Basic Sabermetrics: Win probability added

Christian Petersen

Continuing the Basic Sabermetrics series, we're looking at a statistic used to examine the story of a game: Win Probability Added.

For the second installment of our Basic Sabermetrics series, I'd like to talk a little about the statistic called Win Probability Added, or WPA. Learning a little more about WPA -- to me -- allows us to understand a little more about a core sabermetrics concept: win expectancy. Plus, WPA is fun!

As always, you can pick up on all of our Basic Sabermetrics articles through our All About Sabermetrics page. And if you have questions, comments, anything -- leave them in the comments below.

What is WPA?

Before we talk about WPA, we have to talk --briefly -- about win expectancy. At any given point during any baseball game, we're able to identify a team's win expectancy. Historical data exists that tells us what the odds are of either team winning a particular game given the game state: what's the score, how many outs are there, how many runners are on base and where, who's the home team, etc.

If the home team is batting in the bottom of the seventh inning, down by one run, and with runners on first and second with one out -- then historically, 44% of the time, the home team has won. Therefore, the team's win expectancy is 44%. Win expectancy changes with every play, as the game state changes.

Win Probability Added, or WPA, tells us how a particular player affects a team's win expectancy with his play. WPA is a measure of how much his actions changed the likelihood of his team winning that particular game. For pitchers and for hitters, it changes with each play during the game. And you can add it up for a whole game, or a whole season.

WPA does not specifically take into account baserunning -- unless you account for how it affects a player's ability to stretch one base into two, or three -- and defense.

A WPA of 1.00 is equal to one "win" credited to the player. A WPA of -1.00 is equal to one "loss" credited to them.

How to Calculate WPA

The actual WPA calculation is pretty simple. For a hitter, take the team's win expectancy before a plate appearance, and then subtract it from the team's win expectancy after a plate appearance.

Let's look at an example. Take the first plate appearance by the Mariners' Raul Ibanez back on 07/12/13 of this season. Ibanez came to the plate in the bottom of the first inning with the scored tied at zero, a runner on first base and one out. Prior to the plate appearance, the Mariners' win expectancy was 55%, based on historical data. Ibanez hit a double, driving in the runner aboard, but making an out in the process. The new game state was a 1-0 Mariners lead, two outs, and nobody on, so the new win expectancy was 62%. That shift of 7% is credited to Ibanez as 0.07 WPA.

The pitcher in this instance, Jerome Williams, is also "credited" with the shift in WPA -- only he moved his team's win expectancy backwards, making his team less likely to win. As a result, he's credited with -0.07 WPA for that particular event. But don't worry -- he's got the next hitter (or hitters) to try and bring his WPA back up and bring his team closer to victory.

At the end of the game, you could add up all of Ibanez's plate appearances and get a total WPA for Raul's entire game. Since he homered (+0.075 WPA) to help the team's chances, struck out (-0.001 WPA), and homered again when the game was out of reach (+0.004 WPA) -- he gets a total WPA of 0.148 on the day. Not bad, but had those homers occurred when the game was more hotly contested, you could bet that this number would be a lot higher.

Keep in mind that WPA is a counting statistic, so these numbers add up over a game, over a season, and over a career.

Where to Find WPA

The best place to find WPA is on FanGraphs' player pages. Each player has their seasonal WPA under the "Win Probability" tab. You can also sort their leaderboards* by WPA. You can also find game WPA marks for every player in a game at FanGraphs' game pages ... like this one.

* - For reference, in 2013, Paul Goldschmidt led all qualified position players with a WPA of 7.86. The worst positional WPA belonged to Adeiny Hechavarria of the Marlins, with -3.34. Among qualified starting pitchers, Clayton Kershaw led the way with 4.69 WPA, while Edwin Jackson was the worst with -3.80 WPA.

WPA is also housed at Baseball-Reference, and you could examine a the historical WPA leaderboard (for hitters over a career) here.

You may actually not see WPA referenced in a lot of analysis articles these days, but you will occasionally see it mentioned in a game recap. Our short-lived daily game breakdowns, here at the site, used it frequently in that regard.

Using WPA in Analysis

I've mentioned prior that WPA isn't something that tells us much --if anything -- about how a player will perform in the future.* The game's context matters greatly, and this is a statistic has little to no predictive value when it comes to future performance on it's own.

* - Though WPA isn't highly predictive of future performance, this article at FanGraphs explains that WPA actually does correlate -- a little -- from year-to-year.

What WPA is good for, is telling the story of a game. When breaking down what player added the most value to his team, given the game's circumstances. And while WPA doesn't necessarily tell us anything about how well a player might play in the "clutch" -- especially in the future -- it does tell us which player did the most to shift the odds in his team's favor during that given day, or year, or career -- depending on what kind of sample you use.

Using WPA, you can go back and find which plays were the biggest, or the most exciting. You can determine which hits did the most damage to a team's chances of winning, or which reliever really murdered his team's chances for a win.

WPA doesn't actually tell us which player played "the best." If Josh Hamilton goes 4-for-4 with four home runs in a blowout, his work may not shift the win expectancy very much despite his being awesome. But if David Ortiz hits a walk-off grand slam in the ninth inning, with his team down three runs, expect him to earn a *huge* WPA boost -- almost a full "win" of nearly 1.00 WPA.

Another cool thing about WPA is how it can tell us a lot about relief pitchers -- especially when used to derive shutdowns and meltdowns. Since context is critical for evaluating a relief pitcher's performance, WPA can be used as a shorthand measurement to find out how well relievers performed during those critical moments -- even if this statistic may not be particularly predictive in the future. It does tell us how they performed in the past.

As I mentioned above, like strikeouts or home runs or wins above replacement, WPA is a counting statistic. Players who play the most games, or pitch the most innings, have the opportunity to rack up more WPA than their low-playing-time counterparts. You also need a lot of playing time, and/or a lot of bad performance, to rack up large negative numbers

Associated Statistics

WE: Win expectancy (WE) is the likelihood that a particular team will win a game, based on historical data. WE is measured in percentages ... a team has a certain percentage chance to win a given game.

WPA/LI: Context-neutral wins (WPA/LI), invented by Tom Tango, is a measure of of how much value a player provided to his team, with the leverage of the situation factored out. Think of it as similar to a win expectancy-based version of wins above average.

SD and MD: Invented at The Book Blog, Shutdowns (SD) and Meltdowns (MD) use WPA as the underpinnings of a statistic to measure reliever performance. Scaled to saves, shutdowns are instances when a reliever improves his team's chances of winning by 6% or more, while meltdowns are instances when a reliever decreases his team's chances of winning by 6% or more.

For More Information

WPA - The FanGraphs Library

WPA - The Book Wiki

. . .

All statistics courtesy of FanGraphs.

Bryan Grosnick is the Managing Editor of Beyond the Box Score. You can follow him on Twitter at @bgrosnick.

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