A common theme for Purple Row Academy this entire year has been looking at ways to quantify a player's value to a team, especially through the Wins Above Replacement (WAR) stat used notably by FanGraphs. For those who don't understand what WAR is or how it is calculated, here's a crash course from previous PR Academy sessions:

By looking at the sum for a team of each player on that team's value, one can attempt to measure both how efficient and how effective that team was. But WAR is by definition an individual statistic and judging efficiency by WAR alone would be only the sum of individuals. This is problematic because seldom in baseball does the sum of the individual players' successes accurately measure the team's performance.

A metric measuring team performance to compare to the individual performance calculated by WAR is therefore what we require. What can we use to measure how well and how efficiently the team performed? There's always the simple end of season payroll vs. number of wins linear comparison to figure out MLB payroll efficiency using 3 year averages from 2006 to 2008, which I did a few months back.

But that is assuming that all wins are equal. As any economist worth their salt will tell you, this is patently false. In light of that, I'll go back a little farther back in PR Academy sessions to the concept of Marginal Wins.

If I had to explain this concept in two sentences, I'd say that MP and MW are basically setting a **floor** (minimum possible outcome) for both **payroll** (in 2009, $11.2 million--which happens with 25 players on the active roster plus 3 on the DL making the minimum of $400k) and **wins** (30% of all games, or 48.6 wins, which all but one team has accomplished since the implementation of the amateur draft in 1965). The farther the team reaches from this minimum plateau of wins, the more difficult (not to mention important and expensive) each incremental, or marginal, win becomes.

Marginal Payroll and Marginal Wins

The creator of the system, BP's Doug Pappas, explains that "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" (basically Wins Over Replacement Team). 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. 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)

Since a team's payroll fluctuates throughout the year and I use Opening Day Payroll (ODP) to calculate MP/MW, this metric is probably best used to evaluate the efficiency of the front office's offseason moves and as a gauge for a team's expectations going into the year.

To emphasize the inequity of wins, this is what I said back then:

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.

For example, the average value of a marginal win in 2008 was about $2.7 million, but the value of a win getting you from 89-90 wins was worth almost $6 million.

It isn't a simple concept by any means, but I've found that MP/MW or WORT has produced some excellent results. I'll show how the Rockies did by this metric after the jump.

**Rockies Historical MP/MW Performance**

Using the formula above and FanGraphs WAR data, I've already crunched some numbers for the Rockies as to their efficiency from 2002-2008 (which is as far back as FanGraphs WAR data goes back). That analysis is here:

Given that data, I'll break down the Rockies' 2009 season in a similar fashion.

Rockies Historical Dollar Win Values

#### The Efficiency of the 2009 Colorado Rockies

**Opening Day Payroll**: **$75,201,000**

This season marked the highest ODP on record for the Rockies as a franchise, eclipsing the mark set in 2001 of $71,541,334. This was largely due to the arbitration raises given to six players. With an eye toward next year, the Rockies' ODP for 2010 looks to be higher due to the fact that they have 13 potential arbitration cases coming up this offseason (though they'll likely only have 10 returning to the team).

**W-L Record**: **92-70**

This of course also marks a franchise record, besting the 90-73 mark of the 2007 team. This team was the best compensated Rockies team, and as their record bore out, the best performing team as well.

**Linear Payroll Efficiency**: **$817,402**

This number was found simply by dividing the Rockies' ODP by their win total. While this number is higher than other seasons in past years, this doesn't take into account the fact that ODPs have risen dramatically since the franchise's inception. For example, the Rockies won 67 games in 1993 with an ODP of $8,829,000 (LPE of $131,776). This is yet another reason that efficiency should be judged on the basis of marginal wins.

**Marginal Payroll**:

Formula: ((ODP) - (28 * League Minimum) = (($75,201,000 - (28 * 400,000) = **$64,001,000**

Again, this represents the amount that the Rockies spent above MLB's price floor ($11.2 million). This year's total is second most in team history to 2001's $65,941,334.

**Marginal Wins**:

Formula: ((Winning % - .300) * (# of games played)) = (.568 - .300) * (162) = **43.4 MW**

This number represents the amount of wins the Rockies produced about the floor set by Pappas of 30% of games won (48.6). This total is the most in franchise history, defeating 2007's 41.1 MW total.

**Marginal Payroll / Marginal Wins**:

$64,001,000 / 43.4 = **$1,464,677**

This number represents how much money the Rockies spent per marginal win this year. It ranks below 2007 ($1,065,304) and a number of other years in which the Rockies had a much lower MP. With the salary growth in MLB so explosive these last two decades and considering that the cost of a marginal win in 2008 was $2.7 million, the Rockies' MP / MW number is really quite good. Last year, that number would have been fifth in MLB.

**Team Hitting WAR**: **18.7**

On the whole the Rockies ranked 16th in MLB in this category, though AL teams have a leg up on NL teams because the above number includes hitting by pitchers, who "contributed" a total of -3.7 hitting WAR to the Rockies. That's why they're paid to pitch and not hit. Of course, it also includes Garrett Atkins (-0.5), who owes the Rockies $2.1 million for his "performance" in 2009. Courtesy of FanGraphs, here's a list of the Rockies' contributors to hitting WAR by player.

What is notable is that the Rockies had six players performing at least at a league average (about 2.0 WAR) level in 2009, the highest FanGraphs has measured (in 2008 we only had 3 such players), but had no superduperstar (Tulo's 5.5 WAR is great, but only ties him for 14th in MLB among hitters and 28th for all players). This makes sense, since a major strength of this team was its depth.

Historically, the Rockies' 18.7 hitting WAR puts them well behind 2007 (22.4 WAR) but bests every other season in the FanGraphs era.

**Team Pitching WAR**: **23.6**

With this total, the Rockies tied the Red Sox for the best pitching from a WAR standpoint in 2009. It goes without saying, but this was the greatest pitching staff the Rockies have ever assembled. Here's the final list of 2009 Rockies pitching WAR contributors.

Of note is that all five members of the Rockies starting rotation posted at least league average performances (that's for *any* pitcher). Those five by themselves contributed 18.9 WAR! Ubaldo Jimenez's 5.7 WAR season is also by far the greatest Rockies pitching season ever, besting Aaron Cook's 4.7 last year. In addition to the starters' second place in MLB finish in pitching runs above average, the bullpen was sixth in MLB in PRAA.

The challenge next year will be maintaining both this high level of performance and the remarkable health this year of the entire roster.

**Total WAR**:** 42.3**

A good measure of a team's efficiency at the end of the year involves comparing its WAR totals to its MP / MW totals. If a team's marginal wins total exceeds its WAR total, then the performance of the team as a whole was greater than that of the sum of its parts.

In the case of the 2009 Rockies, this was certainly the case as Colorado finished with 1.1 more MW than their WAR data would have suggested.

**Total Dollar Value of Player Production**:

Here is Dave Cameron of Fangraphs on Dollar Win Value:

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

In other words, Cameron is showing that a free agent, on the whole, cost $4.5 million per WAR as of 2008--whereas an average marginal win in that year cost only $2.7 million. This fact serves to show that looking for marginal wins on the free agent market is an inefficient proposition. It is more efficient to build from within and to get lots of production from young cost-controlled players, as the Rockies have done.

Generally though, this reflection of value is based not on the actual cost of a MW but on the market cost of a MW. As I explained a few months ago:

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.

According to the "dollar value" concept as FanGraphs has it ($4.5 million per WAR), the Rockies as a collection of individuals produced $190,350,000 of value. Hitters were responsible for $84.15 million while pitchers contributed $106.2 million ($85.05 million of which came from the starting rotation). When the whole team is considered ($4.5 million per MW), the value produced is **$195,300,000**--again, the whole equaling more than the sum of its parts.

This valuation is assuming that the Rockies had built their team entirely of free agents, which is obviously not the case. Using my "home brew" calculation of $2.7 million per MW (a reflection of all marginal wins, not just FA MW), the Rockies as individuals produced a more realistic $114,245,023 of value. As a team, the Rockies produced **$117,215,934**. This shows that compared to their ODP in 2009, Colorado had **surplus value of $42,014,934**--a number which would certainly rank very highly in MLB this year (if I had the time I would prove it), though behind the 2007 squad in terms of efficiency.

#### Effectiveness

Of course, the Rockies were far from the most efficient team in MLB this year. That title belongs once again to the Florida Marlins, who had a MP/MW ratio in 2009 of $667,552 per MW. But the Marlins were not the most effective team in baseball, as they did not parlay their excellent marginal wins ratio into a playoff berth (and the revenue that comes with it).

My definition of MLB effectiveness gives a heavy weight to playoff appearances and championships. For that reason, I'd argue that the Rockies this year were the most effective club in baseball (with the possible exception of the World Series winner, as long as it isn't the Yankees). And for what it's worth, any of the four teams still alive that win the championship will have done so inefficiently.

The Rockies have created among the highest marginal win totals in MLB despite having a lower-half payroll (18th) and securing a playoff berth. What is remarkable is that the Rockies can say this for the second time in three years. Truly we fans are lucky to be following a smart organization that seems primed to continue their success in the near future.

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