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Dollars and Sense Part Seven: Dollar Win Values

In this fashionably late edition of Purple Row Academy, I shift gears from Positional Payroll Distribution to an examination of the Rockies' historical Win Value data, courtesy of Fangraphs, compared to both the Rockies' marginal wins over that period and their ODPs. This session is, (for now, at least), the conclusion to my Dollars and Sense series. In two weeks I'll be back with a new area of study for your learning enjoyment.

My analysis on this topic covers the period from 2002 to 2008. Why this period? Well, Fangraphs' win value data only goes back to 2002, and since the Win Value data is comprised of counting stats, the eight weeks of 2009 data available to us can be quite misleading. When calculating payroll efficiency in the past I have used a team's ODP, as it best represents a club's expectations for a full season of how much their players are worth--and applying win value concepts to the Rockies for only part of the 2009 season would be irresponsible. Here is the Rockies' 2009 win values data for those that are interested. It looks like our 3B platoon of Garrett Atkins and Ian Stewart owes the Rockies $7.1 million this year so far.

So how are these values calculated? At the risk of stepping on RMN's toes a little bit, Fangraphs guru Dave Cameron has a seven part series explaining their calculation--basically explaining the WAR (wins above replacement) concept (as well as another seven part series concerning pitchers' win value). For the purposes of this article, though, I looked at his explanation of the conversion of win value to dollar value. The equation heavily involves the concept of marginal wins.

As I wrote in my MP/MW column, the minimum winning % assumed by the formula is .300, or 48.6 wins over a 162 game slate of games. Every team, even spending the minimum on player salary, will surpass this mark. As Cameron puts it, the result of this concept:

There are about 1,000 marginal wins in a major league season. All 30 teams are fighting over these 1,000 wins, each trying to get more than 45 or so to get them in the playoffs.

Every dime a major league team spends above the major league minimum is theoretically spent in an effort to buy as many of those 1,000 wins as possible.

 As I figured out using the MP/MW formula, in 2008 the theoretical minimum payroll was $10.92 million--creating a price floor for MLB of $327.6 million. Note that Cameron has calculated this number as $12 million per team, but this is incorrect according to my methodology. Meanwhile, as I mentioned a few weeks ago, total MLB ODP was $2,697,392,597. Subtracting the price floor from the total payroll and dividing that number by 1000 marginal wins gives the theoretical average cost per marginal win in MLB. For 2008, that was about $2.37 million. According to my own calculations a couple of weeks ago, this number is closer to $2.7 million, but let's run with Cameron's number.

This would be really easy, but as Cameron mentions, many of these players are in the pre-arbitration and arbitration stages of service time--players whose salaries were not determined by the free market system. These players provide their teams with production that comes cheaper than the $2.37 million average cost per MW. In addition, many players simply aren't available to other teams due to their high values to their franchise. These factors make the pool of available marginal wins much smaller than 1000, and much more expensive than $2.37 million.

With his system, Cameron is effectively trying to find out the cost per marginal win of free agency. His definition of the market cost per MW is the mean of the dollars per win handed out to free agents in any given year. In other words, he calculates the free agent class' WAR values from the previous year and divides the total salary pool by that net WAR amount. Here's his calculation from 2007:

90 free agents signed major league contracts last winter, ranging from Alex’s Rodriguez $275 million deal to Josh Towers' $400,000 contract with the Rockies. The sum of those 90 contracts paid out $396 million in 2008. To figure out what the average cost per win of a 2007 free agent was, though, we need to know how many wins that group was worth.

To calculate this, I did a three year weighted average of their win values, then multiplied that value by .95 to factor in aging and estimate what teams considered a player’s true talent win rate for 2008. In total, I came up with 88 wins, or $4.5 million per win. That’s what major league teams were paying for a marginal win last winter, so for 2008, that’s a players dollar per win value as listed on the site. I re-did this for all years going back to 2002, and the dollars per win for each are as follows:

2002 - $2.6m / win
2003 - $2.8m / win
2004 - $3.1m / win
2005 - $3.4m / win
2006 - $3.7m / win
2007 - $4.1m / win
2008 - $4.5m / win

 So, if the Rockies wanted to get into the free agent market this past offseason (not that they really have since the Hampton/Neagle fiasco) , they could expect to pay a staggering $4.5 million per marginal win, more than double the MLB average rate per MW. This inefficiency in the free agent market illustrates the importance of teams (especially those in small markets) getting lots of production from their young cost-controlled players.

Historically, the Rockies have had varying degrees of success on this regard. Due to the nature of the calculation (each WAR in the dollar value calculation being equal to the market cost per MW, which was higher than the average cost per MW), the Rockies are consistently receiving a higher "dollar value" from their roster than their ODP may suggest. However, if this "dollar value" concept would be adjusted to reflect merely the average cost per MW each year (in other words, taking into account all players instead of just free agents), then the "dollar value" numbers would often be below a team's ODP--especially if that team rates low on the MP/MW formula.

Join me after the jump as I briefly examine each Rockies team using a couple different efficiency metrics from 2002 to 2008...

Rockies Dollar Win Values by Year

For each year from 2002-2008, I'll summarize the success of each team through a few different metrics that I've covered this session and in previous sessions. After each season I'll add a little commentary that I found interesting when looking closely at the data. If anyone wants the spreadsheet of win value data that I compiled in researching this article (complete with formulas!), just e-mail me and I'll send it to you.

ODP: $56,851,043
W-L Record: 73-89
Linear Payroll Efficiency: $778,781
MP: $51,251,043
MW: 24.4
MP/MW: $2,100,453
Team WAR: 24.5
Dollar Value of Player Production: $65,700,000

Notable about the 2002 team is the fact that the Rockies' pitching staff, led by Jason Jennings (3.0 WAR), produced a woeful 12.6 WAR--and when you factor in the pitching staff's negative hitting value, this number is an even worse 9.2 WAR. On a positive note, Todd Helton (5.9 WAR) and Larry Walker (5.6 WAR) were worth $16.4 and $15.6 million respectively--accounting for nearly half of the team's entire player production value. In a year in which Helton was paid $5 million, he came at a relative bargain to Colorado.

ODP: $67,179,667
W-L Record: 74-88
Linear Payroll Efficiency: $907,833
MP: $58,779,667
MW: 25.4
MP/MW: $2,314,160
Team WAR: 30
Dollar Value of Player Production: $84,500,000

While on the surface the Rockies were slightly more successful in 2003 than they had been in 2002, they were a markedly less efficient ballclub. With a roster that produced 5.5 more WAR, the Rockies were only able to emerge with one more win. Generally, a team's MW and WAR numbers should be relatively even...with the luckier teams outperforming their WAR. This is reflected in the Rockies' high MP/MW ratio.

Continuing the Helton thread, the ToddFather was even better in 2003--becoming a 6.8 WAR player, worth about $19.1 million to the Rockies for his $10.6 million salary. The Rockies' "top" pitcher in 2003 was none other than Darren Oliver and his 2.7 net WAR. Overall, the pitchers produced 11.3 WAR (with FA busts Hampton and Neagle contributing nothing and -0.6 WAR respectively). Also of note was Garrett Atkins' -1.1 WAR.

ODP: $65,445,167
W-L Record: 68-94
Linear Payroll Efficiency: $962,429
MP: $57,045,167
MW: 19.4
MP/MW: $2,940,473
Team WAR: 25.2
Dollar Value of Player Production: $78,400,000

This team was the least efficient (and very nearly the least effective) team in Rockies' history, with each MW costing almost $3 million. In addition, the Rockies underperformed their WAR by nearly 6 wins and posting their worst year in linear payroll efficiency.

The story of the year was the worst pitching staff assembled by the Rockies during the Humidor Era. They were "led" by Joe Kennedy's 2.3 WAR and produced a net of only 6.5 WAR. Yikes! Helton was paid $11.6 million and produced $21 million (6.8 WAR)--a huge portion of the team's total production. Matt Holliday, Garrett Atkins, and Brad Hawpe also contributed 1.6, 0.2, and -0.4 WAR respectively.

ODP: $48,155,000
W-L Record: 67-95
Linear Payroll Efficiency: $718,731
MP: $39,307,000
MW: 18.4
MP/MW: $2,136,250
Team WAR: 24.2
Dollar Value of Player Production: $83,300,000

While this edition of the Rockies lost one more game than their predecessors and produced less WAR, at least they did it a little more efficiently due to the much lower 2005 payroll. In 2005, the Rockies' pitchers bounced back somewhat with a 9.2 WAR. They were actually led by Brian Fuentes' net 1.6 WAR from the bullpen. Meanwhile, Helton remained the Rockies' top dollar value producer, getting paid $12.6 million to produce $17.4 million (5.1 WAR). Finally, Holliday, Atkins, and Hawpe produced 3.3, 2.5, and -0.6. 

ODP: $41,233,000
W-L Record: 76-86
Linear Payroll Efficiency: $542,539
MP: $32,077,000
MW: 27.4
MP/MW: $1,170,693
Team WAR: 33.1
Dollar Value of Player Production: $121,800,000

In 2006 the Rockies saw the first fruits of Gen-R blossom, enjoying a career year from Atkins--who led the team with 5.9 WAR ($22 million)--and excellent seasons by Holliday (4.4, $16.4) and Hawpe (2.8, $10.5). However, this was the first year in which Helton underperformed his contract, producing 2.4 WAR and $9 million for $16.6 million--illustrating the danger of back-loaded contracts.

The Rockies' pitching also improved markedly, enjoying a renaissance of sorts by JJ (3.5 WAR) that O'Dowd actually took advantage of as well as solid years from Aaron Cook (3.0) and Jeff Francis (2.7)--overall a staff WAR of 15.3. Moving to the efficiency metrics, the Rockies achieved their best rating in linear payroll efficiency and a high mark in MP/MW as well, though they underachieved their WAR by 5.7.

ODP: $54,424,000
W-L Record: 90-73
Linear Payroll Efficiency: $604,711
MP: $43,784,000
MW: 41.1
MP/MW: $1,065,304
Team WAR: 41.6
Dollar Value of Player Production: $170,200,000

Ah, 2007. What a year to be a Rockies fan! According to the efficiency metrics, the 2007 Rockies were hardly a fluke. They simply played up to their WAR production and posted their best MP/MW value while producing an incredible $170.2 million of dollar value. There are too many good things to count that happened in 2007, but here's a few:

  • Matt Holliday was a BEAST (7.9 WAR, $32.2 million)--in other words, this metric suggests that Matt was worth A-Rod money.
  • Troy Tulowitzki put up All-Star numbers (5.3 WAR, $21.6 million) as a rookie.
  • Helton (4.9 WAR, $20 million) once again outperformed his $16.6 million contract.
  • Jeff Francis' 3.7 net WAR led a staff that finished with a 15.5 WAR

ODP: $68,655,500
W-L Record: 74-88
Linear Payroll Efficiency: $927,777
MP: $57,735,500
MW: 25.4
MP/MW: $2,273,051
Team WAR: 31.4
Dollar Value of Player Production: $141,300,000

Given the warm afterglow of the 2007 season as well as the $14 million payroll hike, the Rockies' 2008 season was seen as a great disappointment, and the numbers bear this out. The Rockies regressed to their WAR underachieving ways while producing a poor score in LPE and MP/MW. The good news for the Rockies in 2008 was the tremendous growth of Ubaldo Jimenez, who despite a very poor (-1.5) hitting WAR managed a 2.9 WAR, and possibly the best year by a Rockies' pitcher ever, Aaron Cook's net 4.3 WAR. In all, the staff had a 15.4 WAR.

Instead, it was the Rockies' hitters who regressed in 2008. Despite Holliday's excellent 6.2 WAR, $28 million campaign and Chris Iannetta's dreamy breakout (3.8 WAR, $16.9 million), the Rockies' position players produced only 16 WAR--far less than 2007's 26.1 WAR. The main culprits were the regression of Atkins (0.6 WAR), Tulowitzki (0.8), and Hawpe (-0.7). All of this added up to a disappointing 2008 campaign.

Meanwhile, Helton's injury-plagued 1.5 WAR, $6.9 million season was well below his $16.6 million pay grade. By the dollar value metric, from 2002 to 2008, Helton produced $109.8 million of value (33.4 WAR) for the Rockies while getting paid $89.6 million over the time period. In other words, Helton has been a bargain thus far for the Rockies purely in terms of on-field production.

Unfortunately, Todd is still owed a minimum of $56.9 million more over the next four years (2009 included) and probably won't produce $36.7 million worth of value--though with his hot start this year it is not inconceivable. That and his blocking of young, cost-controlled talent at 1B is the reason that I don't agree with these kinds of contracts, though Todd has certainly done his best to live up to his.


Thus far in 2009, the Rockies' position players have produced a mere 3.5 WAR through 46 games compared to the pitching staff's pretty nice net 5.4 WAR. In other words, the pitching thus far for Colorado has been decent, it's the hitting that has let the Rockies down. I'll be closely monitoring the Rockies' progress this year using these metrics...and unfortunately I predict that we'll end up with a year that could be our least efficient yet as a franchise.

Sources and Additional Reading

Fangraphs! I can't emphasize the awesomeness of this website as a resource for baseball statistics. If you haven't already, make sure to explore the site--especially the links that I posted within the article.

Specifically, look at the Fangraphs Glossary, which explains some of their advanced metrics.

For contract data, I once again used Cot's Contracts by Jeff Euston.

For explanations of some other terms used in this article, see these previous PR Academy sessions:

ODP Analysis

MLB Payroll Efficiency

Marginal Payroll and Marginal Wins