WPA by Steve Slowinski February 16, 2010 Win Probability Added (WPA) captures the change in Win Expectancy from one plate appearance to the next and credits or debits the player based on how much their action increased their team’s odds of winning. Most sabermetric statistics are context neutral — they do not consider the situation of a particular event or how some plays are more crucial to a win than others. While wOBA rates all home runs as equal, we know intuitively that a home run in the third inning of a blowout is less important to that win than a home run in the bottom of the ninth inning of a close game. WPA captures this difference. 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. The pitcher receivers a -0.30. 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 cumulative statistic and is additive. Calculation: WPA is rather straightforward to calculate as long as you have access to the Win Expectancy chart or graph for the game. During each plate appearance, the inning, score, or base-out state changes from the beginning to the end, which leads to a change in Win Expectancy. That change is assigned to both the pitcher and batter (inversely). The sum of a player’s individual WPA generates their WPA for the season. If a batter flies out on the first pitch of the game, the home team’s WE goes up from 50% to about 52%. This means that the pitcher who induced the out gets a WPA of +0.02 and the batter gets a WPA of -0.02. The credits are always symmetrical, meaning that anything that the hitter gains, the pitcher loses, and vice versa. At the end of every game, the winning team’s players will have a total WPA of +0.5 and the losing team’s players will have a total WPA of -0.5. Although it is important to remember that pitchers are held entirely accountable for everything that happens on defense and position players’ scores are unaffected by anything they do while in the field. Average is set to zero, so a season long WPA of 2.0 is two wins better than average, not replacement level. Why Win Probability Added: WPA is the ultimate context dependent statistic. You get credit based on how much your action contributes to the odds of winning, meaning a home run in a 1-1 game in the 9th is dramatically more valuable than one in a 10-1 game in the 9th. For this reason, WPA is terrific at telling the story of the game and the players who delivered in big situations. When did the winning team pull away? Who had the decisive hit? These are questions WPA can answer. It doesn’t tell you how well a player performed, it tells you how important their performance was. How to Use Win Probability Added: WPA is tricky because there’s an innate desire to use it as a measure of “which player has delivered when it matters most!” In reality, it’s far more complicated than that because it’s an additive measure. To accrue big WPA totals, you need to be presented with many opportunities to come through with the game on the line. A player with a 5.0 WPA for the year hasn’t necessarily been more “clutch” than one with a 2.0 WPA, they may simply have had many chances with the bases loaded late in close games. Also, WPA is not a predictive statistic and there is little evidence that there is anything like a WPA-skill. Players who have higher WPAs in one year don’t necessarily repeat that performance in the following year, other than to say good players typically have higher WPAs than worse players. You can view WPA for hitters and pitchers. You’ll notice three columns on the site — WPA, -WPA, and +WPA. The first is the total WPA for the year (or time period), “-WPA” is the sum of all of the negative events, and “+WPA” is the sum of all of the positive events. There’s also single game WPA numbers and play-by-play WPA numbers in the box scores, game logs, and play logs throughout the site. Context: Technically, WPA values for events that contribute positively to a win can range from about 1% (.01 WPA) to 95% (.95 WPA). The extreme swings in WPA are not terribly common, just as walk-off home runs are exciting events we don’t see every day. Cumulatively, season-long WPA is not predictive, making it an ineffective number for projections of a player’s talent. However, it is a good describer of what happened in the game and how a win was achieved. And since +1 WPA equals 100% in win expectancy, +1 WPA is the equivalent of one win above average. For MLB regulars, here’s a quick breakdown on season-long WPA scores: Rating WPA Excellent +6.0 Great +3.0 Above Average +2.0 Average +1.0 Below Average 0.0 Poor -1.0 Awful -3.0 Things to Remember: ● WPA is not highly predictive. Generally, it is not used for player analysis and projecting the future. But it does give us a picture of which players helped their team the most during the course of a game. A fun way to think of WPA is as a storytelling statistic. It highlights the big (and most exciting) moments of a game as well as the players who contributed most to a win (or loss). ● WPA is a cumulative statistic, meaning that players with more playing time will have more opportunities to accrue a higher WPA, but they can also lose WPA if they perform poorly. ● Pitchers receive all of the positive or negative credit on a defensive play. Position players only gain or lose WPA on offense. ● Zero is average, not replacement level. Links for Further Reading: Intro to WPA – Big League Stew Get to Know: WPA – FanGraphs The One About Win Probability – Hardball Times WPA is… WPA is not… – The Book Blog Is WPA Predictive for Batters? – FanGraphs Calculate Your Own WPAs 10 Lessons I Have Learned About WPA – Hardball Times