Getting their money's worth: Reds edition

[Brutus]

I thought it would be interesting to see how the Reds' players are performing their dollar values. So based on their accumulated WAR, based on Fangraphs' Batting-Fielding calculations, I quickly threw their numbers into a spreadsheet.

First, a short primer:

In a full regular season, there are 2,430 total wins accrued during the year. It has been said that a team full of replacement players would win roughly 48 games a season. Using this logic, there are about (48*30) 1,440 replacement wins of the total, though obviously a league of replacement players would still win 2,430 games--but that's a technicality that we won't worry about here. So essentially, there are (2,430-1,440) 990 marginal wins available during the course of a baseball season. The goal is to have as many players on your roster taking those marginal wins (wins above replacement) as possible.

Taking the opening day payroll, we find there is over $2.7 billion being paid out this year in active salaries (technically, MLB defines payroll as all minor league salaries, benefits, pension and other league transaction fees, but we'll keep this to pay that is used on the field). Since a roster of replacement players would cost a team $10 million no matter what (25 players at $400k league minimum), the marginal dollars paid out for a league this year is ($2.7 billion-$300 million) $2.4 billion.

Based on these calculations, we find that for every one of the 990 marginal wins accrued, Major League Baseball teams are paying out $2,455,602. That means for every win above replacement, a player is worth $2.86 million in salary (adjusting for the fact they would also be paid $400,000 for the minimum). This also means being replacement level leaves you valued at $400k.

Another note: fangraphs does something similar to this, though their dollars' calculation is based on free agency dollars, and the market might inflate the values a bit (their current calculations, which is based on free agents only, values each win at $4.5 million for this season). Their values are for the open market, the ones I'm using is simply based on the market share of WAR the players have accrued.

So, here are what the Reds' offensive players have done thus far this season...I will try to get the pitchers done today or this weekend. It is interesting to note that the Reds are losing money throwing Gomes out there everyday--that is provided UZR values are to be believed.

POS	PLAYER	        WAR	SALARY	WORTH	VALUE
C	Ryan Hanigan	1.0	$0.415	$2.855	$2.573
C	Ramon Hernandez	1.5	$3.000	$4.083	$2.046
1B	Joey Votto	5.2	$0.550	$13.167	$12.793
2B	Brandon Phillips 3.8	$6.750	$9.730	$5.146
SS	Orlando Cabrera	1.0	$3.020	$2.855	$0.805
3B	Scott Rolen	3.6	$7.667	$9.239	$4.033
IF	Miguel Cairo	0.6	$0.500	$1.873	$1.534
SS	Paul Janish	0.6	$0.413	$1.873	$1.593
IF	Drew Sutton	0.2	$0.400	$0.891	$0.619
LF	Jonny Gomes	0.0	$0.800	$0.400	-$0.143
CF	Drew Stubbs	0.8	$0.400	$2.364	$2.093
RF	Jay Bruce	1.2	$0.440	$3.346	$3.047
OF	Chris Heisey	1.5	$0.400	$4.083	$3.811
OF	Chris Dickerson	0.0	$0.400	$0.400	$0.128
OF	Laynce Nix	0.8	$0.400	$2.364	$2.093

* All dollar values in millions
** Salary is actual contract value for entire season
*** Worth is the accrued production in dollars a player has accumulated through 110 games
**** Value is the production value, based on WAR, the player has totaled minus the prorated 
salary through this point in the season

(NOTE: prorated salary was calculated only based on percentage of games played through the Reds' 
season, and not the technically correct method of service-based pay done from days on the active roster)