# Payroll Efficiency, by Playoff Odds

For the last decade or so, various versions of payroll efficiency estimators have popped up to measure which teams are getting the most bang for their buck in terms of spending. The late Doug Pappas pioneered this research in MLB, using a formula he called Marginal Dollars, Marginal Wins. That is basically the ancestor of the present \$/WAR calculation we often cite, looking at the cost a team paid to add wins to their side of the ledger. These kinds of calculations have helped identify which teams have invested their resources wisely, and which teams are simply squandering their wealth while getting little in return.

However, there’s always been a bit of a problem with \$/WAR calculations, because we know that the value of each win added is not linear. The value of a win is better described as a curve, with a sharp inflection in the mid-80s when each additional win significantly increases a team’s chance of making the postseason and going on to compete for a World Series title. A team should not be incentivized to pay as much as for their 78th win as they are for their 88th win, and a rational GM would indeed pay more to make a marginal upgrade on a contender than he would if his team was expected to finish out of the running.

\$/WAR calculations ignore the marginal differences in the value of a win, and end up putting too much emphasis on teams that manage to be good and cheap while penalizing teams that are great and expensive, even though the wins added that pushed the great team into that next tier are the ones that make the most sense to overpay for. So, today, I thought I’d try a new spin on the team efficiency calculations, using our expected playoff odds instead of a team’s projected WAR to measure the value of team spending.

For 2014 payroll, I took Wendy Thurm’s estimates from last month and made just a few adjustments, adding in recent signings like Nelson Cruz and Ervin Santana to update the totals. I then pulled in our playoff odds data and matched up those estimates against the payroll estimates. Before calculating the totals, however, I also made one extra calculation, because we don’t want to simply divide the playoff odds by the team’s expected payroll.

What we actually care about is the amount that each team spends above and beyond the minimum payroll, since that is the additional cost that teams are spending to in order to increase their playoff odds. Traditionally, this minimum payroll has always been tied to the concept of having an entire team of replacement level players making the league minimum, so with a \$500,000 salary floor in effect for 2014, a team’s minimum payroll is \$12.5 million. But that’s not actually the league’s payroll floor for each team, and because we’re not using WAR as our win barometer, we’re not tied to replacement level. In reality, MLB enforces a higher level of minimum spending, and if they don’t, the MLBPA files an official complaint until the league directs the franchise to spend more cash on their players. With league revenues pushing over \$8 billion, there is a de facto minimum payroll floor in place, and it’s well north of a \$12.5 million Opening Day payroll.

The effects of the minimum payroll expectation showed up in free agency this winter, as the non-contending Astros gave \$30 million to Scott Feldman and a combined \$14 million to Jesse Crain, Chad Qualls, Matt Albers, and Jerome Williams. The Marlins — the team most often threatened for failing to keep their payroll at acceptable levels — spent \$21 million on Jarrod Saltalamacchia, and then \$14 million combined on Garrett Jones, Rafael Furcal, Carlos Marmol, and Casey McGehee. These are the only two teams in baseball with an expected payroll under \$50 million, and realistically, neither is going to contend in 2014, but both bought veteran free agents because MLB and the Players Association would have yelled at them if they didn’t.

The Marlins, realistically, represent something like MLB’s de facto payroll floor. Whatever the least amount they can spend, that’s what they’ll spend, so I think it’s fair to say that their estimated \$42.5 million Opening Day payroll is about as low as MLB will tolerate, even for a non-contender. So, if we subtract out that essentially required \$42.5 million from every team’s payroll, we get the marginal dollars each team spent trying to win. Those marginal dollars are what we’ll evaluate a team’s playoff odds against to calculate payroll efficiency.

Because we’re using a percentage as the denominator, the easiest way to present the data is to think of it as a World Series valuation. When you buy a fraction of a thing — say, stock in a company — the valuation of that company is based on the assumption that you could continue to purchase all the remaining shares at that same valuation. If you pay \$100,000 for 50% of a company, than the company is valued at \$200,000. We’ll use the same valuation model here, and so the figure listed is the World Series valuation based on the share of WS Odds that a team bought with their marginal payroll.

Team Payroll Marginal Payroll WS Odds WS Value
Athletics \$79,000,000 \$36,500,000 5.2% \$701,923,077
Rays \$75,500,000 \$33,000,000 4.7% \$702,127,660
Cardinals \$108,500,000 \$66,000,000 8.1% \$814,814,815
Nationals \$130,500,000 \$88,000,000 10.6% \$830,188,679
Pirates \$71,500,000 \$29,000,000 3.1% \$935,483,871
Tigers \$161,000,000 \$118,500,000 12.4% \$955,645,161
Red Sox \$158,000,000 \$115,500,000 9.2% \$1,255,434,783
Dodgers \$223,000,000 \$180,500,000 13.0% \$1,388,461,538
Indians \$80,000,000 \$37,500,000 2.6% \$1,442,307,692
Mariners \$87,500,000 \$45,000,000 3.1% \$1,451,612,903
Angels \$151,000,000 \$108,500,000 5.7% \$1,903,508,772
Rangers \$131,000,000 \$88,500,000 4.4% \$2,011,363,636
Braves \$110,000,000 \$67,500,000 2.2% \$3,068,181,818
Royals \$91,000,000 \$48,500,000 1.3% \$3,730,769,231
Blue Jays \$136,000,000 \$93,500,000 2.5% \$3,740,000,000
Giants \$147,000,000 \$104,500,000 2.7% \$3,870,370,370
Reds \$106,000,000 \$63,500,000 1.5% \$4,233,333,333
Yankees \$197,500,000 \$155,000,000 2.8% \$5,535,714,286
Rockies \$91,000,000 \$48,500,000 0.8% \$6,062,500,000
Diamondbacks \$110,000,000 \$67,500,000 0.9% \$7,500,000,000
Brewers \$100,500,000 \$58,000,000 0.7% \$8,285,714,286
Orioles \$113,000,000 \$70,500,000 0.6% \$11,750,000,000
Mets \$82,000,000 \$39,500,000 0.1% \$39,500,000,000
White Sox \$89,000,000 \$46,500,000 0.1% \$46,500,000,000
Cubs \$89,000,000 \$46,500,000 0.1% \$46,500,000,000
Phillies \$175,500,000 \$133,000,000 0.2% \$66,500,000,000
Marlins \$42,500,000 0.2%
Astros \$49,000,000 \$6,500,000 0.0%
Twins \$82,500,000 \$40,000,000 0.0%

(Note that the Astros and Twins are basically considered, by this metric, to have wasted all of their marginal dollars, because we estimate their WS Odds at 0.0%. Of course, winning the World Series isn’t the only goal of spending money, but this measure is only attempting to measure efficiency towards that goal, so they both end up with null valuations. The Marlins are also a null value, even though they are at 0.2% WS Odds, because we used them as the payroll minimum, so they are judged to have spent no marginal dollars. I doubt you care about the payroll efficiency for those three teams anyway, so let’s just move on to the other 27.)

The A’s payroll and chances of WS victory means that they are buying into the World Series at a valuation of around \$700 million, and the Rays are just behind them, close enough that it is essentially a tie at the top. They generally dominate lists like this, so seeing Oakland and TB at #1/#2 is no surprise. However, the value of this measure shows up in the next group, where you see real spenders like St. Louis, Washington, Detroit, Boston, and yes, even the Dodgers. LA’s spending spree has been deemed fiscally irresponsible by many — myself included, on deals like the Boston bailout trade — but based on the share of WS Odds they’ve purchased, they’ve actually been one of the most efficient spending teams in MLB. They’ve spent a lot of money but they have a majority share to show for it, and are one of only three teams with WS Odds over 10%. These are the kinds of teams that get shafted by \$/WAR measurements, but are actually spending in a reasonable manner when you account for baseball’s win curve.

Not every team could be described as a “reasonable spender”, however. Teams like the Diamondbacks, Rockies, and Orioles have run up significant costs without moving their WS Odds needle very much at all, and while they can use their payroll to defend the idea that they’re trying to win, none of them look likely to succeed at that goal. The Mets, Cubs, and White Sox can somewhat be excused for their high values, since they’re not really trying to win, and are simply running higher minimum payrolls based on being large market teams with access to significant revenues, so their own internal payroll floor is likely higher than that of the Marlins or Astros.

But then there’s the Phillies. They are trying to win. They’re not rebuilding, and this team was constructed with an eye on contending in 2014. And yet, while the median World Series valuation for the other teams ahead of them came in at \$3.4 billion, the Phillies share of the WS Odds and the money they’ve spent to get those odds mean that their implied valuation of a World Series title chalks in at an astounding \$66.5 billion. That is what it would cost the Phillies, at their current efficiency of spending, to buy a 100% chance of winning the World Series, if such a thing were possible. \$66.5 billion.

Now, of course, a World Series championship isn’t actually worth \$66.5 billion, or even \$700 million. These implied valuations fall apart because no team can actually buy out all of its competition at the prices that they’re constructing their rosters. We’re mixing some apples and oranges here, so don’t take these numbers and say that Dave Cameron thinks that winning the World Series is worth several billion dollars to a franchise. It’s not, obviously. But I think this does a better job of showing us who is spending their money effectively than simply looking at team spending per WAR, since not every win is created equal.

And once you factor in the additional value of higher win totals, the most efficient spenders aren’t always the cheap guys limping their way to a .500 record. The A’s and Rays still are as good at this as we thought, but a lot of the big spenders are putting their money to good use too. Even those crazy Dodgers aren’t quite as crazy as one might think.

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Dave is the Managing Editor of FanGraphs.

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cass

The Nats have a 5x greater chance of winning the World Series than the Braves? That can’t be right. Same division, same teams faced. Relatively even talent. There’s no way the difference can be that big.

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Blair

You watch the news lately? Planning on joining the rotation yourself?

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Aaron (UK)

The Atlanta Tommy Johns have not just damaged the Braves’ chances, but have also boosted the Nats’ chances considerably, making them look even better in this table. I don’t really think the Nats deserve “credit” for that, though.

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Anon21

Depends on what you mean by “considerably.” Ervin Santana is a pretty close replacement for Medlen, and Beachy is slated to be replaced by four to six weeks of Freddy Garcia plus several months of Gavin Floyd. Projections also didn’t see Beachy as a major contributor anyway.

The Braves have definitely gotten worse with the injuries, but keeping in mind that a) one player rarely makes a difference of more than a couple wins over the course of a season b) Medlen is no Mike Trout and c) the Braves have partially patched the hole left by these injuries, the doom and gloom being forecast is overblown. I think the Braves will beat the Nationals and take the division again, but even if you don’t agree, projecting the Nationals to run away with the division because of the pitching injuries the Braves have suffered is not sound.

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The Foils

The above analysis, besides being a bit cavalier IMO, ignores the hit to depth.

While the loss of one player, on its own, is rarely a big problem, the domino effect sure could be. I know I wouldn’t want to gamble on Gavin Floyd staying healthy and productive enough to prevent Freddy Garcia, #3* starter.

*chosen for hyperbole and a desire to not go look at a depth chart

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Anon21

Freddy Garcia is not an unacceptable sixth starter for a contender. He looks generally comparable to Tanner Roark, the Nationals’ probable sixth starter, and the Nationals will also be in some serious trouble if Roark ends up sliding up to #3.

I agree that the Braves are not particularly deep on starting pitching, but they’re in about the same position as the Nationals in terms of 6-7-8 depth, and the Nationals will be hurt more than the Braves by additional starting pitching injuries because they have a greater proportion of team WAR and salary tied up in the rotation than the Braves do.

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Nick Donohue

Very surprising that Anon21 thinks the Braves will win the NL East! I didn’t even know he was a braves fan!

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Rob

Pretty sure Anon21 also thought the Braves would win the division last year…how did that one turn out?

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Nick Donohue

He was convinced they would in 2012 as well. I think he’s generally ALWAYS convinced the Braves are going to win the division. I don’t think I have seen an article on here without Anon21 bitching about how much FG underrates/is WRONG about the Braves. I love my team too, but I also don’t write 5 paragraph impassioned defenses any time they are “slighted” by FG.

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Anon21

Actually, I think I expected the Phillies to win in 2012, like a lot of people. So no points for me on that prediction.

Anyway, Dave didn’t slight the Braves, but I took issue with some things that commenters had to say about the relative strength of the Braves and Nationals. I do realize that commenting in a comment section is an unpardonable offense in some people’s eyes, and I guess they are technically entitled to their opinions. Some people like discussing baseball, and some people like discussing the way other people discuss baseball. De gustibus non est disputandum and all that.

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AK7007

Anon21, it’s not disagreement or discussion that people are taking issue with – it’s that your disagreement is perceived as irrational due to your fandom. It’s one thing to say that “I disagree with the difference in WS odds between the Nationals and Braves due to reason X,” but you phrase it as “no way the difference can be that great” without really delving into why you think they are evenly matched.

Meanwhile, non-NL East fans see a 6 WAR gap between the two teams. This says that the one with a higher projected WAR is more likely to go all the way. If things don’t go as the projections predict, we recognize that the runs we predict each team to score are actually on a distribution, instead of as proof that projections hate the Braves.

I don’t know what FG has to gain by purposefully making false projections about the Braves. If there is a legitimate discrepancy, meaningful discussion would center around “we can improve projections by…” Not “Fangraphs is WRONG, how dare they slight my precious Braves!”

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Anon21

I didn’t say “Thereâ€™s no way the difference can be that big.” My handle doesn’t even look like the handle of the person who said that. And I didn’t say anything about Fangraphs hating the Braves or any of that other nonsense—that’s just a lazy strawman. I think the Braves will win, and I’ve given specific reasons why. Again, the meta-discussion is pretty boring. If you want to actually talk about which team is stronger, that could be interesting, but talking about the way we talk about is a waste of time.

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cass

For what it’s worth, I made the original comment on this thread and I’m a Nats fan. But I really am uncomfortable with these predictions after what happened last year. I know I’m biased, but earlier in the offseason (and based only on Steamer), the Braves had a slight advantage in expected WAR. I was really surprised losing two pitchers and adding in ZiPS changed things that much.

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David

“projecting the Nationals to run away with the division because of the pitching injuries the Braves have suffered is not sound”… because your analysis is sound, doesn’t agree, and leaves no possible alternatives?

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Kevin

The Nats on paper are a MUCH better team than Atlanta. The Braves are fooling themselves thinking that they re even close to a playoff lock.

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MrMan

Isn’t this EXACTLY what we heard prior to the 2013 season?

Those World Series odds are little better than shots in the dark.

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Kevin

That’s more a fault of variance in baseball than anything else. Things are too random to control. IIRC the Standard Deviation of a teams Pythagorean Expectation is 6.5 wins so to cover 95% of cases you need to add plus minus 13 wins to a teams record.

If you ran a simulation enough times the Nats would win 5x more WS than Atlanta but it’s not like we play the same season 10,00 times.

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Garrett's Mom

Didn’t the Braves have a full rotation heading into the 2013 season, though? They were fortunate that year in terms of the health of their best pitchers. This year… not so much. Right now, they can’t reasonably expect 3/5 of the rotation to be out there after the 5th or 6th. That is not an issue that contending teams have.

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Rob

You do realize the Braves returned just 2 members of their opening day rotation in 2013, right? Medlen had never spent a full season as a SP, Maholm had a career ERA well north of 4, and Teheran was coming off a terrible year in AAA. Throw in the loss of 2 of the best LH setup men in the game and Braves pitching staff was far from settled at this point last year.

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RMD

No they’re not.

The Braves had LITRALLy black holes in 25% of their everyday lineup but still thrived. FanGraphs and Baseball Prospectus both had their underlying stats back up their success. Their rotation will be worse, sure. But look for production from CF and 2B to rise. I also don’t think Jason Heyward will be hit in the face and need another appendectomy this year again. I’ll still take the Nationals, but the Braves are close.

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Eminor3rd

Literally? Black holes?

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bdhudson

No, Eminor3rd, LITRALLy

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Plucky

If the Braves black holes are LITERAL then I really hope you’re over the event horizon by now so we never hear from or see you again

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Kevin

Compare the Nats and Braves by position.

Rotation: Clearly in the Nats favor and it’s not even close.
1B: Braves
2B: Push or Nats
3B: Nats by 1000 miles
SS: Closer but I’d still take Nats.
LF: Nats once again
CF: Hard to say with Upton being such a wildcard
RF: I’d take a healthy Hayward over a healthy Worth but it’s close.
Bench: I don’t know enough to make a solid case for either.

But that’s 3 for Atlanta 6 Washington or so.

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Anon21

ZiPS projects R. Zimmerman for 3.4 WAR and C. Johnson for 1.3 WAR, while A. LaRoche checks in at 1.1 and F. Freeman at 3.6. So if the Nats are ahead by 1,000 miles at 3B, the Braves are ahead by about 1,200 at first. And that’s on the assumption that C. Johnson’s defensive projection measures the damage done to the Braves; I don’t think it does, due to A. Simmons’ range on the left, and I have a full season of batted-ball results to back that up.

At short, you can take Desmond over Simmons, but no projection system does. The closest would be ZiPS (4 to 3.5 WAR advantage for Simmons), but Steamer sees Simmons as nearly twice as valuable. So “on paper,” try again there.

In right, you also need to take into account that a healthy Heyward is much more likely than a healthy Werth.

At catcher, Gattis has a lot of volatility connected to his plate approach, but Ramos has had serious, chronic injuries dog him throughout his career, and I don’t think you can reasonably project him to spend a full season behind the plate. 80% Gattis and 20% Laird vs. half Ramos/half Lobaton, I’d take Gattis/Laird.

There’s a lot of uncertainty. The Braves were the third best-hitting team in the NL last year. They lost McCann, but aren’t likely to see the extremes of terrible performance at second base and centerfield that they endured last season. Moreover, they have a good chance of age-related offensive gains from the Heyward/Freeman/Simmons core. The Nationals had a disappointing lineup that they tinkered with around the margins. (Lobaton is actually a pretty important addition given Ramos’s health, but he’s not an impact bat.) Harper can be expected to contribute more if he’s healthy, but the rest of their squad should be projected to remain about the same (Desmond, Zimmerman, Ramos, Span) or decline (LaRoche, Werth). If they get the Rendon breakout everyone’s so fond of forecasting, that’s a shot in the arm, but overall it’s not an intimidating lineup compared to what the Braves are rolling out.

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Kevin

Both teams have fairly uninteresting lineups. That’s kinda a given. I’d still take Desmond over Simmons any day of the week. Defense has way too much variance to rely on predictions. We could easily see Simmons drop dramatically just based on simple variation. Desmond’s bat over Simmons glove.
1B is the least important position in the game and if the Nats need to they could make an upgrade mid-season.

I agree with you on the RF part of the equation, the Braves likely have a better chance of getting at least 3 WAR from the position.

But in reality even if the Braves beat the Nats in the majority of batting positions their rotation is so above and beyond the Braves can throw out isn’t not even close. Without the injury’s Atlanta had the what 20th best Rotation vs Washington’s 4 overall. Seriously the Braves best SP left is worth less than the Nats 4th.

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Anon21

“Thatâ€™s kinda a given. Iâ€™d still take Desmond over Simmons any day of the week. Defense has way too much variance to rely on predictions. We could easily see Simmons drop dramatically just based on simple variation.”

I don’t know what you mean here. There’s a lot of variance in measuring defense, but all quantitative and qualitative evaluations seem to agree that Simmons is a generational defensive talent. And in terms of the raw results, he helped the Braves to a top-5 finish in groundball BABIP while fielding beside Chris Johnson. It doesn’t seem like he’s any more like to suddenly get bad at fielding than Desmond is to suddenly lose his bat.

“1B is the least important position in the game and if the Nats need to they could make an upgrade mid-season.”

1B is just as important as every other position, no more and no less. And no, I assure you, the Nats are not going to have an easy time hauling in a 4-5 WAR first baseman at the deadline. They are few and far between, and the teams that have them aren’t parting with them.

“Seriously the Braves best SP left is worth less than the Nats 4th.”

Not really. Strasburg and Fister are head and shoulders over everyone else in both rotations, no question. But then you have a group of six pitchers who are all good in different ways, without a lot to differentiate them from an overall production standpoint: Minor, Zimmermann, Wood, Gonzalez, Santana, and Teheran. The Nationals have the advantage in starting pitchers, but that’s not the safest place to build your advantage, since pitchers break.

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John C.

Anon21, I realize that you’re looking at lineups through Barves-colored glasses, but I’ll just note that of the Nats positions they are likely to get significant gains from:

-LF. You failed to mention Harper completely in your writeup, probably because you couldn’t figure out how to award “age related gains” around the diamond for the Braves without doing that for Harper. And that’s putting aside the fact that Harper is likely to play more games, and healthier games, than last year.

-1b. LaRoche isn’t likely to rebound to his career average numbers due to age, but he is quite likely to regress positively to some number between last season and his career averages. Last season was the worst full season of his entire career.

-2b. Rendon doesn’t have to break out to provide a significant bump over the black hole that was Danny Espinosa and Steve Lombardozzi at second last year. If he does break out (and his batted ball and pitch recognition profiles were very last year, that’s just icing on the cake.

-C. Ramos played less than half a season last year. A healthy season from Ramos is a huge bonus, and even Lobaton is a bump from the (lack of) production they got out of Kurt Suzuki and Jhonatan Solano last year. Your point about which catcher tandem, Braves vs. Nats, that you’d prefer is not relevant to the question of whether the Nats will get more offense than last season.

3b. Ryan Zimmerman is only 29 years old and from the middle of the season onwards and into this Spring he has finally been looking like himself again.

So around the diamond that’s five positions that are likely to step up, two (SS, CF) that are likely to stay the same, and one (RF – I’ll allow Werth is unlikely to match his numbers last year). That’s an increase to a “disappointing” lineup last year that finished 6th in runs and 3rd in HRs in the NL.

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John C.

Oh, for an edit function.
Rendon’s batted ball and pitch recognition profiles were very impressive last year.

And to be clear, I think LaRoche’s regression is most likely a dead cat bounce. But there should be a bounce, and after this season he isn’t going to be the Nats’ problem.

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David

Theoretically, a team would only need a literal black hole at one position to have perfect team defense. You’d have to figure out a way to get the ball to cross the plate on the pitch though… and for all the players and fans not to get eaten.

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Bubber Jonnard

Current Bovada odds have Washington at 11-1 to win the World Serious, and Atlanta at 16-1. To win the N.L East, Washington is favored at -140 and the Braves are 2nd choice at +150.

So I guess the gambling public is yet to abandon the Bravos for the Nats.

Make of all that what you will.