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Advanced Stats Primer: Win Probability and WAR


As of this week, the official start of Spring Training is only two weeks away. Since we're getting close to the start of Baseball: 2013 Edition, I thought I would give a basic introduction to some of the advanced stats you'll be seeing on this site and around the internet during the season. There's a lot of information to cover, so I've broken it into three parts: two weeks ago we covered offensive stats, last week we covered pitching and defensive stats, and this week we'll be talking about win probability and WAR.

Win Expectancy

Win Expectancy (WE) quantifies a team's chances of winning a given game, based on the score, the inning, the number of outs, whether or not any runners are on base, and the "run environment."

WE is calculated using historical data from past games. This chart lays out the different scenarios from the seventh inning on, and shows what the home team's win expectancy would be for each one.

There's a good chance you'll see Fangraphs' Win Expectancy charts in articles and in the comments section here on BBB. In big comebacks (or meltdowns) they can be fun (or depressing) to look at. This one is from the Blue Jays' crazy meltdown against the Mariners in 2011, and this one is from the 19 inning game between the Pirates and Braves the same year.


Win Probability Added (WPA) measures how much a player has done to effect his team's Win Expectancy, whether he has a positive impact or negative impact on it.

Taken from the Fangraphs' Sabermetrics Library entry on WPA, here is how it's calculated:

"For example, say the Rays have a 45% chance of winning before Ben Zobrist comes to the plate. During his at-bat, Zobrist hits a home run, pushing the Rays' win expectancy jumps to 75%. That difference in win expectancy (in decimal form, +.30) from the beginning of the play to the end is Ben Zobrist's WPA for that play. If Zobrist strikes out during his next at bat and lowers his team's win expectancy by 5%, his overall WPA for the game so far would be +.30 - .05 = +.25, as WPA is a counting statistic and is additive."

You'll see WPA used on Bluebird Banter every day in the "Jays of the Day!" section of the game recap. Any player with a +.100 WPA or higher gets the "award," while any player with -.100 or lower gets the Suckage Award. But do note that WPA is not a fair way to evaluate players since they don't control the situations where they get to contribute. For example, a first inning homer in a 0-0 game gives a small WPA, but that exact same home run in the 9th will have a large WPA.


WAR (Wins Above Replacement) attempts to quantify how valuable a player has been to his team in one statistic. It's measured in wins, as the name states, and it looks to tell us how much more value a given player is worth than the one we would be calling up from AAA (a replacement player) if that given player got hurt.

WAR for batters and WAR for pitchers is calculated differently, obviously. I won't go into great detail about the differences here (if you're interested in the details, take a look at the links at the bottom of this page) but the basics are as follows:

WAR for batters is calculated by adding wRAA (offense), UBR (baserunning), and UZR (defense) together, adjusting for position (because some positions are harder than others), and converting the numbers to be based on replacement level rather than league average. 10 runs = 1 WAR. WAR for pitchers is calculated using FIP.

Lastly, there are two main versions of WAR: Fangraphs WAR (fWAR) and Baseball-Reference WAR (rWAR or bWAR or brWAR). The main differences are that 1) Baseball-Reference does not use FIP to calculate pitching WAR but instead uses adjusted runs allowed, 2) rWAR uses Total Zone as opposed to UZR for defense, and 3) rWAR uses a slightly different baserunning stat.

And there you have it! You now have a basic, foundational knowledge of the most common advanced statistics. There's a lot more information about sabermetric statistics than what I've presented you with this month, and if you're interested in finding out more I suggest you check out the Fangraphs' Sabermetrics Library. The Fangraphs blog is also a great source of information, as is SB Nation's own Beyond the Boxscore. Happy stat hunting!