Salaries and Win Shares: An Intro

Half the money I spend on advertising is wasted; the trouble is I don’t know which half.
- John Wanamaker

It used to be that baseball fans had the same problem that John Wanamaker had. How much salary should a ballplayer receive? Did he earn his money or not? How much should a pitcher be paid vs. an everyday player?

Times are changing. We now know a lot more about how much each player contributed to his team, and how much he was paid (including some mind-numbing contract clauses). Rotisserie baseball has turned us all into tabletop General Managers. Contracts are fun! And fun to write about, too.

In two recent articles about the Eric Chavez contract, Aaron and Matthew did a nice job reviewing the pros and cons of that deal. In particular, they used a number of baseball stats to assess the value of his six-year, $66 million bonanza. Some of the stats they used include GPA, RCAP, OWP and Win Shares.

Win Shares, in my humble opinion, is a great stat for evaluating contracts. It’s simple: Teams make more money when they win more games. Win Shares measures the contribution each player made to his team’s wins. So Win Shares measures how much each player helped his team make money.

Also, Win Shares allow us to compare all players across positions, including everyday players and pitchers. A dollar is a dollar, regardless of who earns it, and a Win Share is a Win Share, regardless of who earns it. The same can’t be said of most other stats. That’s why Win Shares is one of the best contract evaluation tools around.

So let’s look at Win Shares and dollars, as a way of further discussing the much-discussed Chavez contract.

Eric Chavez created 25 Win Shares the last two years, and 24 the year before that. As Aaron and Matthew pointed out, he’s been tremendously consistent and durable. Here’s Matthew’s take:

“He’s one of the most consistent hitters in all of baseball, batting around .280/.350/.515 in each of the last four years.”

So for simplicity’s sake, let’s assume he’s going to produce 24 Win Shares a year for the length of his contract. (Warning: not an official forecast. Will disavow any knowledge of this sentence in the future.)

First of all, how much did major league teams pay for wins last year? Well, they paid a total of $2.1 billion in player salaries, and they won a total of 2,430 games (30 teams times 81 wins, on average). So they paid about $865,000 for each win. I know these aren’t precise numbers, but you get the drift.

I believe this is why Matthew says, in his article, that wins cost about a million dollars each. Simple math. Since there are three Win Shares for every win, Chavez would contribute eight wins (24 divided by three), which means he’d be worth $7 million a year (eight times $865,000).

Problem is, this isn’t quite right.

You see, there are a lot of good baseball players in the minor leagues, guys who would do reasonably well in the majors if given the opportunity. Some recent examples include Bo Hart and Brian Daubach. Also, they would only make the major league minimum salary, which was $300,000 last year. Sabermeticians call these guys “replacement-level players.”

A team full of replacement players would probably win about the same number of games as last year’s Detroit Tigers (actually, a well-constructed team of replacement players would almost certainly win more than the Tigers did, but that’s another story). So, a major league team could probably win 40 games by only spending around $7.5 million (25 roster spots times $300,000). Dividing the numbers, this would only cost about $187,000 a win.

This is the same territory that Doug Pappas explored in the most recent Baseball Prospectus (if you haven’t ordered a copy, check it out). In an article called “Marginal Payroll/Marginal Wins”, Doug analyzed each team’s salary effectiveness by comparing the number of wins over those achieved by a replacement level team, to the salary dollars paid above the major league minimum.

It’s the wins after the first forty that are tough to get. They require players who are better than replacement players and who usually must be paid more than the major league minimum. Using Doug’s language, marginal wins are more expensive than replacement-level wins.

How much did major league teams pay for each win above replacement-level wins? About $1.5 million each. Here’s the math:

Total salaries paid:                     $2.1 billion
Subtract total minimum salaries paid:    $225 million
                                        -------
Salaries paid above minimum:             $1.875 billion

Total wins:                               2,430
Subtract replacement-level wins:          1,200 (40 wins times 30 teams)
                                          -----
Wins above replacement:                   1,230

Extra salary per win above replacement: $1.5 million ($1.875 billion divided by 1,230 wins)

I don’t know if I’m making sense here. I communicate better with graphs:

image

As you can see, there’s a big difference between replacement-level wins/salaries and marginal wins/salaries. We somehow need to apply this sort of thinking to individual players.

When Bill James rolled out his Win Shares opus, he included a chapter called “Win Shares and Replacement Level (Or…Pandora, shut your trap).” In that chapter, he conceded that the Win Shares work wasn’t quite done, that Replacement-level Win Shares were a logical next step. But the extra work would be complex, and James wasn’t quite ready to tackle it at the time. So this past winter, I gave it a shot.

In particular, I whiled away my time over at baseballgraphs.com, calculating something that I finally called Win Shares Above Replacement (WSAR).

WSAR measures the number of Win Shares a player created, above what a replacement player would have created, given that player’s playing time. In essence, it’s a player-specific representation of the Marginal Wins in the above graph. For pitchers, playing time is measured by innings and leveraged innings. For batting Win Shares, I use plate appearances, and for fielding Win Shares I use innings played in the field.

I didn’t address all the issues that Bill James raised in his book, but I think I came up with a decent approach. And I certainly think that WSAR is preferable to Win Shares, particularly for contract evaluation.

Last year, Eric Chavez created 16 WSAR. At $1.5 million a marginal win, (or $500,000 per WSAR), he’d be worth $8 million (actually, $8.3 million, adding $300,000 to cover the replacement level Win Shares). This is definitely a better estimation of his worth.

Problem is, this isn’t quite the right approach, either.

See, some player salaries are set by the market, but others aren’t. There are three fundamental ways that salaries are set:

  • Free agency, which is basically like eBay but not online
  • Arbitration, which is kind of like government-regulated price setting (think of your local utility board, pre-Enron), and
  • “Not even arbitration,” which is the kind of environment in which Charles Comiskey would be most comfortable.

I classified all 2003 players into one of these buckets (examples: both Mo Vaughn and Esteban Loaiza were free agents, while Albert Pujols and Marcus Giles were not even arbitration eligible) and calculated how much each player was paid above the major league minimum. I then compared their salaries above minimum to Win Shares Above Replacement, and got the following results:


StatusTotal WSARTotal Sal>MinimumSalary per WSAR
Free Agents 1,565 $1,343,141,774 $857,997
Arbitration Eligible 1,026 $450,171,570 $438,823
Not Arbitration Eligible 818 $7,701,444 $9,419
Grand Total 3,409 $1,801,014,787 $528,319

There’s a lot to talk about here, but the bottom line is that free agents cost almost twice as much per WSAR than arbitration-eligible players ($860,000 to $440,000). My guess is that this is partially caused by long-term contracts. The first year of a contract is more predictable, and likely to be a better reflection of intended value, than later years of a contract. Although many owners bemoan the arbitration process, at least it has saved them from handing out even more long-term contracts.

Regardless, players make the most money when teams bid for their services. Chavez is a great case in point, as he will go from $5.2 million this year (an arbitration-eligible year) to $11 million next year (when he’d be eligible for free agency).

So, at $860,000 per WSAR times 16 WSAR, Chavez’s contractual value is close to $14 million a year, and it begins to look like the A’s got themselves a pretty good deal.

Of course, this isn’t quite the right approach, either. It’s closer, but still not quite right. There are a number of other things to consider. For instance:

1) Good third basemen are hard to find.

Here’s a list of total WSAR by position last year:

POS    WSAR
---    ----
1B      296
2B      234
C       226
SS      206
3B      195

Chavez is a very good player at a position without a lot of good options. He probably received a premium because of it.

2) The 16th WSAR is worth more than the first WSAR.

In the May, 2003 Journal of Sports Economics (no, I don’t subscribe), a couple of Loyola College professors — Stephen Walters and John Burger — analyzed the revenue dynamics of a win. Based on data from 1995 to 1999, they found that contending clubs, in general, added $1.5 million in revenue for each additional win, and non-contending teams added only about $250,000 for each additional win. They defined a contending team as any team with 84 or more wins in a season.

This is why contending teams tend to shell out the bucks for the big contracts, and the losing teams try to find cheaper ways to collect talent. The big contract is more likely to pay off for the contending team.

I also believe that major league GMs approach individual players the same way. It’s hard to find players who produce 15 to 20 WSAR, but those are the guys who get you into pennant races. So each additional WSAR is worth a bit more than the previous one, meaning that salaries rise more quickly for the greatest players.

3) Major league GMs tend to overpay pitchers and underpay everyday players.

Here’s a table of salary for each WSAR paid to free agents by position this past year:

Position    Salary per WSAR
   P         $1,050,662 
   SS        $1,019,427 
   3B          $999,730 
   OF          $801,902 
   1B          $747,436 
   C           $698,912 
   DH          $639,304 
   2B          $565,166

Win Shares has been criticized in the past for undervaluing outstanding pitchers. I actually don’t believe that this version of WSAR undervalues pitchers, for several reasons I won’t get into here.

Long-term pitcher contracts are more of a gamble than long-term contracts for everyday players, and these salary figures reflect that. Major league GMs appear ready to take that gamble because of the potential payoff a great pitching year can bring.

4) Wins are worth more for some teams than others.

This, in a nutshell, is the competitive imbalance issue. Walters and Burger found that a win in New York is worth about six times more revenue than a win in Milwaukee (Oops. Sorry, Bud). The local media markets and relative population sizes create more money-making opportunities for their teams.

It’s no accident that the most dominant team in major league history is one based in New York. The Yankees have an aggressive owner, sure, but they also have access to the biggest market, yielding the most revenue, in the country.

5) Most importantly, this is a different market than the one in which most of those free agent signings occurred.

In December of 2000, Manny Ramirez signed a contract that would pay him $18 million in 2003 (and even more than that in later years). It helped that he had just played a career season, with 35 Win Shares. But his 2003 performance was about what should have been expected: 28 Win Shares and 19 WSAR. So he received slightly less than $1 million per WSAR this year.

This year, Vladimir Guerero, who can be expected to contribute 25 to 30 Win Shares next year and 18 to 20 WSAR (if healthy) signed a shorter contract that will pay him $11.5 million next year. If that projection holds, he’ll receive around $650,000 per WSAR.

Times have changed, and we shouldn’t use previous year’s deals to judge today’s deals. A reasonable guess is that players are now receiving 25% to 35% less per WSAR than they received in the past.

Trying to put this all together for the case of Eric Chavez is complex. My fundamental reasoning would be this:

  • Based on current salary payouts, Chavez is worth about $14 million a year.
  • But this market is tougher than the old ones, and I would discount that $14 to $10 million
  • He’s a third baseman, but he’s not a pitcher. Add a million, to $11 million.
  • He signed with Oakland, which is contending but plays in a relatively small market. Let’s call that even. We’re still at $11 million.
  • He’s a durable, consistent performer about to enter his prime, and an elite performer at his position, capable of more than sixteen WSAR. I think the market would pay more for someone like this — maybe $3 million more.
  • He does have a clear weakness which limits his value, which is his reduced effectiveness against lefties. Take away a million, which totals out to $13 million.

Put it all together, and I think Chavez got less than he would have received in the open market. Obviously, staying in one place with a great team in a livable city meant a lot to the guy. And $11 million is nothing to sneeze at, either.

Really, that was all for fun. The numbers should be more precise. But this is just an “introduction” after all, and I wanted to try out the thought process to see if it works. Let me know what you think.

This is the sort of thing that Win Shares Above Replacement can do for you. We’ll be reporting WSAR during the year. Stay tuned.

References & Resources
For more information about WSAR, you can peruse the following articles at the baseballgraphs.com site:
- The Win Shares Baseline
- Extreme Win Shares
- Replacement Level

If you’d like more background on Win Shares in general, here’s a Win Shares resources page.

Doug Pappas is chairman of SABR’s Business of Baseball Committee, and he also maintains his own blog, Doug’s Business of Baseball Blog. For a full view of player’s salaries, you can’t beat Dugout Dollars.

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