WAR Explained: What Wins Above Replacement Counts and What It Cannot
What wins above replacement measures, how hitters and pitchers are credited, why Baseball-Reference and FanGraphs disagree, how to read the scale, and where the statistic stops being reliable.
Wins above replacement, almost always shortened to WAR, tries to answer one question with one number: how many more games did this player win for his team than a freely available substitute would have won in his place? A hitter who is worth 5 WAR in a season produced about five wins beyond what a minor-league call-up or a waiver-wire veteran would have given the club in the same playing time. The answer is built from a long chain of smaller estimates, and the chain is what this article explains.
WAR is popular because it puts every position, every skill and both leagues on the same scale. A shortstop who hits modestly and fields brilliantly can be compared with a first baseman who hits 40 home runs and fields poorly, and the arithmetic says which one helped his team win more. It is also misunderstood for the same reason. A single number looks more precise than it is, and fans sometimes treat a difference of half a win as a verdict. By the end of this article you should be able to read a WAR figure, know which parts of it you can trust, and tell when someone is leaning on it too hard.
This article does not quote any player's WAR. The historical record that powers most statistics on this site carries no WAR, so the figures are best taken from the sources that calculate them, which are named below. What follows is how the statistic is made and how to use it.
Replacement level: the idea at the center
The odd word in the name is "replacement." Ordinary averages measure a player against the typical major leaguer. WAR measures him against something lower: the kind of player a team could find at almost no cost, from Triple-A or from the players released in spring training. If a club loses a regular to injury, the replacement is who steps in.
Why measure against that floor instead of the average? Because an average player is valuable. A team of average players wins about half its games, and average players are paid millions of dollars because they are not easy to find. The real choice for a general manager is not between a 4-win player and an average one but between a 4-win player and whoever else could be had cheaply. Replacement level makes that choice visible.
The published versions place the replacement level at roughly a .300 winning percentage for a whole team. In a 162-game season that is a team of about 48 wins, a figure you will see quoted. For a hitter, the equivalent is about 20 runs below average per 600 plate appearances. These are conventions, not laws of nature, and the sites that publish WAR adjust them from time to time.
From runs to wins
WAR is first calculated in runs and then converted to wins. The rule of thumb is that about 10 additional runs scored or prevented produces one additional win. The figure comes from the relationship between runs and winning percentage that is explained in Pythagorean expectation: a team that scores and allows the same number of runs should win about half its games, and each extra 10 runs of margin lifts that team by about one win. In a high-scoring season the exchange rate is a bit worse, because each run is worth less. In a low-scoring one it is better. Careful versions of WAR adjust the conversion for the run environment.
Everything on the way to that conversion is a number of runs above average, plus the replacement credit. So the shape of the calculation, for a position player, is this:
- Batting runs: how many runs the player's plate appearances added compared with an average hitter.
- Baserunning runs: stolen bases, extra bases taken on hits and outs made on the bases.
- Fielding runs: how many runs the player's defense saved or cost compared with an average fielder at his position.
- A positional adjustment: a bonus or penalty for the difficulty of the position.
- A replacement credit: the runs that come from being above replacement level for the playing time.
Add them up, divide by roughly 10, and the answer is the player's WAR.
A worked example for a hitter
Consider an invented right fielder, not any real player, who comes to the plate 600 times in a season. Batting runs are usually computed from weighted on-base average, or wOBA, a measure that gives each way of reaching base a credit proportional to its run value, so a home run is worth much more than a single and a walk is worth something. Suppose our right fielder has a wOBA of .380 in a league where the average is .315.
The conversion is simple. Subtract the league average to get .065, divide by a scale factor near 1.2 to translate wOBA into runs per plate appearance, and multiply by the 600 plate appearances. The result is about 32 batting runs above average. Say he is a decent baserunner and adds 2 runs, and an average fielder, which adds 0. Right field carries a positional adjustment of about minus 7.5 runs per 162 games on FanGraphs' published scale, because it is an easier position to play than shortstop, and so the player is expected to hit more. Now add the replacement credit of about 20 runs for 600 plate appearances.
The total is 32 plus 2 plus 0 minus 7.5 plus 20, or about 47 runs. Dividing by 10 gives about 4.7 WAR, a very good season. Notice how much of the credit is the replacement term. If the same hitter were a below-average fielder who cost the team 8 runs, his WAR would fall to roughly 3.9. A defense that is worth 8 runs more or less is as important to the total as a rise of a few points in on-base percentage.
The positional adjustment deserves a word. The published figures for a 162-game season run roughly as follows: catcher about plus 12.5 runs, shortstop plus 7.5, second base, third base and center field plus 2.5, left and right field minus 7.5, first base minus 12.5 and designated hitter minus 17.5. The logic is that a first baseman and a designated hitter are expected to be good hitters, so their offense counts for less than the same offense from a shortstop or a catcher.
How pitchers are credited
A pitcher's WAR is built on his innings, and the two major sources approach it differently.
Baseball-Reference's version, often called bWAR (or rWAR), starts with the runs the pitcher allowed. It adjusts for the quality of the defense behind him, the park and the league, and gives credit for innings pitched against replacement level. The reasoning is that runs allowed are what actually happened, so they should be what counts.
FanGraphs' version, fWAR, starts with fielding-independent pitching, or FIP, an estimate of what a pitcher's earned run average should have been based on only the outcomes he controls most directly: strikeouts, walks, hit batters and home runs. The formula is the sum of 13 times the home runs, 3 times the walks and hit batters, minus 2 times the strikeouts, divided by innings, plus a constant of about 3.1 that sets the league average. The method and its cousins are the subject of the article on FIP, xFIP and SIERA.
A sketch with invented numbers shows the difference. Take a starter with 200 innings, 20 home runs, 50 walks, 5 hit batters and 210 strikeouts. His FIP is (13 times 20, plus 3 times 55, minus 2 times 210) divided by 200, plus 3.1. That is (260 plus 165 minus 420) divided by 200, which is 0.025, plus 3.1, or about 3.13. If the league's average is 4.20, he saves about 1.07 runs per nine innings, which over 200 innings is about 24 runs. Adding a replacement credit and dividing by 10 puts him near 4 wins on the FanGraphs method. Baseball-Reference might give a different answer for the same pitcher if his actual ERA was worse than his FIP, for example because of poor defense or bad luck on balls in play, or better if he consistently stranded runners.
A third source, Baseball Prospectus, publishes WARP, which uses a more elaborate pitching estimator. All three differ in detail, and all three claim to measure the same thing. Reliever credit is further complicated by leverage: a closer's innings carry more weight than a mop-up man's, and each source handles the adjustment differently.
Why the sources disagree
It surprises fans that the same player can carry, say, 5.2 WAR on one site and 6.4 on another, a gap of more than a win. The disagreement is not an error. It follows from three places where the methods make different choices.
- Defense. Fielding estimates come from play-level data, and they are the noisiest part of WAR. Different systems, such as Defensive Runs Saved, Ultimate Zone Rating and Outs Above Average, can differ by several runs for the same player in the same season. Baseball-Reference and FanGraphs use different ones and have changed them over time.
- Pitching. The runs-allowed approach and the FIP approach can differ by a win or more for a pitcher whose ERA deviates sharply from his FIP.
- Smaller choices. Park factors, the replacement level, the positional adjustments and the treatment of catchers, including pitch framing, are all parameters that the authors set.
The practical lesson is to look at both sources when it matters and to treat a difference of a win or less as no difference at all.
Reading the scale
Over the years the baseball analytics community has settled on a rough scale for a full season. It is a convention, and published versions differ by a few tenths.
| Season WAR | Common description |
|---|---|
| Below 0 | Worse than a replacement player |
| 0 to 2 | Reserve or part-time player |
| 2 to 3 | Solid regular |
| 3 to 5 | Good player, above-average starter |
| 5 to 6 | All-Star level |
| 6 to 8 | Star, likely among the best few in the league |
| 8 or more | MVP-level season |
The scale makes sense once you know the total. A team of replacement players wins about 48 games, and an average team wins 81, so the difference of roughly 33 wins is divided among a team's players. Across the 30 clubs, that is roughly 1,000 WAR a season spread over everyone who plays. Most regulars sit between 2 and 4, a handful reach 6, and a few hit 8 or more, which is why those seasons stand out so sharply. The same arithmetic works for a whole club: the sum of its players' WAR, plus the replacement baseline of about 48, should land close to its win total.
What WAR cannot do
The limits are worth stating plainly.
- It is a counting statistic. A player who misses half a season because of injury accumulates half as much WAR even if he played at the same rate. Comparing a full-time player with a part-timer on raw WAR measures playing time as well as quality. Some analysts look at WAR per 600 plate appearances or per 200 innings for that reason.
- Defense is estimated with error. A single season of fielding data can be misleading, and defensive estimates are often averaged over three seasons. A player credited with a plus 10 defensive season may be much closer to average in truth.
- It does not capture everything. Pitch calling by catchers, clubhouse effects and the value of a particular lineup slot are mostly left out, and so is much of the effect of leverage for position players. Whether a hit came with the game on the line is not part of the standard calculation. Win probability and leverage, covered in win probability, leverage index and win probability added, are the tools for that question.
- It is not predictive by itself. A player's last-season WAR does not equal his next-season WAR. Projection systems regress performance toward the mean and account for age.
- It is a model, not a measurement. Nobody observed 4.7 wins. They were calculated from assumptions.
The state of the art is sometimes oversold. The honest summary is that WAR is a good tool for sorting players into tiers and a poor tool for ranking two players who are close.
Putting WAR to use
Use it to compare players at different positions, to check whether an award or Hall of Fame argument holds up, and to see how much of a player's value is bat, glove or arm. Look at the pieces rather than the total: a player with 4 WAR from hitting is a different asset than one with 4 WAR from defense, because the batting portion is more stable from year to year.
For Hall of Fame debates, some writers use JAWS, the Jaffe WAR Score, which averages a player's career WAR with his peak WAR and compares the result with enshrined players at the same position. The method is one of several ways of applying WAR to the question that the article on the Hall of Fame debates takes up.
In fantasy baseball, WAR is of limited use. Fantasy scoring counts categories such as home runs and saves, and ignores defense and position scarcity, so a player's WAR and his fantasy value can differ widely. If a number is needed for fantasy, use projections of the categories your league scores.
Common questions
What is a good WAR? For a full season, 2 is a solid regular, 5 is an All-Star-level season, and 8 or more is an MVP-level season. Treat the thresholds as rough.
Is bWAR or fWAR better? Neither is better in general. They answer the same question with different methods, and each is defensible. For a pitcher, bWAR credits what happened and fWAR credits what the pitcher controlled.
Can WAR be negative? Yes. A player worse than replacement level, in a full-time role, can have negative WAR. It usually means a club kept playing someone it should have replaced.
Why does the same player have different WAR on different sites? Differences in defensive estimates, pitcher methods, park factors and replacement level. A gap of a win is normal.
Does the historical record include WAR? No. The historical record carries traditional box-score statistics. For WAR, use Baseball-Reference or FanGraphs.
Where to go next
To see how the same idea works at the level of a single plate appearance, read run expectancy and the 24 base-out states, the framework behind most batting-run estimates. For a simpler pitcher measure that still ignores defense, try WHIP, and to experiment with rate stats yourself, use the stat calculator. The wider topic collection is under stats and analytics.