Sports Reference Blog

Everything You Wanted to Know About Wins Above Replacement (WAR)

Posted by Neil on October 10, 2012

With all of the controversy over the role of Wins Above Replacement (WAR) in the A.L. MVP debate, now might be a good time to remind everyone about our WAR 2.1 guide:

  • WAR Explained - This explains the basics of WAR, the philosophy behind the stat, and some of the changes we made to the formula this past spring.
  • Weighted Runs Above Average (wRAA) Explained - This describes how wRAA, the core hitting stat of WAR, is computed.
  • Position Player WAR Calculations and Details - This explains how we turn wRAA, Baserunning & Double-Play Runs, Fielding Runs, Positional Adjustment Runs, and Replacement level Runs into WAR for position-players.
  • Pitcher WAR Calculations and Details - This explains how we take a pitcher's runs allowed & innings pitched, and turn it into WAR.
  • Converting Runs to Wins - This further describes the process by which Runs Above Replacement (for both pitchers and position players) are converted into Wins Above Replacement.
  • WAR Comparison Chart - This chart shows the differences between the WAR found here at Baseball-Reference and those from a variety of other sources, including FanGraphs & Baseball Prospectus.
  • WAR Data Downloads - If you want to download the raw WAR data yourself and play around with it, you can also get the Batting and Pitching data from our site.

Many of the questions we typically get about WAR can be answered by reading the guide linked above.

36 Responses to “Everything You Wanted to Know About Wins Above Replacement (WAR)”

  1. barkie Says:

    I think I speak for a lot of people when I say we're getting used to the value of WAR more by the day. Sometimes it's the last piece of the puzzle I notice and I say; "well I guess old so-and-so was a pretty solid player".

    That said, I still have two major complaints. 1. WAR gives great advantage to players on crappy teams. I've long complained about the 68 AL pitchers race. Can you make a case that Tiant had a season in the same league as McClain? Maybe. WAR says Tiant crushed him. Why? look at the team records.

    and 2. Sometimes WAR just doesn't pass the sniff test. It's one thing to say Trout had a year in the same range as Cabrera's. WAR says it wasn't even close. Anyone who watched this year can't really say that's even close to true.

  2. erg! Says:


    1. Insert wins-are-overrated argument here

    2. Cabrera is your prototypical one-dimensional slugger. He put up monster numbers to win the Triple Crown, but he's largely a defensive and baserunning liability i.e. David Ortiz incarnate. Meanwhile Mike Trout just had the most sensational rookie season since Fred Lynn, keeping pace with Cabrera in power in addition to having fleet feet and keen defensive skills. Ergo Trout's WAR >>> Cabrera's.

  3. Antares Says:

    "Sometimes WAR just doesn't pass the sniff test. It's one thing to say Trout had a year in the same range as Cabrera's. WAR says it wasn't even close. Anyone who watched this year can't really say that's even close to true."

    That's a hell of a note. Do you speak for "everyone who watched this year"? And what makes you sure that you're right and WAR is wrong? WAR may be wrong in this case, likely due to the valuation of defense, but "anyone who watched this year has to believe that WAR got it wrong" is as far from a compelling argument as possible.

  4. Cabriael Says:

    Who cares about WAR?

    I didn't know Jim Joyce is still in the major league, while Galaraga isn't.

    And good old Jim is still blowing calls.

    I do think that Galarraga should have ended Jim's life at there. At best he would have gotten the Casey Anthony verdict and would have been acquitted.

  5. Alanruns Says:

    You make a change in a derived statistic and suddenly Alex Rodriguez and Rickey Henderson are better than Mickey Mantle?

    Even without this, there is no way you can say that Stan Musial was better than Ted Williams. Throughout the forties and early fifties (prior to Mantle/Mays becoming really good, and the two catchers listed below) they were one-two; but everyone knew that Williams was #1. Always was, always will be.

    And, of course, the most bogus stat for the old timers (forget about the disservice to Cabrera this year) is what it did to the two best catchers in baseball in the 1950s. Between 1951 and 1955 Yogi Berra and Roy Campanella won six MVPs, and led their teams to seven of the ten pennants and 4 of the 5 World Series. Yet in their MVP seasons your WAR stat places Campy 7th twice and out of the top ten once, and Yogi 9th once and twice out of the running. Only one of the six MVP votes was close. Yet the best WAR standing for them was 7th.

    What sees better: the writers' eyes or derived stats?

    Since all this is doing is playing with numbers, how about seeing if anyone (except the Babe or Bonds and his drugs) had a better ten year run than Mantle 1955-1964.

  6. Alanruns Says:

    The Luis Tiant/Denny McLain argument rings true for Felix Hernandez and Dean Chance. Dean Chance? Who's he, and how does he fit here?

    See 1964, where Chance had one of the great seasons of all time: 20-9, 1.65, 15 complete games, 11 shutouts! His team without him was 62-71. 20-9 is .690; 62-71 is .466. Thus he was .224 points better than his team. He had five 1-0 wins and a 14 inning shutout no decision. Yet somehow his WAR was only 9.1!

    "King" Felix: 13-12, 2.27, 6 CGs and 1 shutout. Team without him was 46-91. 13-12 is .520; 46-91 is .336. Thus he was .184 points better than his team.

    The job of a pitcher is to win games. Dean Chance proved that you can be phenomenal on a poor team; he earned his Cy Young award. "King" Felix did not, no matter what a set of derived statistics showed.

    BTW, I loved Luis Tiant. But "there'll never be any like Denny McLain." Especially in 1968/1969.

  7. barkie Says:

    # 4 Cabriel. Funniest thing today!

    As for 68, Denny's season was a lot more than just 31 wins. Look at his start log. It's insane. And Tiant's season was also incredible. Better? Significantly better?

    As for Cabrera being a one dimensional hitter... you're kidding. Adam Dunn is a one-dimensional hitter. Cabrera is a Triple Crown winner, sprays the ball all over the field, reasonable strikeouts and a great late inning hitter.And you know, Sean Foreman took me task once over DHs, saying "their manager chose that position for them". Well, Cabrera was told do move and did a much better job than ANYONE predicted.

    I go back to the beginning. Trout had an incredible year- a rookie year to equal the likes of Fred Lynn. A season in the same league as Cabrera. Better? SIGNIFICANTLY better?

  8. erg! Says:


    Replace "slugger" with "player" (as, admittedly, I should have) and it makes much better sense. Trout was a much better PLAYER this season in terms of contributions to his team. Cabrera was a bit better at the plate, but Trout eviscerated him in everything else. This is what WAR measures--the stuff the Big Three traditional stats cannot.

  9. erg! Says:

    Also, let's get one thing straight: moving off the field to DH is not hard at all, so I don't give Cabrera any "extra credit" for that.

  10. Fred Collignon Says:

    Ted Williams obviously the better player than Musial in the 40's and 50's? Sorry, I heard lots of debates and was pretty convinced in those years as a pre-sabrmetrics fan, that Musial was better - fielding, baserunning, clubhouse "leadership", etc. I thought half the world or more thought Musial the better, though it seemed pretty close to me. It took sabrmetrics etc. to convince me that the batting of Williams made him the more dominant. But I guess other than Mays and Bonds, I haven't seen/heard of a better player than Musial since. Ok, maybe Rodriguez.

  11. barkie Says:

    #9. Cabrera moved to third- a very difficult switch at 29 and took a hefty dWAR hit for it. And my point about the DH was that they shouldn't be seen as in the same caliber of position players since they play so little. Sean and Andy's drumbeat was; "the player doesn't get to pick his position"- maybe Edgar Martinez really wanted to play the outfield.

  12. Ron Johnson Says:

    #11 He also got a ~11 run positional adjustment ( -10 to +1 ) compared to last year. As a group, first-basemen comfortably out-hit third-basemen and WAR adjusts for this.

    The remarkable thing about Cabrer's move back to third is that most people expected a disater. In fact he was seemingly just a tad below average.

  13. Ron Johnson Says:

    #5 As I mentioned in the other thread:

    A) The standard error in a career of 15 years is around 3 wins. In other words there's no real difference between Williams and Musial. That's before addressing the whole issue of credit for missed time due to military service.

    B. Career value and greatness aren't the same thing. To take one example, I regard Mike Piazza as being a greater player than Ivan Rodriguez even though Rodriguez has more career value. He accumulated that extra value as a useful but obviously not stellar player. Piazza burned out more quickly.

    That's why everybody who really understands WAR says it's a good place to start the conversation. It's never the final word (single year or ranking players)

    I miss Dale Stephenson's peak lists. They were a great compliment to any pure career rankings.

  14. Thomas Court Says:

    It doesn't pass the sniff test? If some fans want to hold onto the greatness of a season with great AVG/HR/RBI numbers, that is fine. Cabrera did have a great season.

    But the fact is, if you took a team of 2012 Cabreras and played them against a team of 2012 Trouts for a 162 game season a lot more than the Triple Crown categories would affect the outcome.

    I'll tell you what happens: all of the other important stats that contribute to the outcome of a baseball game start coming into play. Like baserunning (Trout #1), range in the field and grounding into double plays (Cabrera #1).

    The team of Trouts would trounce the team of Cabreras... unless we limit the competition to the batting cage.

  15. KidNesto Says:

    Postseason WAR would be interesting.

  16. sabermetstrics Says:

    #14 Thank you! Yes, Cabrera had a great season. But Trout was better by a wide margin. Cabrera has the edge in batting we can all agree but it's not that much. To put the hitting comparison of the two most important stats Cabrera bests Trout by a small margin. Trout: .399 OBP .564 SLG Cabrera .393 OBP .606 SLG. So Trout actually has the advantage in the proven most important hitting statistic! I will concede that Cabrera's had the better hitting season, but it's the MVP not the MVB (most valuable batter) as stated in a letter to the editor in last week's Sports Illustrated. We all agree that Cabrera costs his team runs on the basepaths and in the field, and Trout certainly is a plus for the Angels with his 49 stolen bases, ability to go first to third and score from first on a double, and his spectacular leaping catches. Mike Trout for MVP!

  17. Raker Says:

    In my opinion, an example where Trout gets an unfair advantage, is him getting a boost in WAR from playing his home games in an extreme pitcher's park.

    While it's true that Anaheim was a pitcher's park for most hitters, it wasn't for Trout.

    Home 300 PA, 16 HR, .976 OPS
    Away 339 PA 14 HR .951 OPS

    But Trout unjustly gets awarded "wins" because his teammates and opponents collectively hit better on the road.

    Then there are the 23 games Trout missed. I understand that WAR is accumulative, but does it subtract the negative WAR of the replacement player CF? It seems like answering the bell for 161 games like Miggy did while using only one game's worth of replacement player, instead of Trout's 139 and 23 game's worth of replacement player should be the obvious tipping point towards Cabrera, if the Triple Crown didn't already do that for you.

    Thomas Court wrote; "But the fact is, if you took a team of 2012 Cabreras and played them against a team of 2012 Trouts for a 162 game season a lot more than the Triple Crown categories would affect the outcome."

    For real? What I mean is you're going to put Trout and Cabrera at all 8 positions? I would say that Cabrera would win by virtue of being an infielder and former outfielder. All infielders can play outfield but virtually no outfielders can play infield. Also, I'm not sure but I would think that Trout sees far more fastballs and strikes than Miggy, but not so in your hypothetical game.

    I'll go with the team with the infielder who has the higher OPS and 112 more HR.

    And that's the thing about WAR, there are a lot of hypotheticals. It's interesting but don't site it as gospel because there are so many things that go on between the lines that it doesn't know.

  18. Neil Says:

    #17 - I'm not sure you're fully understanding the concept of Wins Above Replacement... In the games Trout missed, the theoretical replacement CF wouldn't have negative WAR. He is, by his very definition, a 0.0 WAR player. He adds nothing, and subtracts nothing, relative to himself and others like him.

    As for park factors, we're not saying what a player "would have done" in a different park, we're saying that runs created by Trout were more valuable in terms of wins than runs created by Cabrera because it took fewer runs to get a win in Angel Stadium than in Comerica. It's like monetary inflation -- you can "buy" more wins with runs in a lower-scoring environment than in a higher-scoring one.

  19. Raker Says:

    Neil, I understand the concept, my "negative WAR" comment was dumb by definition, I realized that it's 0.0 after I submitted it but that was just a sm all point. I assume that you are saying that even in 23 less games, Cabrera (6.9) was only worth 64% of Trout's (10.7) value above a replacement player? I think that's where you lose me and other's like me.

    As far as the other point you addressed, I get how you arrive at it, with the run shares and all, but I think it would be dangerous for a GM to think that because Player X had a higher percentage of "run shares" in a specific run enviornment than Player Y did in his, then X is more valuable than Y. (See Adrian Gonzalez).

    Anyway, thanks for the response.

  20. Neil Says:

    Value is retrospective, so the value (in wins) of a player's runs is very pertinent to the question of "Which player created the most wins for his team?"

    The GM, though, would hopefully be looking forward, and that's a question of ability, not value. They're not the same thing:

    Park factors for ability would absolutely say, "Park A treats spray-hitters and power-hitters differently than in Park B". Park factors for value would say, "I don't care how Parks A & B affect different types of hitters, I just want to know how much more runs are worth in Park A than Park B."

  21. Raker Says:

    "even in 23 less games, Cabrera (6.9) was only worth 64% of Trout's (10.7) value above a replacement player."

    So that's a true statement in terms of value from your point of view?

    Don't get me wrong, I appreciate how much thought and work continually goes into WAR but the results don't feel right. The game is so much closer than a 36% differential between two of it's top players. Those kinds of differentials turn a .300 hitter into a car salesman.

    This is kind of a nitpick on WAR, but in wRAA, it sites the 2010 season linear weights applied to offensive events. My take on them is that it overvalues BB, HBP and 1B and undervalues HR. For example, I think the only reason the BB is worth .89 is because of the HR. So yeah, there is value as long as there is a Miguel Cabrera type is behind you, which seems to be taken for granted.

    With appologies to Thurman, Reggie Jackson was right when he said he was the straw that stirred the drink.

  22. Neil Says:

    Those linear weights are derived from the actual base-out-run matrix, though. They can't "overvalue" or "undervalue" an event -- the average value of a HR, BB, etc in terms of runs is what it is. It's a fact.

    In terms of the difference in value, I don't think that's unreasonable. First of all, the 22-game difference isn't as big it sounds because Trout had more PA/game. It's only really a 58-PA difference.

    Also, Trout and Cabrera produced a very similar number of runs with the bat alone, after adjusting for park (Trout had a slightly higher OBP, Cabrera had a 40-point SLG advantage, but that difference gets reduced via park factors and the fact that OBP is worth 70% more to run-scoring than SLG). So if you consider hitting the base from which they're starting, it's pretty even to begin with. Then you add in baserunning (major Trout edge) and defense (major Trout edge), and it makes sense that Trout had a sizable overall edge.

    The conventional wisdom is underrating Trout's hitting and overrating Cabrera's because Trout bats leadoff & Cabrera has the pretty shiny Triple Crown stats. It's also downplaying how much better a baserunner and fielder Trout is. Cabrera is the "Hitter of the Year", but not by as much as you'd think, and total value is more than just hitting. Makes sense to me that, in overall value, it would be a landslide for Trout.

  23. Raker Says:

    "So for example, in 2010 we get a formula for MLB of: wOBA = (0.70 * uBB + 0.73 * HBP + 0.89 * 1B + 1.27 * 2B + 1.61 * 3B + 2.07 * HR + 0.25 * SB + 0.50 * CS) / (AB+BB-IBB+HBP+SF)"

    That's from the link above.

    I assume that HR weight is 3.25?

    How can a single and a SB (1.77 total) be worth more than a double(1.61) when a double moves base runners 2 and 3 bases and a single moves them 1 and 2?

    I still say it's the HR that drives the linear weights meaning the high OBP/singles hitter only rates high because of the HR hitters who turn their trip to 1st or 2nd into runs.

    The Yankees, for example, were 1st in the AL in OBP and HR. They had 2089 times on base and 245 HR. So 11.7% of their times on base were HR but those HR accounted for 397 of their 774 RBI, or 51.3% of their earned runs were from HR. Guys like Ichiro drive in less than half the runs as HR hitters do for a reason.

  24. Neil Says:

    HR weight is 2.07 in the formula above. Also, a single (0.89) plus a steal (0.25) is worth 1.14, which is not more than a double (1.27).

  25. Raker Says:

    OK, I was reading between the asterisks.

    So this is the basis for WAR. A HR is 2.07 runs better than an out. A HBP is .73 runs better than an out. An IBB and sac bunts are subtracted because they don't show any skill, as they are manager decisions. (a HBP is sometimes a manager's decision too).

    Again, the HBP scores .73 because of the HR. Without the HR, it's less than half that total. This way of thinking takes the HR for granted and 3 HBP is worth more than 1 HR.

    Baseball is about bases. Not just the bases accumulated for an individual, but also the bases that said individual moved other runners. That's where RBI comes in, currently the closest measurement of advancing runners. Miguel Cabrea drove in a man from firstbase 23 times but the guy on 1st gets half the credit in WAR.

    The Grand Slam is 10 out of 10 possible bases but it's worth less than 3 times a HBP with 2 outs and nobody on base in WAR.

    Smoltz was about to address this issue on yesterday's broadcast in reference to Cabrera being the hands down MVP but the inning ended and he never got back to it. He called it new-age baseball that doesn't reflect real baseball.

    Ripken said that Cabrera is the best hitter because he sees the fewest mistake pitches in the league, but cripples them when they come and manages to win the TC.

    I say he's the best hitter because he creates the most total bases for himself and his teammates.

    Incidently, Cabrera led the majors in RBI per opportunity rate by a wide margin though Trout was actually in the group behind him.

  26. Neil Says:

    Baseball is not about bases, ironically enough. It's about runs. Runs and outs:

    Every few months, somebody writes in thinking they've "invented" a new stat that basically measures total bases per PA, or total bases per out. It's bogus because total bases are not weighted properly relative to each other in terms of creating runs. That's why linear weights exist.

  27. Raker Says:

    You can't make a run without 4 bases. Bases are the molecules of baseball, not runs.

    Ron Hunt was valuable because he got on and HR hitters drove him in. Try putting 9 Ron Hunt's in a lineup and see what that does to your linear weights.

    Why would you guys ever waste your time figuring out OPS+ if the bases are so wrong?

    Those are a couple of condscending links you posted there. I suppose it doesn't matter to you(or them) that, for example, Hank Aaron drove in the guy from 1B 8.7% of the time and Paul Molitor did it 3.4%?

    Most people would think there needs to be some recogning of that sort of stat in a total value. Those kind of stats get swallowed up in linear weights.

    "Every few months, somebody writes in thinking they've "invented" a new stat."

    I think people would be interested in finding out who had the most real bases, namely 10 for 10 on a GS, 0 for 10 on an out with bases loaded. 4 for 4 on a solo HR, 0 for 4 on a bases empty out....

  28. Neil Says:

    The only thing that a "% of runners driven in" stat would capture that doesn't already show up in the player's wOBA is situational/clutch hitting, which you can get at using RE24 or WPA if you want.

    WAR is a framework made up of different parts (hitting, baserunning, positional value, defense, playing time, etc), and our version uses what most sabermetricians agree are the most useful types of each part. But the beauty of it is that you can take out one type of part and put in another type if you don't like the specifics of the one we were using.

    Btw, Aaron's going to have a greater RBI% (or whatever) than Molitor because Aaron was a much, much better hitter than Molitor in general. You don't need a clutch-leaning stat to know that -- the difference between those two is going to be detected by any stat you use.

    As for OPS+, there's actually been a lot of criticism in sabermetric circles for us using it. The advantages of OPS+ are that, despite the flaws of total bases, OPS still manages to correlate pretty well to run-scoring, and sportswriters are comfortable using it. It would be more scientifically sound to use wOBA instead of OPS as the basis of our flagship hitting rate stat, and we do plan to add wOBA to the site soon, but I consider it a victory if you can get media members to commonly use a park-adjusted rate stat that correlates far better with scoring than mere batting average.

  29. Neil Says:

    Also, the stat you describe ("10 for 10 on a GS, 0 for 10 on an out with bases loaded. 4 for 4 on a solo HR, 0 for 4 on a bases empty out...") is basically a total bases version of RE24. The problem being that, as I mentioned earlier, the weighting of total bases does not accurately represent the relative run values of each offensive event. It just doesn't.

    Give RE24 a chance, though. It tells you how many situational runs a player added in their plate appearances by looking at the difference in the team's expected runs for the inning before the PA began and after the PA was over. It literally measures how the player changed his team's offensive output via his hitting:

  30. Raker Says:

    With all the missing variables, changes and different formulas, where just a minor change can mean 20 or so spots for Mickey Mantle, I'd say WAR is off base (pun intended).

    In real baseball terms, the reason why Aaron did so well in those situations has nothing to do with clutch and everything to do with 1B wasn't open and they had to throw him strikes. And if you can't get that reflected in WAR, and have to combine it with RE24 or WPA then WAR isn't near complete and why not just say Aaron drove in the guy from 1B 8.7%?

    I get it completely now, in your circles linear weights are first and last, it doesn't matter how or why or what drives the linear weights.

    Thanks for the debate Neil!

  31. Doug B Says:

    one more thing I want to know...

    how does dWAR work for players who are primarily DH?

  32. Raker Says:

    PS; I will give RE24 a look, thanks again.

  33. Raker Says:

    RE24/boLI (Situational Runs) AL Leaders


    I think that would be very close to the same order as the 10-10/grand slam theory.

    It's almost exactly how I would order my votes for MVP.


  34. Neil Says:

    RE24/boLI is pretty similar to your theory because it "de-leverages" RE24 while maintaining the run impact of a given event within its own context (as opposed to linear weights, which assumes an average context for every event).

    The funny thing is, however, that RE24/boLI and linear weights work out to be almost the same thing across a big enough sample. For all AL hitters this season, the correlation between RE24/boLI and basic Pete Palmer batting runs was 0.96, meaning 92% of the variation you see in RE24/boLI can just be explained by linear weights.

  35. Raker Says:

    I like RE24/boLI because it agrees with me. :-)

    Really, I like it because it seems to have the HR in proper context. I'll look deeper into the differences between leverage and de-leveraging tonight.

    I will say off the top of my head is the problem I have with linear weights may be that it does assume an average context for every event.

    Thanks again.

  36. Raker Says: