What if We Took Replacement out of WAR?

Probably the most confusing part of the Wins Above Replacement  (WAR) structure is the replacement level concept.  Skeptical fans are critical of the use of replacement level because we are comparing let's say Miguel Cabrera to a "mythical player".  Some want Cabrera to be compared to the player who would have replaced him if he got injured.  Similarly, they want Prince Fielder, Mike Trout and every other real player to be compared to their actual replacements.

There are two problems with assigning a different replacement player for every player.  First, we don't have any way of knowing what the actual replacement would have done.  Even if we could identify specific players, we don't know whether they would have had good or bad seasons.  Not only that, but it would be quite impractical to do this all for all players throughout the history of the game.

Thus, it is desirable to have a common replacement level for all players.  What if we had no replacement level and just compared Cabrera to a zero player?  We would be assuming that his replacement would have batted .000/.000/.000.  Making that assumption , how many wins would Cabrera have been worth in 2012?

The calculation would start with Weighted Runs Created (RC).  Cabrera had 137 RC in 2012.  The other WAR numbers (for FanGraphs) are:

Ballpark -1.4 runs because Comerica Park slightly favors run scoring.
Base Running: -2.8 Runs below average
Fielding -10 runs according to UZR (yes, fielding metric are iffy but that's for another post)
Position +1.5 because 3B is a relatively difficult position.

Adding the four numbers above yields -12.7 Runs for his non-hitting stuff. Subtracting 12.7 from 137 equals 124.3 Runs.  Every 9.5 runs is worth about one win, so he had 137/9.5 = 13.1 Wins Above Zero (WA0).

Table below 1 shows RC and WA0 for Tigers in 2012.  You can see that everyone had a positive value as even Ryan Raburn was better than nothing.  The problem is that nobody would ever be replaced by a zero player and the result is that players get more credit for their offensive production than they should.

Table 1: Calculating Player Wins for Tigers in 2012 Using Different Baselines

Player	PA	RC	RAA	RAR	WA0	WAA	WAR
Cabrera	697	137	57.3	81.2	13.1	4.7	7.2
Fielder	690	125	46.1	69.8	10.7	2.4	4.9
Jackson	617	98	28	48.6	10.8	3.4	5.5
Hunter	584	86	19.4	39.3	10.2	3.2	5.3
Infante	554	65	-2.4	17.2	8.2	1.1	3.2
Peralta	585	60	-6.7	13.2	7.5	0.5	2.6
Avila	434	54	4.2	19.3	6.2	1.0	2.6
Dirks	344	54	14.7	26.5	4.5	0.4	1.6
Young	608	65	-4.8	16.4	4.4	-2.9	-0.7
Berry	330	35	-2.6	8.6	3.8	-0.2	1
Boesch	503	46	-11	5.8	2.9	-3.1	-1.3
Santiago	259	17	-13	-3.6	1.9	-1.3	-0.3
Raburn	222	8	-17.6	-11.7	0.6	-2.1	-1.5

What if we assume that  Cabrera's replacement would be an average hitter?  Since there were 21,017 runs scored in 184,179 plate appearances in 2012, the average PA resulted in 21,017/184,179 = .114 runs.  Thus, the average hitter would have created .114*697 = 79.5 runs in 697 PA.

Subtract 79.5 from Cabrera's 137 RC and he had 57.5 Runs Above Average (RAA).  Now subtract the -12.7 for non-hitting elements and Cabrera was worth 44.8 runs.  Divide that by 9.5 and he was 4.7 Wins Above Average (WAA).

Just 4.7 wins?  If that seems low for Cabrera, it's because it is in comparison to an average player.  In reality, an average player is a pretty good player and it's not likely that one would be readily available in the case of an injury to Cabrera.

Some analysts believe that WAA is useful in evaluating Hall-of-Fame status, because they don't want to give too much credit to compilers - players who were good (but not great) for a long period of time.  Using a baseline of average makes sense for the Hall of Fame because we are not really interested in how elite players compare to bad players.  We are more interested in how they compare to long-time players, who were pretty good but not Hall-of-Fame quality.

However, WAA usually doesn't work as well for annual analyses where we want to determine how many wins a player added to his team.  This is illustrated by Table 1 which shows Jhonny Peralta (0.5 WAA) and  Andy Dirks (0.4) had almost no value by that measure.  In actuality, It is not likely that either one would haven been easily replaced if they had suffered a season-ending injury in May. 

Since WA0 inflates a player's worth and WAA underestimates it, we need something in between.  Based on research over several year on which past players were added to rosters during a season and able to earn significant playing time, analysts have arrived at the typical replacement player.  The FanGraphs replacement player hits roughly 70% as good as an average player. Other sites have slightly different percents, but I'll go with 70% here.  Does 70% of average sound more real than "mythical player"? 

Remembering that the average PA results in .114 runs, 70% of average is .080.  So, the typical replacement player would create .080 by 697 = 55.8 runs. Subtract that from 137 and Cabrera was 81.2 Runs Above Replacement (RAR).  Subtract the -12.7 for everything beyond hitting and Cabrera was worth 68.5 runs.  Divide by 9.5 and he was 7.2 Wins Above Replacement (WAR).

You don't have to use the 70% of average replacement player if you don't want.  That's a good number to use if you are playing general manager, but a fan could use WAA if he/she just wanted to know how many players on their team are above average. Chances are a team with a lot of those players will win a lot of games.  Choose whatever baseline you want if you are willing to do the calculations.  Just beware that various baselines have different meaning and can produce very different values and ranks.