FanGraphs WAR = fWAR
Baseball-Reference WAR = rWAR (or bWAR)
Baseball Prospectus WAR = WARP
Position Players:
Each site uses a different hitting, running, and fielding metrics. FanGraphs uses wOBA as it’s baseline hitting stat, but the other two sites use metrics built on a similar linear weights framework. For base running, each site has it’s own version of base running runs, which we abbreviate to BsR. For fielding since 2002, we use Ultimate Zone Rating, while B-Ref uses Defensive Runs Saved and BPro uses Fielding Runs Above Average. Prior to that, we use Total Zone, which appears to be B-Ref’s choice as well. Baseball Prospectus is the only site that has incorporated catcher framing into their calculations.
FanGraphs and Baseball-Reference use the same replacement level calculation of 1,000 WAR per MLB season. Baseball Prospectus’ appears to be slightly different.
Pitchers:
While WAR for position players is different among the three sites, it is nothing compared to the differences for pitchers. Generally speaking, the three sites take a run prevention estimate (more on this shortly) and scale it to how much the pitcher has pitched that season. The big difference is that each site use a much different run prevention estimate. Each site adjusts for league and park, so I’ll exclude that from the comparison for clarity.
FanGraphs uses Fielding Independent Pitching (FIP) as our baseline. However, given that infield fly balls are very similar to strikeouts in terms of being automatic outs, we treat them as strikeouts in our WAR calculation even though they aren’t include in the general FIP calculation. In addition, we include a leverage component when calculating our reliever WAR. I don’t know if/how the other sites use leverage for relievers.
Baseball-Reference uses a pitcher’s runs allowed and then adjusts that value based on the overall quality of their defense that year.
Baseball Prospectus uses their custom Deserved Runs Average (DRA) metric as a baseline. DRA is a significantly more complicated model that attempts to control for factors like catcher framing, defense, etc within the run estimator itself.
https://www.fangraphs.com/library/war/differences-fwar-rwar/