Back in 2004, the late Doug Pappas came up with a simple way to evaluate how well each team was spending their money: marginal payroll per marginal win. Here’s Doug’s original formula:

(club payroll – (28 x major league minimum)) / ((winning percentage – .300) x 162)

Simple enough, and it managed to give us yet another way to show how great Billy Beane and the A’s were. But while it was a decent first step, it failed even the simplest laugh tests: were the Yankees really one of the bottom ten teams, even when they were running away with their division every year? Are the Marlins consistently one of the best-run teams, just by virtue of not spending much beyond the minimum on payroll? Probably not.

Looking at it now, the biggest problems are fairly obvious. First off, not all wins are created equal-as Nate Silver touched on in Baseball Between the Numbers, a team’s ninetieth win creates significantly more marginal revenue than its seventieth (see chart below). Also, each team has its own marginal revenue curve-the Yankees’ ninetieth win is much more valuable than the Marlins’ ninetieth win, at least in terms of pure revenue potential.

So while Doug’s original formula punished large-market teams for spending significant sums on payroll, the reality is that the Yankees would have to have a brain lapse to cut their payroll below $100 million. The question really should be: How well are they spending their $200 million, and is that the right number, given their competitive position and market size?

Neil deMause was on the right track two years ago when he added Nate’s marginal-revenue-per-win curve to Doug’s method. But we need to go a couple steps further. Here’s how we’ll do it:

  1. First, we need to know how much marginal revenue each team is likely to bring in, based on its win total and market size. To do this, we’ll use Nate’s MR/MW curve, updated for 2009 revenues. We’ll then assign each team a market-size factor based on its 2007-2008 gate receipts. (We already know that this is the only short-term revenue source that significantly impacts a team’s payroll spending). The Red Sox won 95 games last year, which should generally lead to $108 million in marginal revenue. Multiply that figure by Boston’s market-size factor (2.48), and we get expected revenue of $267 million.

  2. Next, we’ll use a regression equation (MW = 0.1106*MP + 22.538) to determine how many games a team should win-and, therefore, how much revenue it should bring in-based solely on its payroll. For example, Boston’s $133 million payroll in 2008 should have led to 86 wins. According the win curve, multiplied by the team’s market-size factor, that would create $165 million in marginal revenue.

  3. Then we just divide these numbers: 267 / 165 = 1.61. In other words, given their payroll and revenue potential, the Red Sox performed about 61 percent better than average in 2008.

Let’s compare the top and bottom teams from 2008, first using Doug’s approach, and then using our new one:


Marginal Payroll Marginal Wins


Marlins $10,636,500

36 $300,466


$32,620,598  49


Twins $50,982,767 

40 $1,293,979


$36,767,126  27


Diamondbacks $55,002,713 

34 $1,646,788
—- —-




$43,761,000  11


$62,477,617  15


Yankees $197,881,579 

41 $4,898,059 
Tigers $127,485,197  26 $5,019,102 


13 $8,612,418 

Of the top five teams, only one-the Rays-actually made the playoffs, and of the other four, only the Twins should have even been close. The Marlins, D’backs, and A’s performed reasonably well given their small payrolls, but still only averaged 80 wins.

Let’s see how those results compare to our new method:

Team Marginal Revenue Expected MR

MR / ExpMR
Rays $51,461,633 $23,524,473 2.19

Angels $115,533,623

$64,051,489 1.80
Cubs $185,744,330




$132,870,709 $78,183,106

Red Sox

$267,185,811 $165,780,654




—- —-

Yankees $228,824,384

$302,239,343 0.76
Tigers $46,166,722




$26,758,423 $53,501,930


$26,758,423 $42,507,738




$55,863,187 0.58

This seems a lot closer to reality. The Rays run away from the pack, with the 100-win Angels and 97-win Cubs coming in a distant second and third, respectively. Instead of punishing large-market teams, the system accounts for their inherent advantage, and judges them on how well they actually use it. The Yankees remain in the bottom five-which is actually identical to the previous list, just with a different order-but it’s no longer their fait accompli, as they would have finished in the top half had they played up to expectations. The Red Sox, for example, finish nineteenth on the old list despite winning 95 games, as compared to fifth on the new list.

If we want to make it even more meritocratic, we can use third-order wins instead of actual wins, in order to strip out some of the luck involved:

Team 3rd-Order MR ExpMR MR3/ExpMR

Rays $51,461,633

$23,524,473 2.19
Red Sox $290,486,158



Blue Jays

$66,790,624 $39,300,599


$175,942,093 $106,445,281




$100,454,854 1.28

—- —-

—- —-
Padres $41,255,570




$51,211,783 $67,111,767


$30,054,408 $42,507,738




$20,635,720 0.70

Mariners $35,986,509

$55,863,187 0.64

The Rays remain in front, while the Red Sox, Blue Jays, and Dodgers all move up a few spots.

Here’s the same chart for 2009, assuming each team’s current third-order winning percentage holds:

Team 3rd-Order MR ExpMR


$50,733,695 $24,508,966




$91,143,942 1.99

Rockies $58,385,603

$38,702,035 1.51
Rangers $41,117,147



Red Sox

$217,262,599 $152,072,010


—- —-




$19,530,582 0.80

Mets $94,833,032

$124,697,984 0.76
Pirates $15,300,110




$49,817,523 $66,058,454


$24,847,828 $33,316,875


You can see the full data here.

If there’s still a piece missing, it’s the value that comes with finishing last. The first pick in the draft is worth a lot more than the fifth or the tenth or the fifteenth, so a team that wins 59 games, as the Nationals did last year, should have that factored into its marginal revenue figures. But we’ll leave that for another day.

For now, some other notes on the data we do have:

  • Andrew Friedman and the Rays are clearly the class of Major League Baseball right now. Ignore their actual 2009 record; first-, second-, and third-order wins have them as the second-best team in the American League, and they’re only trailing a team that will spend three and a half times as much on payroll. Combine that with a runaway victory in 2008, in both actual and third-order MR/ExpMR, and it’s hard to argue they’re not the best around right now.

  • The Yankees are currently twelfth in MR3/ExpMR (we seriously need a name for this, if anyone has any ideas), but only 27th in the classic MP/MW-despite being on pace to win 101 games. I think the new method is a pretty fair approximation; the marginal returns clearly diminish very quickly after about $120-$130 million (which is where the Red Sox usually are), and the Yankees could obviously win a lot of games with a $150 million payroll, if managed correctly. That they’re about average seems right-when you spend fifty percent more than anybody else, you probably should win 101 games.

  • The Mets are a disaster.

  • The Pirates, Royals, Orioles, and Nationals would definitely benefit if we included the value of their ensuing draft picks. Of those teams, I’d guess that the Pirates are the only one that actually understood this coming into the season.

  • It doesn’t surprise me that the Nationals aren’t in the bottom five-they’ve tracked well ahead of their actual record all year, and they actually aren’t that far behind the Mets in the adjusted standings.

Now, about that name…

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Revenue Above Yearly Standard.
RAYS, hahaha.
The Dodgers' front office does pretty well here, despite the fact that they're regularly lambasted here and by stat minded Dodger fans everywhere (me included). I wonder if this is a short term phenomenon based on the very valuable draft and development run that coincided with the first few years of Logan White's tenure as scouting director or if they're just better than is often presumed.
I was wondering the same thing about Toronto - the general feeling from BP recently has been: "They would be division leaders somewhere else" followed almost immediately by "how bad a GM Riccardi has been."

I've noticed this disconnect. He isn't responsible for the divsion he plays is and while some of his contracts are horrid he still comes in above the line on efficiency and did very well last year.

In fact I think I'll send this in as a request for the next BP roundtable - compare your perceptions of Riccardi as GM to the results he has achieved - I think he may be getting the short end of the publicity stick.
I think that's because Riccardi is GM of a team that IS in the AL East, and isn't in another division and he knows it. But his goal as a GM seems to be merely to create a good team. And that good team may be enough to win in another division in any given year, but it's not enough to win in the AL East, the division his team actually is in. Good is merely average or worst in the AL East. You need to build great to even have a shot. And Riccardi never tried to build great. You have to build your team for the division you are actually in, not the one you wish you were in.
Other than Juan Pierre, this year's contracts are pretty good. Loney, Kemp, Ethier and Martin are products of the minor league system and thus a good value. Hudson a valuable piece of the puzzle. The fact that they don't have to pay a fortune for a limited value closer makes them even more efficient.

Now if they can just find a GM to believe in the Juan Pierre pixie dust...
I was thinking something that emphasized efficiency - what you are really measuring is the ROI (Return on Investment) of the teams expenses. The higher the number the better ROI the team is getting from their sunk costs.

I wanted to call it organizational OROI (O-Roy!) but not only is that stupid, but I hope someday someone will make this include the entire organization just not the majors so we should reserve the O for that ;-)
Shawn, I love the article and think it finally gives us a robust standard for judging effectiveness. I'm not sure if I agree that the Rays are "the class of Major League Baseball right now." Their low cost per marginal win is based on years of high draft picks as they sat at the bottom of the standings. This isn't sustainable now that they're successful. As their core of young players reaches arbitration and then free agency, they'll need to pay more to retain that talent or start losing more to restock cheaply with the draft.

In other words, if the Rays stick with their small budget, I'd expect their MR3/ExpMR to do something like y=sin x, while the Red sox seem to have achieved a sustainably high MR3/ExpMR. Perhaps a more accurate measure would be an average MR3/ExpMR over several years to account for past advantages (or to adjust for a previous GM's albatross contracts).
I see this claim made a lot, and I think it's overstated a bit. There are four high draft picks (of their own) on the Rays' current roster, two players drafted from the second round on, one acquired in a trade by LaMar and 18 acquired via trade or free agency by Friedman. Seems to me front-office savvy has had as much to do with the Rays' success as 10 years of sucking, and that's plenty sustainable.
I don't think it's out of the question that they could be a 90+ win team for a couple more years going forward. And if we added the value of the draft picks, they'd probably still be top 2 or 3 in MLB even if we looked at the last five years cumulatively.
And even if that's a case, I think the Rays (and the Marlins strategy) of trying build a cheap team filled with great young players and then trying to win it all over a 3 or 4 year period before you have to blow it all up and rebuild is a far better plan than teams like Toronto who seem to consistently strive for being decent, but never great.

Flags fly forever, consistently being average gets boring.
I understand wanting to use the 3rd order winning percentage to remove the luck, but I don't think it should be in the final form of the statistic. GMs don't get paid for expected wins, they get paid for wins and they have to hope the luck will average out. We don't recalculate slash stats based on line drive/gb/fb/bip percentages, we calculate slash stats based on results. Performance stats should grade out results. MR/eMR could be reduced to MeM.
I think it's important to stick to 3rd-order wins. Much as pitcher wins and RBIs have been forgotten by the statistically-minded, we want to make sure that we judge GMs by what they have control over. They have control over making sure their team has talent on the roster that can win, but if terrible luck in one-run games leads to a .500 record by a team that outscored their opponents by 90 runs, we can hardly blame the GM for poor talent management.
I think you and tballgame are both correct (this is such a weenie comment...). Actual wins should be used to evaluate how a GM has performed, and expected wins should be used to judge how a GM will perform in the future.

By the way, using actual wins and the data provided, the best GMs in 2008 and YTD 2009 are those of the Angels and the Phillies, followed by the GMs of the Rays, Red Sox, Marlins and Cardinals.
"The Pirates, Royals, Orioles, and Nationals would definitely benefit if we included the value of their ensuing draft picks. Of those teams, I'd guess that the Pirates are the only one that actually understood this coming into the season."

Can you clarify that last sentence?
I believe he is referring to the possible perception that the Pirates were the only ones who were willing to publicly show that they are building for the future instead of weak attempts to placate fans with noise about winning this year.

After all, you have not seen the Royals, Orioles or Nationals tear apart their roster like the Pirates did this year. Of the 3 teams I mentioned, only the Orioles seem to be actually trying to build something sustainable. The Royals and Nationals seem poised to,well, stay bad for quite some time.

Strasburg might be awesome, but I can't shake the feeling that by the time he is a front-line talent he will be pitching somewhere other than Washington.
I think when you begin the season with Alfredo Simon, Mark Hendrickson and Adam Eaton in your rotation you aren't exactly signaling "Hey, we're making a run at .500!" The Orioles have almost completely turned their roster over in the past three years. They traded Sherrill and Huff this year, and Mora will finally be gone after this season. I think it's pretty clear the Orioles understood winning 72 games instead of 68 had no real value.
It's more than what the O's are tearing down. The real issue for a rebuilding team is whant they are building up. This year the O's have integrated the following rookies into their starting lineup/rotation - Wieters, Reimold, Tillman, Matusz, Begersen, Hernandez, Berken, Uehara. In addition the following have been added to the bullpen - Meredith and Mackolio (sp?).

This is how you build a team, even if they are not winning.
For the name, I nominate some way of naming it after long-time Rays GM Chuck Lamarr...
I love this, if anyone has any specific ideas.
How about LAMaR - Leverage Above Marginal Revenue
Leverage Adjusted MArginal Revenue
or leverage adjusted marginal annual revenue

annual is kind of a throw-in.
Can you explain a bit how you figured this:

"For example, Boston's $133 million payroll in 2008 should have led to 86 wins."

Ignoring the issue of Dice-K's posting fee, it seems like the Sox spent a lot more money than average to secure just 5 more expected wins than average.
The Yankees throw things off a bit, because they're so far above the mean. I'm gonna keep playing with this and see if there's a more logical way to do it. I don't think the Red Sox's standing here would really be negatively affected.
The Mets are a disaster sums it up very well. Omar must go.
Agreed, but it starts at the top. Who will fire Jeff Wilpon?
Well, Bernie Madoff tried to take him out...
How about Marginal Revenue Ratio (MRR)?
scaled marginal apportionment return tier

scaled-to-market assessment of return per team

not too satisfied with what t stands for, but both should acro to S.M.A.R.T.
I like this, but if the Giants ever accidentally came in first one year....
What he says.
That the Mets are a disaster is a fine observation. But we are still not the Knicks! (and i'll note apparently not worse than last year's yankees.

I think this is really great analysis. Any more backward looking in the works? I would consider this a great litmus test of the legacy of certain GM's.

On the other hand, I trust the work of the great nate, but how sticky are marginal earnings? Are the shea faithful really going to spend 30 million less to see this team than they would have to see that team we paid for? Thats not an excuse for ineffectiveness, but it portends seriously for a team like the ray's future.
Doesn't the presence of a constant (22.538) in the regression equation [MW = 0.1106*MP + 22.538] imply that the base number of wins for an all-minimum wage payroll isn't 49.6? If I'm understanding correctly, this suggests that a team that spends zero on marginal payroll will still end up with 22.5 marginal wins, or 71 wins on the season? Something's not right (quite possibly with my brain or how I'm understanding this regression).
Perhaps it's an issue with the regression equation not being applicable to points outside the data-set. For 2009, the lowest payroll (Marlins) was $35mm, far above the theoretical $12.5m replacement level payroll.
This is going to be an issue no matter how big the data set is, since no team has ever spent 0 MP. That said, it's definitely something I'll look at next time around.
Wouldn't it make a bit more sense to regress the team's winning percentage in a log function? Just as the marginal value of a win is nonlinear, the marginal cost of those wins would likely be similarly nonlinear. Running it in excel from 2002-08, I get xW=162*(0.0812*LN(Payroll) - 0.9716). Granted that doesn't make any adjustments for year over year changes in the league payroll structure. But by this method, going from a 20M payroll to a 30M payroll nets about 5 additional expected wins, an increase from 90M to 100M nets another 1.4 wins, and going from 200M to 210M nets only 0.6 wins:

Payroll xW
20,000,000 63.7
30,000,000 69.1
40,000,000 72.9
50,000,000 75.8
60,000,000 78.2
70,000,000 80.2
80,000,000 82.0
90,000,000 83.5
100,000,000 84.9
110,000,000 86.2
120,000,000 87.3
130,000,000 88.4
140,000,000 89.3
150,000,000 90.2
160,000,000 91.1
170,000,000 91.9
180,000,000 92.6
190,000,000 93.4
200,000,000 94.0
210,000,000 94.7
220,000,000 95.3
If you are going to adjust for payroll you've got to adjust for draft position. Draft position is a resource, just like payroll.

Also, I'm not sure that there's a conclusion to this analysis: is the GM who uses his resources most economically efficiently necessarily the best GM?
ARe the best CEOs the most efficient?
Aren't there other things involved?
Regarding the Rays (and other teams with high draft picks).

Assuming those teams must fork over substantially more signing bonus money than teams behind them in the draft, should we somehow incorporate signing bonus money into the "team payroll" being analyzed?

(And yes, I do realize many teams of late ignore the "guidelines" and offer draft picks substantially "over slot", somewhat negating the higher bonuses theoretically attached to the Rays of the late 90s/early 00s)
Sorry greensox ... I think I just reiterated some of your point. :-)
Makes sense, but curious if there is source or metric that relates payroll to expected probability of making the playoffs. For example, winning 70 games is probably a very low probability, while winning 90 games has a high probability. All this takes is computing wins to expected probability of making the playoffs, maybe by division (different for AL East vs. NL Central, for example).

I get that making the playoffs is more valuable to big markets vs. small, but curious to just the probability for making it.
Check out Nate's chapter on this in BBTN. The marginal revenue per win curve is largely based on the probability of making the playoffs with x amount of wins.
Revenue Exceeding eXpectations - REX?
Loved the article. That being said, are we really rating GMs or organizations as a whole? Granted GM's have a lot of say, but you're also talking about farm system competency, scouting, etc.

As for an acronym, I like something that includes efficiency. Perhaps something like WRE for Win-Revenue Efficiency or OWRE Organizational Win-Revenue Efficiency pronounced like the word "ore" or like "over" but with a "W" instead of a "V"
If I'm reading the full chart correctly, Billy Beane is dead average...
Because he has been arb'd out of getting undervalued players...
The article attempts to incoporate an assumption that all wins aren't created equal. Fair enough.

But are all $ created equal? Does a $ mean the same to the Yankees as the Rays?

No, but that's what the denominator is there for -- to put their dollars in context.
The Mets are terrible....but jesus folks....they've had more injuries than most teams get in TWO fucking years, yet alone one.

This is all well and good - but it completely ignores that fact.
There has to be a way to incorporate injuries... sometimes injuries really are crazy flukes (CM Wang's foot injury last year strikes me as a decent example). Other times, they're really rather predictable (Posada last year was an old catcher. Delgado this year, old guy. They get hurt and/or decline quickly). Maybe tie it up with Will Carrol's system (if a "green" player gets hurt, this system softens the impact so the GM isn't blamed too much. If a "red" player gets hurt, this system shrugs and doesn't care - that's on the GM).
Well, not really... the ability to avoid injuries and rehabilitate successfully (and quickly) from injuries is determined by the trainers/doctors hired by the GM. In addition, managing injuries falls under the hitting and pitching coaches, who are also hired by the GM. Lastly, the GM goes about acquiring the players in the first place and if they acquire injury-prone player, then that reflects the level of risk the GM is willing to take on.
The problem with that "hump-backed" marginal revenue curve is that no team REALLY knows where it's going to be on it before the fact.

There's so much uncertainty in baseball, a good GM might think "I've got an 85-win team (50th percentile forecast!). So the hump-backed MR curve says getting a 5-win player will add about $20M to my revenues. Woo-hoo; I go out and sign that guy."

But then random variation inperformance, or injuries, keep the team from its 50th percentile forecast, and it wins... maybe 85 anyway. The GM looks like a boob, but was just unlucky. You can also get the breaks and look like a genius on the other side of the randomness mountain.

Expected marginal revenues MR (as opposed to realized, after the fact MR) are probably best classified as either "non-contender status MR" or "contender status MR." The idea that a GM can and should make fine delinieations about MR for each win from 85 to 95 seems unrealistic, given how much "variance happens."
I got stuck on the first point of methodology:

"First, we need to know how much marginal revenue each team is likely to bring in, based on its win total and market size. To do this, we'll use Nate's MR/MW curve, updated for 2009 revenues. We'll then assign each team a market-size factor based on its 2007-2008 gate receipts."

Wouldn't basing market size on gate receipts be a poor indicator of market size where big markets have bad teams? The fact that last year's receipts affect this year's management decisions notwithstanding, it would seem that the potential for marginal profits from a boost in attendance would be greater in a place like DC, where half the stadium is empty almost every night. I would think, therefore, that using gate receipts as an indicator of market size would actually understate the revenue-generating potential of improvements in attendance.
I'm with you on this objection. Something is off.

One straightforward method to evaluate GMs is just on revenue growth. This method penalizes them for their success in that regard.

I think there's something squishy about what exactly we're taking the measure of. If profit is the goal, measure that and forget about wins. If efficient use of payroll for competitive advantage is the sine qua non, this method is inferior to the previous. If efficient use of available payroll is more fair, put in a factor for revenue pct used.

This method is neither fish nor fowl.
Third-Order Marginal Effectiveness (TOME)

If you want to know how well a Front Office is doing, it's all in the TOME.
It's a tacky article.

You can politely say that you are building on the work of your predecessors, which both acknowledges your intellectual debt while obviously implying that you intend to make an improvement. When you know that a writer (a) died prematurely and (b) had a loyal following, you ought to think twice before writing that one of his better-known formulas "failed even the simplest laugh test." Just do your own work without running down others' work.

Maybe it just rubbed me the wrong way: it doesn't look like anyone else commented on it.
Good stuff. Only thing I'd change in the linear nature of converting Marginal Payroll into Marginal Wins. It's a lot easier to spend efficiently with a low payroll (paying mostly guys in their first three years) than with a high payroll (with significant spending going to free agents). Tom Tango and David Gassko have found a logistic regression equation works pretty well:

ExpWins = (P + 2*L) / (P + 5*L) * 162

Where P is team payroll and L is league-average payroll. I think I saw something recently where Tom may have changed his preferred weights on the L's.

Some reading is here: