Replacement level is set at a .294 winning percentage in order to maintain continuity with BaseballReference's version of WAR (rWAR). Also, BaseballReference's year and league "level of competition" adjustments are also included.
The PythagenPat method is used when converting runs to wins and also uses .285 as the exponent in the formula.
The Offensive component uses Base Runs to estimate a player's value (in runs) above/below average. Individual player's Base Runs are calculated using the theoretical team method.
LgR/G (League's adjusted runs per game) = League's Runs/Game multiplied by Team's park adjustment
RAA = Player's Base Runs above average
G = Player's games played
TmR/G = LgR/G + RAA / G
exponent = (TmR/G + LgR/G)^.285
Offensive WAA = ((TmR/G^exponent / (TmR/G^exponent + LgR/G^exponent))  .5) * G
LgR/G (League's adjusted runs per game) = League's Runs/Game multiplied by Team's park adjustment
RAA = Player's Base Runs above average
RAR = Player's Base Runs above replacement
G = Player's games played
oWAA = Offensive Wins Above Average
TmR/G = LgR/G + (RAA  RAR) / G
exponent = (TmR/G + LgR/G)^.285
Offensive WAR = oWAA  ((TmR/G^exponent / (TmR/G^exponent + LgR/G^exponent))  .5) * G
oWAR = Offensive Wins Above Replacement
PA = Player's plate appearances
Offensive WAG = oWAR  (PA / 600) * 3
The Fielding component uses a multiyear average of Defensive Regression Analysis (DRA) to estimate a player's value (in runs saved) above/below average. DRA was created by Michael Humphreys and its method is described in the book Wizardry.
LgR/G (League's adjusted runs per game) = League's Runs/Game multiplied by Team's park adjustment
DRA = Player's runs saved above average (from all positions)
G = Player's games played
TmR/G = LgR/G + DRA / G
exponent = (TmR/G + LgR/G)^.285
Fielding WAA = ((TmR/G^exponent / (TmR/G^exponent + LgR/G^exponent))  .5) * G
In order ot maintain continuity, BaseballReference's positional adjustments are used. By default, positional adjustments are NOT INCLUDED in offensive and fielding WAR. This can be changed by using the customized metric option.
LgR/G (League's adjusted runs per game) = League's Runs/Game multiplied by Team's park adjustment
posR = Player's positional adjustment in runs (from all positions)
G = Player's games played
TmR/G = LgR/G + posR / G
exponent = (TmR/G + LgR/G)^.285
Positional Adjustment = ((TmR/G^exponent / (TmR/G^exponent + LgR/G^exponent))  .5) * G
There are 2 versions of Pitching WAR. The first is based on runs allowed à la BaseballReference. The second is based on FIP (Fielding Independent Pitching), à la FanGraphs. By default, the runs allowed version is included in gWAR, but this can be changed when using the customized metric option.
Both versions are calculated using the same formula. The only difference is the runs allowed above average (RAA) variable.
LgR/G (League's adjusted runs per game) = League's Runs/Game multiplied by Team's park adjustment
RAA = Player's runs allowed above average (with positive being better)
G = Player's games played
aLI = Player's average leverage index when entering the game
TmR/G = LgR/G + RAA / G
exponent = (TmR/G + LgR/G)^.285
Pitching WAA = (((TmR/G^exponent / (TmR/G^exponent + LgR/G^exponent))  .5) * G) * ((1 + aLI) / 2)
LgR/G (League's adjusted runs per game) = League's Runs/Game multiplied by Team's park adjustment
RAA = Player's runs allowed above average (with positive being better)
RAR = Player's runs allowed above replacement (with positive being better)
G = Player's games played
pWAA = Pitching Wins Above Average
TmR/G = LgR/G + (RAA  RAR) / G
exponent = (TmR/G + LgR/G)^.285
Pitching WAR = pWAA  ((TmR/G^exponent / (TmR/G^exponent + LgR/G^exponent))  .5) * G
pWAR = Pitching Wins Above Replacement
IP = Player's innings pitched
Pitching WAG = pWAR  (IP / 525) * 2.5
The rate of a statistic over the course of 162 games. This is based on the player's entire career. Position players and pitchers games played are treated differently.
Batting Seasons = Games appeared as a position player divided by 162. (G / 162)
Pitching Seasons = Games appeared as a pitcher plus Games Started, divided by 68. ((G + GS) / 68)
Seasons = Batting Seasons + Pitching Seasons
Total = Career Total in that statistic
per 162 = Total / Seasons
Developed by Jay Jaffe in 2004 at Baseball Prospectus. It is meant to gauge a player's Hall of Fame credentials by comparing them to Hall of Famers at the same position. JAWS is the average of a player's career total Wins Above Replacement and the total of their seven best seasons (peak).
Since not all positions are represented equally in the Hall of Fame, JAWS requires a minimum # of players at each position. Currently, the position with the most players in the Hall of Fame is RF, with 24. To meet the required minimum, the calculation includes the average position player's JAWS score for each player that it is short of the minimum (Starting and Relief Pitchers are not subject to this minimum requirement).
For example, there are currently 14 catchers in the Hall of Fame, which is 10 players short of the minimum. The JAWS calculation will find the average of the 14 catchers AND 10 average Hall of Fame position players to determine the average Hall of Fame catcher's JAWS score.

