SoSH Glossary: Win Expectancy and Win Probability Added

Baseball is filled with statistics, rules, and archaic terms that can often form what sounds like a foreign language.The Sons of Sam Horn glossary provides a better understanding of these terms through straightforward definitions, clear explanations, and examples pulled straight from the baseball world. If there is anything you would like us to add to our glossary, please contact us.

Win Expectancy and Win Probability Added

Win Expectancy, or WE, is the probability that a team will win a game based on the current inning, score, and base/out situation, while assuming that both teams are average and all events going forward will be average. Each game begins with the win expectancy at 50%. The WE at any given moment is taken from the actual performance of MLB teams from the past in those exact situations. If a team has a WE of 43%, then 43% of MLB teams that have found themselves in that situation have won. The probability for extra innings is treated the same as the ninth inning since the conditions are the same for the home team (if they take the lead they win). The maximum run differential in either direction is 11 – after that the chances remain the same.

Enter WPA

Win Probability Added, or WPA, is the change in win expectancy from one plate appearance to another. WPA awards the pitcher and an offensive player a positive or negative quantity based on their impact on win expectancy from the result of a given play.

How is WPA Calculated?

The calculation for win probability added is simple as long as you have the proper win expectancy chart or graph for the game in question (they can be found at Fangraphs or Baseball-Reference). You then need to take the WE at the end of the play and find the change from the beginning of the play. The player whose team benefitted from the change earns WPA equivalent to the percent change in WE, so that a 2% improvement would give a player .02 increase in his WPA. Each play will net out to 0 WPA, resulting in a league-average WPA of 0.0.  

During baserunning plays – such as a stolen base, passed ball, wild pitch, balk, etc. – the baserunner, or lead baserunner, earns all WPA for the offensive team while the pitcher still earns all WPA for the defense. If a batter strikes out and there is a stolen base attempt on the same play, the batter is docked whatever change the strikeout caused, and then the result of the SB attempt is given to the baserunner. The pitcher in that scenario is awarded/docked the net of the play.

What else is WPA good for?

For the graphs, of course! Baseball-Reference and Fangraphs each have their own unique take on the win probability charts and they are presented below. Baseball-Reference publishes theirs after the games are over, while Fangraphs allows you to follow along live.
BRef-10-30-13

Source: FanGraphs

Parting Words of Wisdom

It is important to remember that Win Probability Added is a context-driven statistic that awards players for performing at the correct moment. It is not a proper way to evaluate talent, rather a method to evaluate the narrative of a game and season.

One thing that WPA does is treat outs as if they were units of time – since they basically are in baseball. As time runs out, each event carries more narrative weight and the swings in win expectancy can become more drastic.

Additionally, WPA distills all of the statistics of a given play down into one number: the change in the likelihood that a team will win. Just remember – that likelihood is based on assumptions that all things are average – WPA doesn’t know if Mike Trout or Mookie Betts is lurking in one of the dugouts with a bat on his shoulder.

As Tom Tango explained, win probability captures “the quantification of your feelings as the game unfolds, assigned to the players involved.”


Follow Pete on Twitter @PeterWHodges.

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