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Value for money, Part I: What are Marginal Wins?

This afternoon's victory means that the 2009 season is over for the D-backs. Now, we begin the task of analysis. What happened? How do we stop it next year? And, most importantly, can we blame Wailord? These tasks will keep us busy for most of the winter, though we'll have to hold off a bit, until all the interesting statistical sites have updated themselves. At the moment, all we have are W-L records. But that's enough for the purposes of this article...

Analyzing baseball expenditure has been one of the popular topics of baseball number-crunchers, at least since the late Doug Pappas introduced the concept of 'marginal wins' back in 2004. The idea was that the simple approach - dividing a team's salary by its number of wins - isn't as accurate as it could be, because of the lower limits that apply to both salary and wins. You can't spend zero dollars on a team and even a team consisting entirely of replacement level-players won't lose every game.

He came up with a formula to take these factors into account, and work out what teams were most efficient with regard to their spending: who spent wisely and who blew up the bank to no good effect? What we'll be doing in this series of pieces, is taking a look to see what Marginal Wins has to say about the 2009 regular season - and also what it has to say about the dozen years of the Diamondbacks' history. We'll also see which teams had the hardest task of staying competitive, because the opposition they faced had most money to spend.

Pappas decided that a team of 28 replacement-level players - allowing for three on the DL at any time - all earning minimum wage, would have a winning percentage of .300. That works out to 48.6 victories over the cost of the season, and seems to make sense, as only two teams in the past fifty years have had a lower W%: the 1962 Mets and 2003 Tigers. So, plugging in numbers for this year, the 'marginal cost' would be the salary above $11.2 million and the number of 'marginal wins' the wins over 48.6, and For Arizona in 2009, those numbers would be $62.32 million and 21.4, meaning our marginal cost per marginal win (MC/MW) was 2.91 million dollars..

How does that compare to the numbers posted by the other 29 major-league clubs this year? Here are two tables, with the salaries, win totals and marginal cost per marginal win for each team - I've split them up by league, as AL wins are probably more valuable than NL ones, so should be kept separate. Note that the Pirates and Cubs each played one game less than the regulation 162, so the marginal wins deduction for those two is 48.3. I've also excluded the result of tomorrow's play-in game between the Tigers and Twins.

National League American League
Team Salary ($m)
Wins MC/MW
Mets 149.4 70 6.46
Cubs 134.8 83 3.55
Phillies 113.0 93 2.29
Astros 103.0 74 3.61
Dodgers 100.4 95 1.92
Braves 96.7 86 2.29
Giants 82.6 88 1.81
Brewers 80.2 80 2.20
Cardinals 77.6 91 1.57
Rockies 75.2 92 1.47
Reds 73.6 78 2.12
Diamondbacks 73.5 70 2.91
Nationals 60.3 59 4.72
Pirates 48.7 62 2.72
Padres 43.7 75 1.23
Marlins 36.9 87 0.67
Team Salary ($m)
Wins MC/MW
Yankees 201.4 103 3.50
Red Sox 121.7 95 2.38
Tigers 115.1 86 2.78
Angels 113.7 97 2.12
Mariners 98.9 85 2.41
White Sox 96.1 79 2.79
Indians 81.6 65 4.29
Blue Jays 80.5 75 2.63
Royals 70.5 65 3.62
Rangers 68.2 87 1.48
Orioles 67.1 64 3.63
Twins 65.3 86 1.45
Rays 63.3 84 1.47
Athletics 62.3 75 1.94


As you can see, there's a huge disparity in the amount teams paid for their wins, with each marginal win for the Mets costing nine times what the Marlins paid. Franchises can basically be grouped into four general categories, bases on whether they spent more or less than average for their league (the AL average MC/MW being $2.47m; the NL, $2.31m, and also whether they had a winning record this year or not.  While this is a simplistic approach, the following chart does just that, putting teams in the appropriate box based upon their MC/MW and the number of victories they posted in 2009. The columns are in ascending order of MC/MW, so the closer to the top-left a team is, the better.

a little
a lot

Red Sox

Lost Padres

Blue Jays
White Sox

Ideally, a team would want to be in the upper-left hand quadrant. Those are teams that didn't spend much money, and still had fairly successful seasons. The poster-child for this would be the Marlins, whose total payroll was less than $37m, but who still were in the wild-card race until the last week or two. However, I note that the salary was a near-70% increase over the 2008 number, yet was rewarded with less than a handful of extra victories. The top-right and bottom-left quadrants are more ambivalent: expensive, winning teams (Yankees) or cheap, losing ones (Padres), and in both, you more or less get what you pay for.

Franchises definitely want to avoid being in the bottom-right, which might as well be sponsored by the New York Mets. In the past three seasons, they have spent more than $400m in salaries, and never reached the playoffs. In 2007 and 2008, they at least came close. This season... not so much. The bad news is, that's where we also find the 2009 Arizona Diamondbacks. Our salary bill has gone up each year since 2007; unfortunately, the wins totals have gone in the opposite direction. However, I'll get into that more in the next part, which tracks the MC/MW rate through Diamondbacks' franchise history.