pWins vs. WPA
Baseball Player Won-Loss Records
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pWins vs. Win Probability Advancements (WPA)

The central building block in calculating my Player won-lost records (pWins, pLosses) is the concept of Win Probability.

Win Probabilities are probably best known through a statistic called WPA (Win Probability Advancements). Player won-lost records, pWins and pLosses, are built from the same building blocks as Win Probability Advancements. In effect, the base for pWins is what Baseball-Reference (and others) calls WPA+, "positive Win Probability Added", and the base for pLosses is WPA-, "negative Win Probability Added". I do not end there, however, so that pWins are not simply equal to either WPA or WPA+ (nor are pLosses equal to WPA-).

As I explain in the basic article describing how I calculate pWins and pLosses, I normalize Win Probability Advancements (what I call "Player Game Points") by Game. The total number of Player Game Points accumulated in an average Major League Baseball game is around 3.3 per team. This number varies tremendously game-to-game, however, with some teams earning 2 wins in some team victories while some other teams may earn 6 wins in team losses. At the end of the day (or season), however, all wins are equal. Hence, in my work, I have chosen to assign each team one Player Win and one Player Loss for each team game. In addition, the winning team earns a second full Win, while the losing team earns a second full Loss. Ties are allocated as 1.5 Wins and 1.5 Losses for both teams. Context-neutral player decisions (eWins/eLosses) are also normalized to average three Player decisions per game. For eWins and eLosses, this normalization is done at the season level, rather than the game level, so that different numbers of context-neutral player decisions will be earned in different games.

pWins vs. WPA, Example 1: How Many Wins can One Player Get in One Game?

Win Probability Advancements are structured such that net Win Probability Advancements (WPA+ minus WPA-) sum to exactly 0.5 for every team win and exactly -0.5 for every team loss. Hence, team wins are equal to exactly two times WPA. In Game 6 of the 2011 World Series, David Freese and Lance Berkman accumulated a combined WPA of 1.8 (according to Baseball-Reference). In other words, Freese and Berkman combined to "win" 3.6 games that night - and their teammates (mostly the Cardinals' bullpen) combined to "lose" 2.6 games. But, of course, when Game 6 of the World Series was over, the Cardinals had only won 1 game, not 3.6, and they had certainly not lost 2.6 games.

Normalizing the Win Probability Advancements of the St. Louis Cardinals in that game, the players on the Cardinals earned a combined 2 pWins and a combined 1 pLoss by construction. And how many net pWins did Freese and Berkman combine for? It turns out that David Freese and Lance Berkman earned a combined 0.81 net pWins.

Sure, they were more responsible for that win than any of their teammates, but at the end of the day, it was still just one win - a very important, very dramatic win, but just one win.

pWins vs. WPA, Example 2: Solo Home Runs in 1-0 Games

Consider, for example, two games during the 2002 season which the Los Angeles Doders won at Dodger Stadium by a score of 1-0 with the only run of the game scoring on a solo home run.

A comparison of these two games gives a nice example of how my Player wins differ from a straight application of Win Probability Advancements.

On August 28, 2002, starting pitcher Odalis Perez hit a solo home run with two outs in the bottom of the fifth inning off of Arizonaís Rick Helling for the only run in a 1-0 Dodgers win.

On September 27, 2002, Paul LoDuca led off the bottom of the tenth inning with a home run off of San Diegoís Jeremy Fikac to break a scoreless tie and give the Dodgers a walkoff 1-0 victory.
From a context-neutral perspective, Perezís and LoDucaís home runs were exactly equal in value: 0.1448 wins, since both home runs took place in the same run-scoring environment Ė Dodger Stadium in 2002. From a prospective perspective, on the other hand, LoDucaís home run, which ended the game, was more than twice as valuable, 0.4089 wins, as Perezís home run, at 0.1814 wins. These values correspond to a WPA valuation system: Baseball-Reference.com, for example, reports the WPA of these home runs as being 37% for LoDuca and 17% for Perez.

In retrospect, Perezís home run was more valuable than it seemed at the time, however, as it turned out to be the difference in the game. The normalization process which I employ reflects this by boosting the final value of this home run, relative to its prospective (WPA) values, to a final value of 0.2724 wins. On the other hand, LoDucaís home run is reduced in value retrospectively to 0.3620 wins since the high context at the time of LoDuca's home run was created in large part by the events which came before (most notably the fine pitching of LoDuca's teammates Omar Daal and Eric Gagne). The final result is that LoDucaís home run is still more valuable than Perezís, because it was a game-ending home run, while the Diamondbacks still had four more innings to come back from Perezís home run. But LoDucaís home run is not twice as valuable as Perezís but instead is less than one-third more valuable.

This is all summarized in the table below.

Player Wins
Prospective Contexts
Date Batter Situation eWins Inter-Game WPA (BB-Ref) pWins Inter-Game Intra-Game Combined
8/28/2002 Odalis Perez Two out, bottom of 5th inning 0.1448 0.1814 0.17 0.2724 1.2527 1.5015 1.8810
9/27/2002 Paul LoDuca Leading off bottom of 10th 0.1448 0.4089 0.37 0.3620 2.8233 0.8853 2.4995


I think that these results are a reasonable reflection of the relative value of these two home runs.

pWins vs. WPA, Example 3: Value of Breaking a Game Open Early vs. Coming up Clutch Late

In a separate article, I compare the 2005 seasons of David Ortiz and Alex Rodriguez when they finished 1-2 in voting for the AL MVP award.

David Ortiz's MVP candidacy that year rested in large part on his having been particularly clutch. For example, Big Papi led the American League in Win Probability Added (WPA) that season. WPA tracks what I call inter-game win adjustments. But I also adjust for what I call intra-game adjustments, which normalize the total number of pWins (and pLosses) to be constant across all team wins and losses.

While David Ortiz beat Alex Rodriguez (and everybody else) in inter-game win adjustments, Rodriguez beat Ortiz in intra-game adjustments. A comparison of two of their games is instructive in this regard.

On September 29, 2005, David Ortiz went 3-5 including a home run leading off the bottom of the 8th inning to tie the score 4-4 and a walkoff RBI single with one out in the bottom of the 9th inning. Baseball-Reference credits Ortiz with a WPA of 0.584 for the game. Obviously, those hits were huge for the Red Sox and Ortiz was rightly celebrated as the hero of that game.

On April 26, 2005, the Yankees defeated the Los Angeles Angels of Anaheim (or whatever they were calling themselves that season) 12-4. The Yankees took a 3-0 lead in the bottom of the first inning and led 10-2 by the end of the 4th inning. Obviously, there weren't a lot of "clutch" situations in this game. It was over early. Do you know why it was over early? Because Alex Rodriguez hit a 2-out, 3-run home run in the bottom of the first inning to give the Yankees that 3-0 lead, he hit a 2-out, 2-run home run in the bottom of the third inning to extend the Yankees' lead to 5-2, and he capped it off with a 2-out grand slam in the bottom of the 4th inning to give the Yankees that aforementioned 10-2 lead. For all of that, Baseball-Reference only credits Alex Rodriguez with a WPA of 0.490 for that game.
Take Ortiz's two RBIs off the scoreboard for the Red Sox in that September 29th game, and the Blue Jays would have won that game 4-3. Then again, if Ortiz made a (single) out in his final at-bat, Manny Ramirez would have come to bat with the potential winning run still in scoring position (albeit with two outs).

Take Rodriguez's ten RBIs off the scoreboard for the Yankees on April 26th and the Angels would have won that game 4-2. Moreover, all three of Rodriguez's home runs came with two outs in the inning. Turn them into outs and the Yankees would have had no further opportunities in any of those innings.

In retrospect, Alex Rodriguez's performance that day was not merely every bit as valuable as Ortiz's, but almost certainly more so, even if it was less "clutch" by a conventional inter-game "win probability" reckoning. My Player won-lost records credit David Ortiz with a batting won-lost record that day of 0.48 - 0.02, good for 0.46 net wins. Alex Rodriguez had a batting won-lost record on his big day of 0.91 - 0.02, good for 0.89 net wins.

As with the example of the home runs at Dodger Stadium, I think my adjustments result in more reasonable measures of the relative values of these two batting performances.

All articles are written so that they pull data directly from the most recent version of the Player won-lost database. Hence, any numbers cited within these articles should automatically incorporate the most recent update to Player won-lost records. In some cases, however, the accompanying text may have been written based on previous versions of Player won-lost records. I apologize if this results in non-sensical text in any cases.

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