How much does a run cost? How much will your team pay?

A tip of the cap within the network to Fire Brand of the American League, where they discuss the Red Sox and recently were wondering about the unfortunate signing in the off-season that was Julio Lugo.  Writer Tito Crafts gathered together some interesting data on the Red Sox from Baseball Prospectus, especially from their Runs Above Replacement family of stats.  For those unfamiliar, the idea is this: pick any player and suppose that he decided to change careers tomorrow and become a Trappist monk.  (Pick a really good one.)  If he were gone, it’s not like his team would just leave his spot in the lineup blank.  Someone would have to replace him, probably someone from the bench, or AAA, or the waiver wire who plays the same position.  Now, the replacement guy’s on the bench or in AAA or on the waiver wire for a reason: he’s not good enough to be a starter, but he’s not simply a decorative lawn statue.  He’s bound to do something during his time in the lineup, but there’s going to be a drop off from a starter to the replacement.  How much?  This is the basis of replacement level, and it’s a good measure of how valuable a player is to a team.  The actual mechanics of how runs above replacement is calculated is a little messy to detail here.  If you got the previous few sentences, that’s all you need for now.
Good players are worth a lot more than guys on the waiver wire, so they should be paid for their considerable talents, right?  Well, salaries are generally negotiated before the players take the field, so there’s a lot of room for error.  Some players (like Lugo), are making millions and millions and doing not much more than a replacement player.  Forecasting the future is not an exact science.  In fact, the correlation between runs above replacement (I added together pitching, batting, and fielding) so far in 2007 (as of the All-Star break) and a player’s salary is only .412.  That’s a medium size correlation, meaning good, but not great.
But, what are teams generally paying so far in 2007 for one of these runs above replacement levels?  We can create a regression equation that tells us, on average, what teams are paying for a run above replacement.  I got runs above replacement from Baseball Prospectus.  (I made sure to turn off my subscription, so that I wasn’t using anything that wasn’t available to the general public.  You can get all of these numbers from BP’s Davenport Translation pages.)  Salary numbers came mostly from USA Today and a few came from ESPN.  If I couldn’t find a salary, I assigned him the MLB minimum ($380,000).  I cut all numbers in half to reflect how much each player has earned so far this year, something that Mr. Crafts also did.
I checked to see what the best type of equation would work best for this data set.  A simple linear equation had an R-squared value of .171, a quadratic (ax^2 + bx + c) had an R-square of .173 and a cubic checked in at .176.  The cubic is technically better, but hell to interpret, and the difference in R-squared is negligible.  A simple linear model will do. 
It turns out that just showing up and playing at replacement level (in other words, the Washington Nationals’ plan for this season) is worth $561,155.27.  (MLB’s minimum salary is $380,000, by the way.)  For every run above that, a player is, on average, paid another $56,447.66.   Now, that’s just an average and I’m probably violating assumptions of normality all over the place.  As mentioned before, the correlation between these two was not very strong, meaning that there are plenty of players who are being paid more or less than they are worth.   In his book, the Baseball Economist, J.C. Bradbury (proprietor of the excellent Sabernomics blog) does some similar work, although with some different statistics, but finds similar results.  Some teams, he points out, are very good at underpaying and some are very good at overpaying.
Wanna name some names?
The ten most overpayed players in baseball not named Roger Clemens (because of the way his contract is structured, it’s hard to get a fix on his exact income).

  1. Jason Giambi
  2. Derek Jeter
  3. A-Rod
  4. Bartolo Colon
  5. Jason Schmidt
  6. Manny Ramirez
  7. Richie Sexson
  8. Bobby Abreu
  9. Andy Pettite
  10. J. D. Drew

Notice something about that list?  Yes, I know A-Rod is having an outstanding season.  He’s also making $22.7 million this year, which is way out of line with what the league would pay for a man of his contributions.  In order to justify what he’s made relative to the rest of the league’s pay scale, A-Rod would have to have put up an additional 135 runs, or roughly about 4 times what he’s already done.  Jeter is a similar case.  Good year… huge salary.  But, it’s filled with Yankees making huge salaries with not a lot of return.
Ten biggest bargains in baseball?

  1. Kelly Johnson
  2. Jamie Shields
  3. Russ Martin
  4. Dan Uggla
  5. John Maine
  6. Chris Young
  7. Joe Blanton
  8. Ian Snell
  9. Curtis Granderson
  10. Hanley Ramirez

Which teams are overpaying for talent, and which teams are the most frugal?
The best penny pinchers are the Tampa Bay Devil Rays.  I’m serious.  On average, they’re getting roughly $617,000 more value per player than the rest of the league could buy, on average, for their payroll.  The rest of the top five: Florida, Washington, Pittsburgh, and Arizona.  You’ll notice something about that list… none of those teams, save Arizona, have a winning record.  San Diego, Cleveland, and Milwaukee are #7, 8, and 9 on the list and all three are in playoff spots right now.
The biggest over-spenders for talent?  Do I even have to say it?  The Yankees spend $2.2 million(!) more per player(!!!) than they have to given the production that they’re getting.  This is $1.4 million more than the team in second place, the Red Sox.  The rest of the top 5? Seattle, the White Sox, and the Dodgers.
As for Lugo, he’s #59 on the list of the overpaid (out of 1000 players).  However, only 30% of players were actually overpaid, according to this model.  Lugo has put up 3 runs above replacement (-9 with his bat and 12 with his glove), which should earn him around $730,000.  He’s been paid $4.125 million so far.  How big a bust has he been in his half season in Boston?  Julio Lugo is being paid about five and a half times what he’s been worth compared to what the Red Sox could have gotten by finding a shortstop from the bottom of the barrel.


2 Responses to How much does a run cost? How much will your team pay?

  1. DanC says:

    One question: does this analysis take into account time on the DL? Because that might change the top 10. Not drastically, though. All of those guys are overpaid regardless.
    I said one question, but I have a second: were there any guys making $8-10mil and up who were rated as a bargain?

  2. Pizza Cutter says:

    I didn’t factor time on the DL in. Then again, a guy still collects a paycheck on the DL and isn’t producing. So, Jason Giambi will actually become more overpaid as the season wears on.
    The highest paid underpaid player was actually Dice-K (he’s making 6.33 M this year), followed by John Lackey (5.83 M), and Chase Utley (4.79 M). The best underpaid players in terms of RAR were Jake Peavy, Utley, Dice-K, and Dan Haren.

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