: if he were contributing less than his salary, he'd be fired. If he were contributing more, it would probably be worth hiring another similar employee, and another, and another, at diminishing returns, until, finally, the last one hired would produce output almost exactly equal to his salary.

So, generally, salary equals productivity.

But that applies only in a free market for labor. The baseball labor market isn't free. Specifically, there are classes of players (inexperienced and arbitration-eligible) whose wages are artificially kept low. And, more importantly, teams can't keep hiring until equilibrium is reached, because they're only allowed 25 players on the roster, and only nine on the field. So it seems to me that the logic that says a player's salary should be exactly equal to his productivity simply doesn't hold under baseball's arbitrary labor-market rules.

In the McDonald's case, the only alternative to hiring a "free agent" cashier is hiring nobody, and paying zero for him. In baseball, the alternative is grabbing a replacement level player, a minor leaguer or reserve, at the major league minimum. Because of that difference, Bradbury's measurements of productivity (or, in economics terms, "marginal revenue product") are reasonable, but their conversion to salaries is not.

Here's what Bradbury does. He takes the total expected revenue for each city, and figures out the dollar value of a win. He then assigns that total value among the players, based on how many plate appearances they had. Finally, he adds or subtracts salary from each player by the amount by which his production was above or below average. The overall effect, I think, is to assign salary proportional to the total number of runs the player contributed to the team.

This is reasonable at the margins – if runs are worth $127,000 in revenue (as Bradbury calculates), and Joe creates 10 more runs than Jim, then, all things being equal Joe's salary should be $1.27 million more than Jim's. However, I would argue that isn't the case for all runs – just runs above what a minimum-salary player (the so-called "replacement player") would create.

The major-league minimum salary is $380,000. For that amount, a team can pull a player out of the minor leagues, and he'll create a certain number of runs – let's say, for the sake of argument, 38 runs in a full-time season. So that player's runs are worth only $10K each.

Now, suppose that minor-leaguer has the job, but then another player comes along who can create 39 runs. How much should he be paid? Well, if his team replaces the 38-run guy with the 39-run guy, it would earn an extra $127,000. So the new guy should be paid, at most, $380K plus an extra $127K, for a total of 507K. Repeat, one run at a time, until you get to your favorite superstar. And it will work out that all the runs up to the replacement level are worth $380K total, and only above that level will salary get bid up to market value per run.

But Bradbury's method doesn't do it that way. It values all runs equally from zero, so he'd rate the 39-run guy at about $5 million. Clearly, that's not right.

Take, for instance, Juan Pierre in 2005. Pierre created 3.89 runs per game. If a team of 9 Pierres had an average pitching staff, who gave up 5 runs per game, it would still play only .377 ball. That's 61-101 – and that's with an average pitching staff. If it had a crappy expansion-team pitching staff, which gave up, say, 6 runs per game, it would go 48-114. Clearly, Pierre was worse than expansion team level, since even expansion teams usually win more than 48 games.

The conclusion is that you could find a minor league player who could play at Pierre's level for $380,000 a year. Pierre couldn't have been worth more than that.

But by valuing all his runs equally, The Baseball Economist has him worth $5.2 million.


In a related study, Bradbury evaluates the management of all 30 MLB teams.

The best? The Marlins and Indians. Those two teams are considered the most efficient, partly because they wound up with the best ratio of wins per dollar over the past few years.

But that isn't such a difficult achievement. Any team can have a great ratio, just by finding the best 25 players who can be paid the MLB minimum salary. A team like that would cost only about $10 million, but would win about 50 games. The average team spends about $80 million, and wins 81 games. So, if you want, you can spend 12% of the average, but win 60% of the average. If you want. You'll still be in last place.

Perhaps realizing this, Bradbury combines this measure with a second one, a straight-up measure of winningness. He then combines the two measures, arbitrarily, by ranking them from 1 to 30 and summing the rankings.

But why? Why weight them equally? Why sum the ranks? Obviously, I'm not convinced that this ranking measures anything real.


There are similar methods in the book that leave me perplexed. There's a chapter that finds that big city teams win more games than small-market teams, by one win per 1.58 million extra residents. The Yankees "should" average 88 wins based on their population alone; the Brewers, only 70.

But, so what? First, wouldn't it be safe to assume that the difference in wins is due to team spending decisions, rather than the size of the city itself? I'm sure the Brewers could win like the Yankees if they spent like the Yankees. If the point is that they can't afford to spend like the Yankees, because of lower revenues, it's well taken. But then why not show how revenue corresponds to population, instead of wins? (And, maybe the Yankees revenues are higher partly because they win so much – how do you untangle the population effects from the success effects?)

In any case, Bradbury says "the difference in market size explains about 40 percent of the difference in wins between the top and bottom markets." He argues that the other 60 percent is management. "If you are looking to blame something for the woes of your favorite small-market club, don’t just jump to blame [the city]. Small minds can be just as dangerous as small markets."

Point taken. But I'd bet that if you consider the substantial variance due to luck, and consider that some of the remaining variance consists of teams spending more (or less) than their market size suggests, you wouldn't really have a whole lot left to blame on management. Bradbury wants to show that, despite the differing size of the cities, the league is nonetheless reasonably fair to the fans of the low-spending teams, because they can win if only their management is smart enough. But Bradbury's analysis doesn't really support that argument. I'd say it supports the opposite view. 18 games in the standings is very hard to make up, no matter how inspired your personnel decisions.


A lot of the studies in the book depend on linear regression. That's not necessarily a bad thing; a lot of events in a baseball game are so dependent on multiple factors that regression may be the only way to isolate them. Part of the reason is that all the low-hanging fruit, the simpler cause-and-effect studies, have already been done.

Back in the 80s, for instance, Bill James found that pitchers who strike out a lot of batters have longer careers than seemingly equal pitchers who don't. Bill's method was simple: he found a bunch of power pitchers, searched for the most comparable finesse pitcher, and compared the rest of their careers. It was obvious from the results that the strikeout pitchers lasted much longer.

Now, in 2007, J. C. Bradbury wants to find out if losing teams tend to hit more batters than winning teams, perhaps out of frustration or retribution. How would you check? You could count HBPs when teams are losing, and compare the numbers to when teams were winning. But even if you found an increase, maybe it's just because the pitchers are bad – that would account both for the HBPs and the fact that their teams are behind.

Or perhaps it's because the other team's batters are better, so they're being pitched to more carefully. After all, if they're winning, they probably do have better batters than average.

And let's suppose you even find that hitters are more likely to get plunked after their own pitcher has plunked the opposition. Must that be revenge? Perhaps the other plunking tends to widen a lead, and teams are more likely to hit batters when they're winning.

The nice thing about using a regression is that it automatically lets you control for all these things. Bradbury did that, and found, among other interesting things, that losing teams do indeed hit more batters than winning teams, even after all these other factors are taken into account.

That was Chapter 1. In Chapter 2, Bradbury uses regression again, this time to check whether the quality of the on-deck batter affects the current batter's performance. Conventional wisdom suggests that it does: with a bad hitter coming up, the pitcher is more likely to issue a walk to get to him. But with Barry Bonds on deck, pitchers are going to try to get the hitter to put the ball in play, instead of risking giving Barry an extra baserunner to drive home.

Bradbury (and Doug Drinen, with whom he collaborated on these two studies) found that, after using regression to control for all sorts of factors, there indeed was some "protection" afforded to batters with a powerful on-deck hitter, in that they walked less. More interesting is that they also hit worse than usual in all respects. That is, with Barry Bonds on deck, the pitcher deliberately pitched with more effort than usual, knowing that this plate appearance is more important than average. (In all cases, though, the effect was very small.)

These are important studies, among the best in the book, and the results are quite interesting. What bothers me a bit about them, and, in fact, all the regression studies in the book (I think each of the first seven chapters features a regression), is that we don’t see the details of the regression itself. This is understandable, in a book that's intended for the typical baseball fan, but we still have to take Bradbury's word for it. With Bill James, we didn't – the entire study was laid out for us, all the assumptions and details, and we could reproduce it if we wished. Unfortunately, but quite reasonably, we can't do that here. And I found that a bit disconcerting.

But all is not lost; the full studies on which these two chapters were based can be found online. I reviewed the protection study on my blog here, and the hit batsman study here.

As for the other regressions, they may be online somewhere, but the book doesn't say.


There are several non-statistical chapters in the book, and I found those to be the ones where the logic is strongest. Bradbury, as an economist, is in his element there, with clear, straightforward explanations of some economic aspects of baseball. In a chapter about steroids, he explains that steroid use for baseball players is like the famous Prisoner's Dilemma – the players are better off if they all agree to stay away from steroids, but each individual player is better off if he breaks the truce and uses them anyway.

In another chapter, Bradbury shows that even though MLB has a nominal monopoly, the fact that they still have to compete with other sports means that they haven't been able to take advantage of the consumer to earn excess monopoly profit.

All these explanations come clearly and naturally; the economic jargon follows the explanations, rather than driving them. Indeed, almost every one of Bradbury's chapters includes a little bit of economics – if you don't know what rent seeking is, or how monopolies set prices, you will find out, effortlessly, in the course of reading the baseball examples in the book.

Still, as I said, there are several of Bradbury's conclusions with which I disagree. And so I would hesitate to recommend this book to readers who are looking only for firm numerical answers to the questions it addresses. But those readers who are willing to ignore the flaws and think further about ways to address the issues – or those who are happy to ignore my criticisms and judge for themselves – will probably enjoy The Baseball Economist, and find it well worth the read.



Phil Birnbaum has his own blog on sabermetric research and edits "By The Numbers" which is a publication of the SABR Statistical Analysis Committee. He lives in Ottawa, Ontario.

2007-04-18 07:36:35
1.   studes
Hope you guys read and review Vince Gennaro's new book. He also takes a marginal revenue approach to salary, but in a different way.

I wonder about the monopoly fidnings. JC looked specifically at ticket prices, but what about television contracts and the like? Also, what about the fact that MLB pays players minimum salary for the first three years they play? Think they'd get away with that if they didn't have a monopoly? And don't those factors drive up profit?

2007-04-18 07:57:12
2.   110phil
Hi, studes,

Just ordered the Gennaro book yesterday. It should arrive soon.

On the monopoly issue ... you're probably right. High TV contract prices are the reason that "Extra Innings" is so expensive, and why I can't get all the Blue Jays games for free.

On player salaries, the MLBPA also has a monopoly on labor. If both the MLB and the MLBPA had free competition, salaries would probably be lower, not higher -- a lot of guys would play baseball for free, almost (and did, in the past), and that would drive everyone else's salary down. I think. Wouldn't it? These things are sometimes subtle.

2007-04-18 22:17:48
3.   El Lay Dave
I would think that Baseball has to compete for my disposable income on all fronts, tickets, TV, internet, etc. At some point, the consumer has to decide if his/her entertainment dollar is going to be spent on Extra Innings, the NFL Network, 2-1 drink night at the corner bar, iTunes, internet porn or whatever.

What do you mean by "if ... MLB ... had free competition"? If there was an alternate top-level professional league? If combined with a disbanding of the MLBPA, don't you think the top-echelon players would make even more as the big draws, and the rest of the players would make less, e.g., one doesn't have to overpay for average players because there is a large pool of them.

2007-04-19 07:00:18
4.   Vishal
why no comments on the injury post up top?
2007-04-19 20:07:05
5.   110phil
3: Hmmm ... Barry Bonds' "new" salary would depend on how much extra revenue he can bring to a team in the "new" freely-competitive world vs. the old one. Judging by college sports, where there are hundreds of teams (at varying levels of ability), I think you may be right, he'd still be worth a lot.
2007-04-20 05:59:36
6.   110phil
OK, thought about it a bit more.

Replacement players will make zero, say. All other players will make the "marginal revenue product" of their contribution above replacement.

There would be more teams and more baseball without the monopoly. So replacement level would be lower. All things being equal, this means more money for players.

But they are paid the amount by which their productivity above replacment makes money for the teams. Would that go up or down? It depends -- do teams make more money, or less? Probably less. If it were more, MLB would have already expanded or changed to this new system. So all else being equal, this means less money for players.

So salaries go up because of lower replacement, but down because of lower revenue per win. Unless there are ways of quantifying the effects, we don't know which effect is larger.

Assuming I have this logic right ...

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