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Advanced baseball stats: Explaining WAR and its variations

What does WAR really measure and how is it calculated?

Atlanta Braves v Colorado Rockies Photo by Doug Pensinger/Getty Images

Of all of the advanced metrics cited in modern day baseball conversations, perhaps none is referred to more frequently than Wins Above Replacement (WAR). This makes sense: WAR aims to consolidate a player’s entire performance into one concise number, making comparisons across the league as simple as quoting a single statistic.

Though the output is a clean, shiny number, the work that goes into WAR is a complex maze. There are dozens of components that go into the formula, and there are multiple official leaderboards that calculate WAR differently. It can be difficult to have a valid argument without knowing the whole story, yet many fans and writers struggle to completely grasp the metric.

This post will give an overview of what WAR represents, how it is calculated at a high level, and what some of the different metrics floating across the internet mean. There will be more digging that we can do in the future, but it is most important to get an idea of the general concepts first.

What is WAR?

WAR is a single number that takes all of the factors of a player’s game (hitting, fielding, running, pitching, etc.) and combines them into a single number, typically falling between 0.0 and 6.0 for a single season, although the 2018 season saw the range stretch from -3.1 (Chris Davis) to 10.4 (Mookie Betts).

The word “replacement” represents a hypothetical player between Triple-A and MLB, someone who a team could more or less grab off the street. Therefore, if a player has a 5.0 WAR, he is worth about five wins above a replacement-level alternative, and is significantly more valuable than a player worth just 1.5 WAR.

WAR includes a positional component, making it possible to compare players at different positions because the degree of impact and difficulty is already built into the formula. It is designed to be neutral across eras and ballparks, meaning it can be used to fairly compare any players.

How is it calculated?

The formula for WAR is actually straightforward at its core. For position players, WAR sums “wins” earned from batting, base running, and fielding, and then factors in a few adjustments. For pitchers, WAR looks at Fielding Independent Pitching (FIP) or runs allowed and then adds adjustments. Wins are typically calculated in “runs” first; each component is scaled to correlate to how many runs a player adds to his team, and runs are then scaled to translate to wins.

The math behind each component is full of complex formulas, which makes WAR hard to calculate by hand. However, understanding what goes into the components is much more important than memorizing the formulas themselves, which is near impossible.

  • Batting wins are centered around Weighted on-base average (wOBA), which is an all-in metric for a hitter’s value
  • Base running wins use metrics such as Ultimate Base Running (UBR) and Weighted Stolen Base Runs (wSB), which value a player’s ability to advance extra bases and avoid being caught on the base paths
  • Fielding wins utilize either Ultimate Zone Rating (UZR) or Defensive Runs Saved (DRS) which are the two most prominent defensive metrics at this time
  • FIP is similar to ERA, but only accounts for strikes, walks, and home runs, outcomes that do not involve the defense

All of these factors become scaled and adjusted for a player’s home ball park, the averages across the years he played, and his position. Every single adjusting factor is meticulously calculated to ensure that the averages tie perfectly across players, positions, and years.

The calculation of WAR is complicated, but should not turn fans away. Instead, informed fans should be able to tell how factors within a player’s game will flow through the formula. For example, a great hitter who has lousy defensive metrics could see a lesser hitter end up with a higher WAR, even though more traditional stats may favor him.

What is the difference between bWAR and fWAR? oWAR and dWAR?

Because WAR is dependent on a host of components that are based on advanced metrics, different outlets calculate the stat slightly differently. The two leading sources are FanGraphs (fWAR) and Baseball Reference (bWAR), who often end up in the same general area for a player but do show some differences.

FanGraphs uses UZR for fielding wins and FIP for pitching wins, while Baseball Reference chooses DRS and actual runs allowed, and along with a couple other nuances form the delta between the two. Neither is “better” than the other, and it can be up to writers to choose their preference, so long as they are clear which stat they are using.

Baseball Reference has also introduced statistics called Offensive Wins Above Replacement (oWAR) and Defensive Wins Above Replacement (dWAR), although these metrics do not have the exact same purpose as bWAR. oWAR looks to calculate a player’s offensive contribution alone, completely removing his fielding. It does adjust for position, however, which can make a big impact. Meanwhile, dWAR compares a player’s defensive efforts to a league-average fielder, again adjusting for position.

Though oWAR and dWAR do isolate the two halves of bWAR, they cannot be summed to reach the overall figure. There are a lot of minor intangibles that are too particular to dive into here, but the basic roadblock is the positional adjustment. bWAR, oWAR, and dWAR all incorporate some sort of adjustment for position, making it possible to compare shortstops to first baseman. But because oWAR and dWAR both include an adjustment, summing them would double the magnitude of this factor as compared to bWAR.

This should not turn anyone away from utilizing oWAR or dWAR, but it is important to remember that the separate values are not the exact components of the total. To isolate a player’s contribution on one side of the ball, metrics like wOBA, UZR, and DRS can do the trick as well, although they are not scaled to WAR.

As stated at the onset, WAR has found its way into everyday baseball conversation, and for good reason. There are few better ways to making sweeping comparisons across large subsets of players, and it even can be used at a team level. The 2018 Tigers were 27th with 8.0 fWAR for position players and 24th with 8.8 fWAR for pitchers; those numbers should match the eye test pretty well.

Use WAR, but know what the number means. Understand that there are multiple components feeding into the formula, and recognize that there are a handful of adjustments used to account for situations like Coors Field or the Dead-Ball Era. No single statistic can ever tell the whole story by itself, but WAR can get pretty close. Knowing how to interpret it correctly can be a vital tool for any baseball fan.