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Dollars and Sense Part Five: Marginal Payroll and Marginal Wins

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In this fashionably late session of Purple Row Academy, I expand on last week's column about payroll efficiency by focusing a little more heavily on the concept of marginal wins and their relationship to marginal payroll.

Marginal Payroll and Marginal Wins 

Though my primary reference last week, the Baseball Analysts' Rich Lederer, touched on marginal wins, the real pioneer in this area was the late, great Doug Pappas--who wrote about marginal wins for BP in 2004. I'll be going off of his work for this article.

To refresh your memories, marginal wins are wins by teams that are achieved above a minimum plateau, which every MLB team reaches. The farther the team reaches from this minimum plateau, the more difficult (not to mention important and expensive) each incremental win becomes. As I put it in last week's session:

Though it can be (and has been) done by a small payroll team, going from 60 to 80 wins in MLB is an insignificant accomplishment on a macro level because those teams still miss the playoffs. In moving from 80 to 90 wins, however, a team goes from an also-ran to a bona fide playoff contender. After all, 68 of 78 teams (87%) in the last ten years that crossed the 90 win threshold made the playoffs, making these marginal wins much more important and therefore expensive.

Pappas goes into much more detail on this concept, especially concerning the topic of "small market" teams. The term "small market" is often used to mean "small revenue", which is obviously not always correct. The Rockies brought in huge sums of money when they were selling out their stadiums for the first eight years or so of their existence despite playing in a smaller market than their expansion twin, the Florida Marlins.

A more important factor in the success of small market teams is how well they are run--developing a strong farm system, drafting well (not wasting top draft picks), and capitalizing on roster surpluses are some areas that come to mind.

To measure a front office's efficiency, Pappas developed the Marginal Payroll/Marginal Wins (MP/MW) formula. As I mentioned last week, every team in MLB will win a certain amount of games even with a roster of players getting the minimum, so that minimum games won number should be the base-line and not zero. The number used in this exercise by Pappas as the minimum is a .300 winning percentage--which translates to 48.6 wins over a 162 game season. This number has been eclipsed by every ML team except the 2003 Tigers since the amateur draft was instituted in 1965. However, Pappas does allow for strike shortened years in his formula by separating the minimum winning percentage variable from the length of the season.

 In addition, a team can't pay their players no money--they must pay the 25 players (plus an allowance for three players on the DL for 28 total) each $400,000 (the major league minimum in 2009), creating the payroll base-line for this formula. Therefore, the lowest possible payroll a major-league baseball team could have is $11,200,000. Notice that the Marlins only eclipsed this by $10.5 million last year and won 84 games!

Here is Pappas' explanation and his formula:

The Marginal Payroll/Marginal Wins (MP/MW) system evaluates the efficiency of a club's front office by comparing its payroll and record to the performance it could expect to attain by fielding a roster of replacement-level players, all of whom are paid the major league minimum salary. The formula is:

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

The first half of the equation measures the club's marginal payroll and the second measures the marginal wins. It should be noted that the club payroll numbers reflect the Opening Day Payroll of the club, not the end of season payroll because the ODP more accurately reflects the expectations of a team entering the season. Teams that have success during the season often add payroll while those that do not often seek to dump payroll, distorting the data but also limiting its scope somewhat. The MP/MW equation as currently constructed could be better defined as the efficiency of a club's FO measured by their off-season moves.

The figure reached by dividing MP by MW reflects how much money a club has spent, per win, above the theoretical minimum of $11,200,000 (for 2009's minimum salary). The lower the number, the more efficiently the club spent its cash. Comparing this number to the club's actual winning percentage provides another way to evaluate teams. As Pappas explains:

Low MP/MW, good record: Efficient ballclub (2003 Marlins, Athletics)
Low MP/MW, bad record: Not spending enough to compete (2003 Devil Rays)
High MP/MW, good record: Spending its way to the top (2003 Yankees)
High MP/MW, bad record: Poorly-run club (2003 Mets, Rangers)

Updating this to the 2008 season, here's an example of teams in each category:

Low MP/MW, good record: Tampa Bay Rays, LA Angels
Low MP/MW, bad record: Florida Marlins (more on this later), Pittsburgh Pirates
High MP/MW, good record: Boston Red Sox, Chicago White Sox 
High MP/MW, bad record: Seattle Mariners, San Diego Padres

Using data gleaned from the USA Today Salary Database and the major league minimum of $390,000, the Rockies' MP/MW in 2008 would be calculated thusly:

($68,655,500 - (28 x $390,000) / (((74/162) - .300) x 162) = $57,735,500 (marginal payroll) / 25.4 (marginal wins) = $2,273,051 per MW

To put this in a better context, the Rockies during their NL Championship run in 2007 had a MP/MW of $43,784,000 / 41.1 marginal wins = $1,065,304 per MW, near the top of the league. This number is unusual because the Rockies played 163 games, but as I mentioned above the formula is designed to take neutralize that variable by separating games played from winning percentage. With a 162 game schedule, the Rockies would have had a MP/MW of $1,083,762 as the game 163 victory would have been erased.

For more data and analysis using this MP / MW formula, join me after the jump...

MP/MW Data

Let's look at the league through the spectrum of MP/MW data, as provided conveniently here by Maury Brown. He presents the data straight up, without any adjustments to the formula. From this data, I found that the average cost per MW for MLB in 2008 was $2,700,828. In the AL this number was $2,887,536 and in the NL it was $2,537,459. 

Beyond the Box Score's Sky Kalkman provides his MP/MW list with an adjustment to the MP/MW data by adding two wins to AL teams and subtracting two from the NL teams to account for the talent gap between the leagues and the inherently higher cost of winning in the AL. While this variable certainly has some analytical value as the raw data shows, the adjustment made in his chart is too arbitrary for my tastes and therefore was not included in this analysis. Sky Kalkman does however make some excellent notes on the data, such as the fact that with his adjustment the average cost per marginal win is only $2.4 million. I'd highly recommend checking his post out.

Efficiency vs. Effectiveness

One of the biggest limitations of evaluating front offices in MLB by using the MP/MW is that it is a tool that measures efficiency--not the effectiveness of the team on the field. As a result, many low-payroll teams that failed to make the playoffs will rank highly in this metric while big market perennial playoff contenders like the Yankees and Red Sox will rank poorly.

High Efficiency, Low Effectiveness

Last year the Florida Marlins were on a pure numbers standpoint the most efficient team in baseball--perhaps in baseball history considering the swiftly escalating salary structure. In their 84 win season, the Marlins achieved 35.7 marginal wins despite a marginal payroll of only $10,916,500! This came out to an obscene MP/MW efficiency number of $305,784 per MW. When one considers that the Yankees had a marginal payroll of $198,161,579 last year and only achieved 40.4 marginal wins, the efficiency of the Marlins really sticks out. And the Yankees weren't even in the bottom two of payroll efficiency last year!

The problem with teams like the Marlins and the A's ($1,387,533 MP/MW) is that while they were wildly efficient last year, they didn't make the playoffs, placing them in the "high efficiency-low effectiveness" quadrant of MP/MW. In other words, if the Marlins had spent at a respectable level last year, they might have stormed into the playoffs last year. Depending on how one measures success, the Marlins failed on the diamond because off the diamond they were far too thrifty.

Low Efficiency, High Effectiveness

On the other end of the spectrum are the LA Dodgers, who were quite inefficient last season, spending $3,040,001 per MW. However, the Dodgers won the NL West and advanced to the NLCS. In other words, their effectiveness was high but their inefficiency was low. The Red Sox ($2,640,518) and White Sox ($2,748,944) are more examples of this trend. 

As a fan, I would far prefer to root for a team that consistently had this problem (but as a result made the playoffs often) than one like the Marlins. Then again, most of these teams play in big markets and can afford to throw their money around.

Low Efficiency, Low Effectiveness

Then there are the teams that score low on both efficiency and effectiveness, the head-scratchers. Last year the most inefficient, ineffective MLB franchise by far was the Seattle Mariners. Despite their $107,073,982 marginal payroll, the Mariners only got a measly 12.4 marginal wins--resulting in an incredible cost per MW of $8,634,999! The Tigers ($5,030,126), Yankees ($4,904,990), Padres ($4,358,168), and Nationals ($4,115,981) round out the top five of inefficiency.

High Efficiency, High Effectiveness

Finally, then there are the teams that score highly in both efficiency and effectiveness. These teams are the envy of every GM in MLB. Far and away the best example of a team in this quadrant last year was the Tampa Bay Rays. The Rays' MP/MW number of $679,764 was only slightly less efficient overall than the Marlins and they went all the way to the World Series. Comparisons to the 2007 Rockies in this case are particularly apt, as both squads were rated very highly in MP/MW, lagging behind the Marlins and lost in the World Series. Other playoff teams with great numbers in this quadrant are teams like the Phillies ($2,012,670 per MW),  LA Angels ($2,106,933), and Milwaukee Brewers ($1,692,854).


For the sake of convenience, here are the 2008 and 2007 MP/MW efficiency numbers for teams in the NL West:

2008 Cost per MW
AZ Diamondbacks: $1,655,171
CO Rockies: $2,273,051
SF Giants: $2,819,850
LA Dodgers: $3,040,001
SD Padres: $4,358,168

2007 Cost per MW
AZ Diamondbacks: $1,000,665
CO Rockies: $1,065,304
SD Padres: $1,186,922
LA Dodgers: $2,936,064
SF Giants: $3,563,797

As you can see, the cost per marginal win in 2008 was much higher for the NL West than it was in 2007, likely due to the fact that the division was much more successful in 2007.

Rockies' Historical MP/MW Data

Over the last three decades the cost per marginal win has increased throughout MLB as the payroll threshold required to compete for the playoffs has increased at a rapid rate. To illustrate this, I have made this table of the Rockies' historical MP/MW numbers from 1993 to 2008:

Year ODP ($) MP ($) Win PCT MW Cost / MW ($)
1993 8,829,000 5,777,000 .414 18.4 313,967
1994 22,979,000 19,927,000 .453 17.9 1,113,240
1995 31,146,135 28,094,135 .535 33.8 831,187
1996 34,918,490 31,493.814 .512 34.4 915,227
1997 42,870,501 38,670,501 .512 34.4 1,124,142
1998 47,433,333 42,673,333 .475 28.4 1,502,582
1999 54,392,504 48,792,504 .444 23.4 2,085,150
2000 61,314,190 55,714,190 .506 33.4 1,668,090
2001 71,541,334 65,941,334 .451 24.4 2,702,514
2002 56,841,043 51,251,043 .451 24.4 2,100,453
2003 67,179,667 58,779,667 .457 25.4 2,314,160
2004 65,445,167 57,045,167 .420 19.4 2,940,473
2005 48,155,000 39,307,000 .414 18.4 2,136,250
2006 41,233,000 32,077,000 .469 27.4 1,170,693
2007 54,424,000 43,784,000 .552 41.1 1,065,304
2008 68,655,500 57,735,000 .457 25.4 2,273,051
Average 48,585,492 42,315,824 .470 26.88 1,641,030

Maybe it's the fact that the Rockies have been consistently unsuccessful, but the Rockies' cost per MW actually hasn't increased that much aside from their inaugural year in MLB. If anyone wants the spreadsheet with the data I'll be more than happy to e-mail it to them.

Sources and Additional Reading

Cool stuff for payroll geeks like me:

Marginal Payroll/Marginal Wins, Doug Pappas (Baseball Prospectus)--Read this!

2007 Marginal Wins Payroll Analysis, Maury Brown (The Biz of Baseball)

2008 Marginal Wins Payroll Analysis, Maury Brown (The Biz of Baseball)

2008 Marginal Wins Standings Chart, Maury Brown (The Biz of Baseball)

2008 Marginal Payroll/Wins Table, Sky Kalkman (Beyond the Box Score)

MLB Minimum Salaries, 1967-2000, USA Today

Player Salaries, Organizational Efficiency, and Competitiveness in Major League Baseball, Herbert F. Lewis, Thomas R. Sexton and Kathleen A. Lock (Journal of Sports Economics 2007)