Are All “Wins” Created Equal?

WAR is considered by many members of the baseball community to be the best all around evaluator of a player’s value to his team.  It is used to evaluate player’s of different positions and from different eras.  However this might not be as useful in looking at players from different position.

I have developed a model that shows that one win at each position is not actually created equal.  This season Buster Posey and Ben Zobrist have a similar WAR — 5 and 4.9 respectively — but I don’t think anyone will argue that Posey is the better player. In order to determine how much more valuable Posey actually is I created a regression equation.  In order to develop this equation I took stats from the past 5 full seasons (2009-2013).  I took each team’s total number of wins and found the average win total over those 5 seasons.  Then I used the FanGraphs section that allowed me to look at each team’s total WAR by position.  For each position I took the total WAR and divided it by number of games “played” at that position and then multiplied it by 162 to find a season equivalent for each team at each position.  For starters and relievers I just took the WAR numbers and divided by 5.  Then I took these numbers for each team and regressed it against average wins.

Note: I did not include DH as the stats that come from the DH are included in other positions (ex: If Joe Mauer DHs then his stats are included in the catcher WAR).

The resulting equation is as follows:

Wins= 49.3870 + 3.3251 * C + 0.9527 * 1b + 1.5122 * 2b + 1.4703 * SS + 1.5447 * 3b + 1.0027 * Rf + 1.4031 * Cf + 0.4450 * LF + 0.7521 * SP + 0.5137 * RP

R: 0.95

R-squared:0.91

A few quick observations of the equation make sense. An additional win at the catcher position is worth much more than any other position because teams value catchers who can both hit and play solid defense but are extremely willing to sacrifice offense if the guy can play defense. Additionally it supports the theory that the best teams are strong up the middle with SS, 2B, and CF being more valuable than corner OF spots and 1B.

While it is regressed against wins I don’t feel the best application of this model is to predict a team’s wins.  The best application of this will be to evaluate the players to sign in free agency.  This past offseason the Yankees did not sign Robinson Cano to a large contact and instead signed players like Jacoby Ellsbury, Brian McCann, Kelly Johnson, and Brian Roberts.  Johnson and Roberts were supposed to split time at second and Ellsbury and McCann were supposed to be upgrades and C and CF over what the Yankees had had.

	2013	2014	Diff
C	0.72	2.6	1.88
CF	3.6	4.7	1.1
2B	6	0	-6

Looking at this chart this shows the WAR by position extrapolated for 162 for the three positions where the Yankees made major changes this offseason. Using the model the moves the Yankees made have actually led to a decrease of over one win.  While that may not seem like a very large difference the Yankees are in the middle of the wild card chase and could fall around one game out the playoffs.  Additionally, the lack of Cano and the struggles of Johnson and Roberts forced the Yankees to go out and trade for Martin Prado and Stephen Drew.  Without the contributions from Prado the Yankees second base position would actually have a WAR of below 1 which would have created an even bigger difference caused by not re-signing Cano.

This model is extremely useful for teams with limited budgets as it could help them determine what players and what positions they should sign in order to maximize their win totals.