Win expectancy is an estimation of the probability that a given team wins the game. It is variable, and shifts after each play. Using data from every baseball game in Major League Baseball history, a win probability can be calculated for any combination of inning, score, number of players on base, and outs. Win probability added (WPA) is the change in the win expectancy at the end of a given play. Since win expectancy is simply the given probability of a team winning given the in-game situation, we can take the win expectancy from a given in-game situation and subtract it from the previous win expectancy to see the WPA of a given play. Confused? Let's consider an example. It's the top of the 4th inning in a game between the New York Mets and the Cincinnati Reds. The Mets are winning 2-0, and are batting with 2 outs and nobody on base. The Mets' win expectancy is 69% or .69. Francisco Lindor hits a homerun to extend the Mets lead to 3-0 and increases the Mets win expectancy to .78. Therefore, Lindor's WPA associated with the homerun is 0.09.
There are numerous flaws with both win expectancy and WPA. Firstly, it doesn't account for the specific players playing in a given game. Win expectancies are simply probabilities associated with every possible in-game situation based on historical data. Secondly, WPA only assigns credit and blame to the batter and pitcher. Fielders or baserunner who obviously play a substantial role in the ultimate outcome of a given play are not considered by WPA.
Art Shamsky
On August 12th, 1966, the 58-55 Cincinnati Reds hosted 67-56 Pittsburgh Pirates. Art Shamsky, a 24-year old outfielder in just his 2nd Major League season, started the game on the bench. In a game consisting of 5 future Hall of Famers and the MLB all-time hits leaders, Shamsky appeared to be at best a marginal figure in the game. The game was a back-and-forth affair, with both teams exchanging leads on 5 occasions in the first 7 innings. As the Reds prepared to bat in the bottom of the eighth, the Pirates held an 8-7 lead.
Leo Cárdenas led off the inning for the Reds with a single, but Jimmie Coker followed with a bunt to the pitcher who got the out at 2nd base. With the Reds pitcher Joe Nuxley due up to hit, the Reds' interim manager Dave Bristol called upon Art Shamsky to hit. Going into the game, Shamsky had struggled to hit for average, batting just .224 on the season. Despite his low batting average, Shamsky had demonstrated significant power throughout the season. In limited playing time, Shamsky had hit 12 homeruns and had a slugging percentage of .497. Shamsky demonstrated his power by hitting a homerun over the centerfield fence to give the Reds an 8-7 lead. Prior to Shamsky's at bat, the Reds' win expectancy sat at .31. After Shamsky's homerun, the Reds' win expectancy rose all the way to .85, giving Shamsky a WPA of .54.
Despite Shamsky's heroics, the Reds failed to put away the Pirates. With one out in the top of the 9th inning, Jerry Lynch hit a homerun off of Reds' closer Don Nottebart to tie the game 8-8. After the Reds failed to score in the 9th, the game went to extra-innings.
Following a Willie Stargell homerun in the top of the 10th inning, the Reds came to bat trailing 9-8. With one out and nobody on base, Art Shamsky stepped up to the plate for the second time in the game. Prior to the at bat, the Reds' win expectancy sat at .11. Shamsky, just as he had done prior, homered, this time to right field, to tie the game 9-9. Shamsky's second homerun in as many at bats propelled the Reds' win expectancy to .58, giving him an additional .47 WPA.
Shamsky improbable evening wasn't done, as he came to bat yet again in the bottom of the 11th with a runner on first base and two outs trailing 9-11. With the Reds' win expectancy sitting at just 0.05, Shamsky homered to right field, tying the game and increasing the Cincinnati's win expectancy to 0.54. Despite Shamsky's efforts, the Pirates would score three times in the 13th inning and hold on to beat the Reds 14-11.
In just three at bats, Shamsky, who didn't appear in the game until the 8th inning, had accumulated a WPA of 1.53. Looking at the top five plays of the game by WPA, Shamsky's three homeruns accounted for the top three.
It wasn't simply that Art Shamsky had a clutch game, he had the most clutch game by WPA in MLB history. All three of his at bats resulted in homers that either tied or took the lead in the 8th inning or later. Average Leverage Index (aLI) attempts to calculate the pressure a pitcher or a batter faced in a given game. Shamsky's aLI of 2.51 was the highest of any player on either team with at least 2 plate appearances. On average, Shamsky was under the most pressure of any batter in the game and was still able to homer in every at bat.
What makes Shamsky's performance even more remarkable is that the Reds lost the game. Looking at the top 10 WPA games by hitters in MLB history, all of the other hitters' performances resulted in their team winning the game. Shamsky was the only player whose team ultimately lost the game.
Shamsky homered in first at bat during the Reds' next game, making it four consecutive at bats with a homerun. He'd finish the season with 21 homeruns in just 271 at bats (12.9AB/HR), in what would be the best power season of his career. Shamsky would play six more relatively uneventful seasons, winning a World Series with the Mets in 1969 before retiring in 1972 at the age of 30. For his career, Shamsky had a WPA of 1.00, 0.53 less than he accumulated in just those three at bats on August 12, 1966.