Wins above replacement (WAR) or wins above replacement player (WARP) is a non-standardized sabermetric baseball statistic developed to sum up "a player's total contributions to his team".FanGraphs: WAR A player's WAR value is claimed to be the number of additional wins his team has achieved above the number of expected team wins if that player were traded for a replacement-level player: a player of common skills who may be added to the team for minimal cost and effort.
Individual WAR values are calculated from the number and success rate of on-field actions by a player (in batting, baserunning, fielding, and pitching), with higher values reflecting larger contributions to a team's success.Schoenfield: 2012 WAR value also depends on what position a player plays, with more value going to key defensive positions like catcher and shortstop than positions with less defensive importance such as first base. A high WAR value built up by a player reflects successful performance, a large quantity of playing time, or both.
Overview The basis for a WAR value is the estimated number of runs contributed by a player through offensive actions such as batting and base running, and runs denied to opposition teams by the player through defensive actions like fielding and pitching. Statistics such as weighted on-base average (wOBA), ultimate zone rating (UZR), ultimate base running (UBR), and defense independent pitching statistics (DIPS) measure the effectiveness of a player at creating and saving runs for their team, on a per-plate appearance or per-inning basis. These statistics can be multiplied by the playing time of a player to give an estimate of the number of offensive and defensive runs contributed to their team.
Additional runs contributed to a team lead to additional wins, with 10 runs estimated to be equal to roughly one win. Therefore, a 1.0 WAR value for a player signifies a contribution of roughly 10 more runs than a replacement-level player, over a specified period of time. A replacement-level player is defined by FanGraphs as contributing 17.5 runs fewer than a player of league-average performance, over 600 plate appearances. Therefore, a 1.0 WAR player has contributed an estimated −7.5 runs relative to average over the same number of plate appearances, a 2.0 WAR player has contributed +2.5 runs, and a 5.0 WAR player has contributed +32.5 runs.
For an individual player, WAR values may be calculated for single seasons or parts of seasons, for several seasons, or across the whole career of the player. Collective WAR values for multiple players may also be estimated, for example to determine the contribution a team receives from its outfielders, its relief pitchers or from specific positions such as catcher. It is also possible to extrapolate a future WAR value from a player's past performance data.
Calculation No clearly established formula exists for WAR. Sources that provide the statistic calculate it differently. These include Baseball Prospectus, Baseball-Reference, and FanGraphs. All of these sources publish the method they use to calculate WAR, and all use similar basic principles to do so. The version published by Baseball Prospectus is named WARP,Kaufman and Tan: 2012. Page XIV. that by Baseball-Reference is named bWAR or rWAR ("r" derives from Rally or RallyMonkey, a nickname for Sean Smith, who implemented that site's version of the statistic)Baseball-Reference.com: WAR Comparison Chart and that for Fangraphs is named fWAR.Fangraphs: What is WAR? Compared to rWAR, the calculation of fWAR places greater emphasis on peripheral statistics.
WAR values are scaled equally for pitchers and batters; that is, pitchers and position players will have roughly the same WAR if their contribution to their team is deemed similar. However, the values are calculated differently for pitchers and position players: position players are evaluated using statistics for fielding, base running, and hitting, while pitchers are evaluated using statistics related to the opposing batters' hits, walks, and strikeouts in FanGraphs' version and runs allowed per 9 innings with a team defense adjustment for Baseball-Reference's version. Because the independent WAR frameworks are calculated differently, they do not have the same scaleDarowski: 2010 and cannot be used interchangeably in an analytical context.
Position players
Baseball-Reference Baseball-Reference uses six components to calculate WAR for position players: batting runs (Rbat), baserunning runs (Rbaser), runs added or lost due to grounding into double plays in double play situations (Rdp), fielding runs (Rfield), positional adjustment runs (Rpos), and replacement level runs (Rrep). The first five factors are compared to league average, so a value of 0 represents an average player.
The term may be calculated from the first five factors (Rbat + Rbaser + Rdp + Rfield + Rpos), and the other term from Rrep. After each of these components is computed and summed, runs are converted to wins by dividing by a runs-per-win value determined using Pythagenpat.
Rbat is based on Weighted Runs Above Average (wRAA), which in turn is calculated based on wOBA. However, Baseball-Reference uses a modified version of wOBA dubbed rOBA. Rbat is also adjusted for park and league factors.Baseball-Reference.com: wRAA For Position Player WAR Explained Rbaser is computed by considering expected runs from stolen bases. Additionally, Rbaser considers non-basestealing baserunning by comparing the player's baserunning results in specific scenarios to the league average, and multiplying those results by the expected number of runs per base (or runs per out). Rdp is computed by first finding the difference in the player's expected number of double plays (based on league average) and their actual number. This is multiplied by the expected difference in runs scored between grounding into a double play and not, which averages to 0.44 across seasons, but varies with the run environment.
Rfield uses DRS for the 2003 season and beyond, and Total Zone (TZ) for earlier seasons. Defensive Regression Analysis (DRA) is used for Negro League seasons. Rpos is calculated based on the player's position: +9 for a catcher, −9.5 for a first baseman, +3 for a second baseman, +2 for a third baseman, +7 for a shortstop, −7 for a left fielder, +2.5 for a center fielder, −7 for a right fielder, and −15 for a designated hitter. These values are set assuming 1,350 innings played (150 games of 9 innings). A player's positional adjustment is the sum of the positional adjustment for each position played by the player scaled to the number of games played by the player at that position, normalized to 1,350 innings. An additional adjustment is made so that the Rpos of all the players in the league sum to 0. Rrep is added to give the player credit for the additional runs a league average player would be expected to score over the same number of plate appearances compared to a replacement level player.
FanGraphs Similarly to bWAR, FanGraphs uses six components to calculate fWAR for position players. These components are all on the scale of runs, and are then converted to wins based on a runs-per-win value that changes each season based on the run environment. The formula used is Fangraphs: Calculating WAR for Position Players
Batting runs is based on wRAA, adjusted using park and league factors. As of 2024, , where XBR is Statcast's baserunning metric and wSB is Weighted Stolen Base Runs. For seasons prior to 2016, Ultimate Base Running (UBR) and Weighted Grounded into Double Plays (wGDP) are used in place of XBR when available. Fielding runs for non-catchers is based on either Outs Above Average (OAA) converted to runs above average, Ultimate Zone Rating (UZR), or Total Zone (TZ), depending on era. For catchers, depending on era, either Statcast metrics, a combination of Stolen Base Runs (rSB) and Catcher Framing (FRM), or TZ is used. The positional adjustment is calculated as follows, where adj is a run value dependent on the player's position: +12.5 for a catcher, −12.5 for a first baseman, +2.5 for a second or third baseman, +7.5 for a shortstop, −7.5 for a left or right fielder, +2.5 for a center fielder, and −17.5 for a designated hitter.Cameron: 2008
The league adjustment is a minor adjustment (usually 0-5 runs per season) added so each league's runs above average balances out to zero. Finally, since all the previous run values are relative to league average, replacement runs are added to compare the player to a replacement level player.
Baseball Prospectus Baseball Prospectus (BP) uses WARP (Wins Above Replacement Player). WARP relies on BP's proprietary set of statistics called "Deserved Runs", including DRA ("Deserved Runs Allowed") for pitchers and DRC ("Created") for batters. BP claims that DRC is the superior metric for comparing player performance when the player changes teams, and also when accounting for changes to the physical game ball year to year. The WARP formula for position players is
BRAA = "Batting Runs Above Average is the number of runs a hitter produces relative to an average hitter, adjusted for park."
BRR = "Baserunning Runs measures a player's contributions on the basepaths based on activity during the run of play, on stolen base attempts, from tag-up situations, and other advancement opportunities. BRR is calculated as the sum of various baserunning components: Ground Advancement Runs (GAR), Stolen Base Runs (SBR), Air Advancement Runs (AAR), Hit Advancement Runs (HAR) and Other Advancement Runs (OAR)."
FRAA = "Fielding Runs Above Average...measure(s) the defensive contributions made by players in the field."
Infielders, outfielders, and catchers are evaluated differently. For outfielders, fielding impact is calculated by comparing their "assist opportunities" with the actual change in run expectancy on each play. Evaluating catchers includes measuring SRAA (Swipe Rate Above Average, or opponent base-stealing success) and TRAA (Takeoff Rate Above Average, or opponent base-stealing attempts), both of which are also used for calculations for baserunners and pitchers. Catchers are also evaluated by their "framing" skills (making balls outside of the strikezone appear to be strikes to the umpire) via CSAA (Called Strikes Above Average) as well as their skill at blocking errant pitches, via EPAA (Errant Pitches Above Average).
POS_ADJ = "The defensive value of the position a player plays, in total runs relative to the average player." BP does not make publicly available what values it uses for this adjustment.
REP_LEVEL = "The number of runs an average player would have produced relative to replacement level."
RPW = Runs Per Win.
The formula could then be written explicitly as
Pitchers
Baseball-Reference Baseball-Reference uses two components to calculate WAR for pitchers: runs allowed (both earned and unearned) and innings pitched. These statistics are then used in a number of further calculations to better contextualize the numbers.Baseball-Reference.com: Pitcher WAR Calculations and Details
FanGraphs Rather than focus on actual runs allowed, Fangraphs uses fielding independent pitching (FIP) as their main component to calculate WAR as they feel it better reflects the contributions of the pitcher.
, the calculation of pitching fWAR is summarized as
lgFIPR9 and pFIPR9 are modified versions of league and player FIP, respectively. Unlike standard FIP, these values treat infield fly balls as strikeouts, are scaled with respect to RA9 instead of ERA, and are park adjusted. As of 2019, catcher framing is also considered for seasons with framing data. The difference between league and player FIP gives the pitcher's runs above average per 9 innings (RAAP9). dRPW (dynamic runs per win) converts RAAP9 to wins per game above average. The exact value of dRPW varies between players since pitchers directly influence their run environment.