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
Padres	$86,000,000	$43,500,000	1.1%	$3,954,545,455
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.