Sporting Charts

Ultimate Guide to Wins Above Replacement - WAR

Although Value over Replacement Player (VoRP) presents a player's value in terms of how many runs he adds to his team total offensively, or prevents his opponent from scoring on the pitching mound, the statistic does not take defense into account and also does not show a player's true impact on his team's chances of winning. Fortunately, there is a statistic that does such a thing, and while it is similar to VoRP, Wins Above Replacement (WAR) explicitly shows how much of an impact a player had on his team's season, in all areas measured for both hitters and pitchers.

Calculating Wins Above Replacement - WAR

As detailed in the article regarding VoRP, the first step to determining WAR is to find the replacement-level averages-not the league averages-for each position. The formulas for both pitchers and hitters to determine replacement-level can be found in the article defining and detailing VoRP.

Like VoRP, the formulas for pitchers and hitters to find WAR are different to measure how each one impacts his team's success. For hitters, the WAR formula takes hitting, base-running, and fielding into account to determine WAR. For those on the mound, the formula depends primarily on the factors within a pitcher's control while on the mound. Above all though, the key to WAR is runs.

Hitter's Wins Above Replacement

For hitters, the three statistics used to determine WAR are wRAA (Weighted Runs Above Average), UBR (Ultimate Base-Running), and UZR (Ultimate Zone Rating).

wRAA is a number used to determine how many offensive runs a players contributes to his team's total over what is contributed at an average level, and then calculated over the replacement-level as well.

UBR gives positive and negative credit to base-runners based upon the plays they make on the basepaths. For instance, advancing from first to third on a single would be credited positively, while being thrown out trying to advance from third to home on a short fly ball would be credited negatively. 

Of the three formulas used to calculate WAR for offensive players, UZR is by far the most complicated to calculate. UZR quantifies how many extra runs a fielder either saved from scoring or gave up via their performance in the field. Briefly, the four stats used to determine UZR are Outfield Arm Runs (ARM), Double-Play Runs (DPR), Range Runs (RngR), and Error Runs (ErrR). ARM measues how many runs above average an outfielder saves by preventing runners from taking extra bases. DPR measures how many runs above average an infielder saves with the turning of double plays. Range Runs helps us to understand how many more or less balls in play a fielder gets to in order to make an out than the average fielder does, and Error Runs is used to show how many more errors a fielder commits than an average one, and how many runs those lead to. 

With wRAA, UBR, and UZR in place, the numbers are added together and adjusted toward each position since some positions require more defensive effort than others. Then, the average for the replacement-level figure is subtracting from the player's total to show how many more runs the player is worth over the replacement-level player. Because every 10 runs added is roughly equivalent to one extra win, the number of runs added is divided by 10 to determine the player's WAR.

Pitcher's Wins Above Replacement

On the pitching side, the formula is not nearly as complicated. For this position's WAR, one stat is used to help us calculate it, called Fielding Independent Pitching (FIP). FIP is a stat that measures the factors of pitching that a pitcher can totally control, and they are described as being Strikeouts (K), Walks Allowed (BB), batters hit by pitches (HBP), and Home Runs allowed (HR). The FIP is calculated via a formula that uses all four of these basic statistic to come up with a number that is then put on an ERA-type scale via a constant that is usually around 3.20. 

FIP = ((13*HR) + (3*(BB + HBP - IBB)) - (2*K)) / IP + constant

The FIP value is then compared to the replacement-level FIP to determine how far above the replacement-level a player is, and then divided by 10 to determine the WAR.

How To Evaluate Wins Above Replacement

In addition to formulas, a scale exists to give a rough estimate of a player's value as a result of his WAR.

  • 8+ - MVP Quality
  • 5+ - All-Star Quality
  • 2+ - Starter
  • 0-2 - Reserve
  • < 0 - Replacement-Level

As evidence of the importance of WAR, the league's top award-winners last season posted some of the league's highest totals in the category.

  • AL Cy Young and Most Valuable Player: Detroit P Justin Verlander, 8.2 WAR
  • NL Cy Young: Los Angeles P Clayton Kershaw, 6.8 WAR
  • NL MVP: Milwaukee OF Ryan Braun, 7.7 WAR


To note, like VoRP, these totals accumulate throughout the season.  See our VoRP Guide.


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