Win Probability Added

Win Probability Added (WPA) is the difference in Win Probability (or Win Expectancy) between two game states (inning, score, base, out) as a result of a specific play. An average team, at any point in a game, has a certain likelihood of winning the game. For instance, if you're leading by two runs in the ninth inning, your chances of winning the game are much greater than if you're leading by three runs in the first inning. With each change in the score, inning, number of outs, base situation or even pitch, there is a change in the average team's probability of winning the game.

The concept of WPA has been around for a long time, and primary credit probably belongs to the Mills Brothers, who published a book called Player Win Averages in 1970 that essentially presented the concept and stats for all players in the 1969 season. In 2007, Jeff Sagarin duplicated the Mills' Brothers technique and produced Player Win Averages for all seasons from 1957 through 2006.

It has cropped again many times since 1970 and has gone by many names: "Player Win Averages" (Mills brothers), "Player Game Percentage" (Bennett), "Win Probability Added" (Drinen), "Win Advancement" (Tango Tiger), "WXL" (Baseball Prospectus), "Game State Wins"(Rhoids website), "Player's Win Value"(Ed Oswalt) and "WRAP" (Lonergan and Polak).

The concept is relatively straightforward. For every base/out situation, there is an expected number of times the team will score a specific number of runs. For instance, with a runner on second and one out, the average team in a run environment of 4.5 runs a game can be expected to score zero runs 60% of the time, 1 run 24% of the time, 2 runs 9% of the time, etc. etc. The math for calculating these probabilities was nicely summarized by Keith Woolner in Baseball Prospectus 2005.

Therefore, with a runner on second, one out and the score tied in the bottom of the ninth, the probability of the home team winning is 70%. You can see this by assuming that the home team and away team both have a 50% chance of winning if the score remains tied. The WPA framework essentially takes this logic and applies it backward to all possible base/out situations during a game.

There are many uses for WPA, such as tracking the progress of a game as it progresses, assessing the criticality of a situation to guide strategy and assigning credits and debits to individual players for a team's wins and losses.

Pros and Cons of WPA

WPA is a real-time assessment of a team's chances of winning a game. As such, it is a fantastic statistic for those aspects of the game that require real-time insight, such as when to bring in a reliever. WPA game graphs can also serve as a good gauge of the fans' heartbeat during a game. A WPA graph, combined with a boxscore, can be powerful tools for telling the game story.

When it comes to assessing the contributions of individual players, WPA has its strengths and weaknesses. Its greatest strength is that it is the cleanest way to attribute team wins and losses to individual players. The logic is sound, and it doesn't have any of the pitfalls of other systems that estimate each player's win contributions, such as Win Shares.

On the other hand, WPA is dependent on the game situation, so that a home run in a close game is worth more than a home run in a runaway. What's more, a home run late in a close game is worth more than a home run early in a close game. Depending on your viewpoint, you may find this aspect of WPA useful or detrimental.

Other External Links

Information for this article was summarized this articlefrom this article, by the original author.

WPA game progress graphs and individual WPA totals are available at Fangraphs.

You can download an Excel spreadsheet containing all the logic and a user interface for calculating WPA for specific situations.