What exactly is “Replacement?”
The concept of Wins Above Replacement (WAR) has been around for years now; basically it attempts to capture all of a player’s value in one number, which is translated to the number of wins he produces over some stiff that could be grabbed out of Triple-A. Dave C. at FanGraphs wrote a good primer on the topic a couple of years ago if you want to learn more.
Again, it attempts to measure everything a batter does at the plate and in the field, taking into account what position he plays and how much he plays. For example, simply playing in 150 games produces more value than playing in 100 games because you keep the “Replacement Stiff” out of the lineup. Admittedly, it does not include too much baserunning data besides stolen bases and caught stealing, and no one really has any idea yet how to measure a catcher’s defense. For pitchers, it includes number of innings pitched, home runs, walks, strikeouts, as well as the run environments they pitch in (quality of hitters, ballparks, etc.).
Anyway, something I’ve always struggled with regarding WAR is the “wins” portion of it. If I trade Justin Morneau for Albert Pujols, does that get 1 more win? 2 more wins? If I remove Pujols from the lineup entirely and call up my 30-year-old Triple-A first baseman, is it really only 8 wins? Or is it EIGHT wins? I’ve never had a good grasp on whether that was a lot or not or whether the wins were actually “wins,” as in, on-the-field wins. The logic was sound, but for some reason I couldn’t get my head around it.
Data for WAR are available back to 2002 (when the defensive data collection began), and so I looked at the 2002-2009 seasons to try to get a better understanding of what WAR means. First I just copied all of the WAR and standings data for each season for each team. The resulting table shows the league average for those 8 seasons, as well as the current 2010 data (through Saturday, 6/12):
|Wins / Losses||80.8||81.0||80.9||81.0||81.0||81.1||80.9||81.0||31.1|
|Wins – WAR||45.4||46.0||46.1||45.6||46.4||46.3||45.9||45.9||17.3|
The first thing I noticed was that the average number of WAR per team seemed about right. I had always heard that a replacement level team would win somewhere between 40 and 50 games; from this exercise, that number appears to be about 46 wins, more precisely. To check though, I wanted to see what kind of WAR showed for the worst teams over those 8 seasons. I took the bottom 10 percent of teams (in terms of wins) and compared their WAR numbers.
The 25 teams averaged 60.4 wins per season; by the Pythagorean formula for win-loss records, they “should” have won 62.7 games. All told they combined for 521 WAR, or about 20.9 per team. Subtracting their WAR from their records, both actual and Pythagorean, a replacement level team should win about 40-42 games. Being major league quality teams, they were probably slightly better than that, just unlucky. Only the 2003 Tigers (43 wins) and the 2004 Diamondbacks (51 wins) had win totals anywhere close to the replacement level. Those two teams also had the lowest WARs over the 8 seasons, 2.7 and 11.1 respectively (although your 2010 Pittsburgh Pirates (1.1 WAR overall) and Houston Astros (-2.3 WAR for the hitters) are threatening to become the poster-child for “WAR ineptitude.” Side bar: I will never forgive the 2003 Tigers for winning 5 of their last 6 games to avoid becoming the “losingest” team ever. Damn you, Mike Maroth.
Having done this, I wanted to see if the teams at the top were being given too little or too much credit. The 26 teams in the top 10 percent (ties included) averaged 99.0 wins per season; by the Pythagorean formula for win-loss records, they “should” have won 96.2 games. All told they combined for 1,249 WAR, or about 48.0 per team. From the average in the table above, this should equate to about 94 wins. So some funky things happen at the outer edges. but well within reason. To see if the middle showed that kind of error, I looked at the 10 percent of teams closest to 0.500 also. 33 teams finished within 2 games of 0.500 (79 to 83 wins) in these 8 seasons. They’re averaged 81.2 wins, “should” have won 81.7 games, and averaged 35.0 WAR. This equates to a 46-win replacement-level team, exactly what the averages tell us.
If winning teams are not given enough credit, and bad teams are given too much credit, then it’s possible that definition applied to “replacement-level” is off. To be honest, I made a mistake the first time through the calculations and really dug into the components of WAR to make sure I wasn’t missing something important. I was considering the ramifications of my (erroneous) findings, and starting thinking that the standard needed to be raised slightly (creating fewer WAR), and the multipliers applied to the components of WAR be raised (creating greater separation between players; for example, what currently are 2 WAR and 8 WAR players might become 3 WAR and 12 WAR players).
It appears though that WAR does equate on a team scale, just like it’s supposed to. After all, isn’t that the reason the thing is defined like it is? If Chase Utley is worth 7 wins and Robinson Cano is worth 4 wins, then them trading teams for a full season should make nearly a 3 game difference. I can feel confident saying that, in 2005, Carl Everett was exactly a replacement-level player and that A-Rod produced more than 9 wins.
I have some other things I want to do with this data, but I wanted to share the spreadsheet I compiled in case anyone wants to do some tests of their own.