(Updated) Know Your Stats: Win Probability Added (WPA)

Every play in every game has some effect on the odds of winning a baseball game. Whether you are down by ten runs in the second inning or tied up in the bottom of the ninth, every action can be measured.

Baseball has been played for over a century and a half. Major League Baseball has been around for over a century, and most situations have been played out over and over again hundreds of times, so we have a good idea of how every action affects a team’s chances. This is called Win Expectancy. We can use those thousands upon thousands of games from history, and look at a team in a particular situation and know their odds. We know that if a team is down by one run in the bottom of the seventh inning with runners on second and third with no outs, they will win approximately 66% of the time, because roughly 66% of teams in the past have won in those cases.

To utilize these win expectancies in analyzing how each action affects the odds, we simply take the difference between the old and new win expectancy and award it to the player who accomplished the action, and penalize the pitcher who allowed it. It’s simple and easy.

There are some issues with WPA, however. While it finally solves the problem of context-neutral stats like Batting Average, On-Base Percentage, and Weighted On Base Average, it’s only good at telling a story, not predicting the future. Many of the new sabermetric statistics are predictive, but this one is certainly not. It also brings up an issue that comes up frequently when talking about RBI and Runs Scored. A player can only change the course of a game so much with his bat if he isn’t put in the right spot at the right time by his teammates. Someone might not get the opportunity to hit a walk-off home run just by chance, therefore losing out on the opportunity to pad their WPA numbers.

One thing WPA definitely solves is this: No more arguing about the turning point of the game. Instead of looking at a play as a “clutch RBI hit,” you can now define how much that run-scoring double in the eighth inning meant to the overall outcome. Take game 4 of the 2004 ALCS for example. That was the year the Red Sox were down 3-0 in the series, and won a hard-fought 12-inning game to stay alive. Here is how the win expectancy shifted throughout the night:

wpa chart 1

This is a very handy chart from Fangraphs that shows the leverage (how important a moment in the game was going to be) and how the action that took place affected the odds of one team wining. As you can see, the game starts with each team at 50 percent and ends with one team at 100 percent, with fluctuations in between. The most important moment of the game was David Ortiz‘s walk-off home run, bringing the odds of Boston winning from a shade above 73 percent to 100 percent, ending the game.

Overall, Win Probability Added is a great way to see how influential moments in a game were, but it does not tell the story of how good a player really is. In order to conduct a complete evaluation, we must use context neutral statistics like wOBA and wRAA, as well as stats like WPA.

In Context

wpa chart 2

In every game, a player, in theory could have a WPA of -1 to 1, or even more extreme than those numbers. In practice, it is usually close to zero, but a player’s actions could almost completely determine the outcome of a game in rare scenarios. For David Ortiz’s walk-off home run in the 2004 ALCS, he added about 25% (73% WE to 100% WE) on that play alone. For that, he was awarded roughly 0.25 WPA. In every game, the WPA of each player on the winning team will amount to 1 and the WPA of each player on the losing team will always amount to -1. Over the course of a season, a player can have a negative WPA or positive, with each integer representing a win. Last season, Mike Trout finished the year with a 5.32 WPA, meaning in terms of win probability, he was worth over five wins.

Further Reading

(Both charts courtesy of Fangraphs.)

About Connor O'Brien 337 Articles
Connor O'Brien is a fourth-year economics student at Rutgers University, a longtime writer here at MetsMerized Online, and an aspiring economist. He embraces sabermetrics but also highly values scouting. Follow him on Twitter at cojobrien.