1. WHAT IS THE BEST WAY TO INTERPRET OSWC?
OSWC distributes credit among the players for outscoring the opposing team. The calculation of OSWC ensures that credit is distributed according to mathematical fairness axioms so that players who deserve credit are given credit in exact proportion to their direct contributions. The total OSWC allocated among the players must exactly equal the number of team wins, so credit is fully distributed with none left over.
2. WHY IS CREDIT AWARDED FOR OUTSCORING THE OPPONENT?
Offense and defense play complementary roles in baseball. The offense’s job in any particular game is to score more runs than its defense allows, while the defense’s job in any particular game is to allow fewer runs than its offense scores. Hence, the offense’s credit for winning is allocated based on each player’s role in helping the team outscore the opponent. It is for this reason that there is an “O” in OSWC.
3. WHY ISN’T THERE A DEFENSIVE SHAPLEY WIN CREDIT OR AN OVERALL SHAPLEY WIN CREDIT?
I are working on it! Creating the value function for defensive production is trickier than for offensive, but I have made some progress. Stay tuned!
3. HOW ARE SRC AND OSWC RELATED?
SRC and OSWC assign credit for different types of offensive production. SRC assigns credit for scoring, while OSWC assigns credit for outscoring the opponent. All else being equal, scoring more runs increases the chances of winning, so SRC will be positively correlated with OSWC on the winning team. Yet, in general, the allocation of credit by SRC and OSWC will differ because OSWC also takes into account the number of runs scored by the opponent.
To see the difference between SRC and OSWC, consider Table 1 which reports the OSWC for the Los Angeles Dodgers for game 6 of the 2020 World Series, holding fixed the Dodgers’ actual offensive events but assuming different runs scored by the Tampa Bay Rays.
Table 1: OSWC for Dodgers, Game 6, 2020 World Series, by Rays’ Runs Scored
| Player | SRC | Rays 0 | Rays 1 | Rays 2 | Rays 4+ |
| M Betts (RF) | 2.00 | 1.00 | 0.667 | 0.333 | 0 |
| C Seager (SS) | 0.50 | 0 | 0.167 | 0.333 | 0 |
| J Turner (3B) | 0 | 0 | 0 | 0 | 0 |
| E Hernandez (2B) | 0 | 0 | 0 | 0 | 0 |
| M Muncy (1B) | 0 | 0 | 0 | 0 | 0 |
| W Smith (DH) | 0 | 0 | 0 | 0 | 0 |
| C Bellinger (CF) | 0 | 0 | 0 | 0 | 0 |
| C Taylor (2B-LF) | 0 | 0 | 0 | 0 | 0 |
| AJ Pollack (LF) | 0 | 0 | 0 | 0 | 0 |
| J Pederson (PH) | 0 | 0 | 0 | 0 | 0 |
| E Rios (3B) | 0 | 0 | 0 | 0 | 0 |
| A Barnes (C) | 0.50 | 0 | 0.167 | 0.333 | 0 |
| Team Total | 3 | 1 | 1 | 1 | 0 |
Betts has two-thirds of the total SRC allocated among the Dodgers, but his share of OSWC depends on whether the Dodgers win and by how many runs they win. The proportion of OSWC that Betts is allotted can vary from all of the credit if the Rays score 0 runs to an equal share of the credit if the Dodgers win by 1 run. Thus, although SRC is correlated with OSWC, the correlation is not perfect because SRC and OSWC are crediting different types of production.
4. WHY DOES OSWC DEPEND ON THE OPPONENT’S SCORE?
Winning the game depends on how many runs a team scores but also on how many runs the opposing team scores. The opposing team’s score must thus factor into the distribution of credit for outscoring the opponent.
See Table 1 above for an example of how OSWC depends on the opponent’s score. OSWC can be clustered around fewer players in blow-out wins because some of the players’ contributions will not be necessary to outscore the opponent. OSWC tends to be more equally distributed when the score is close because most or all of the players’ contributions will be necessary to outscore the opponent.
5. CAN I CALCUATE OSWC MYSELF?
Like SRC, you can calculate OSWC yourself, and you can even do it by hand for a game with a small number of runs scored. In general, however, it is best left to a computer.
As with SRC, there are two main challenges with calculating OSWC. The first is conceptual: before making the final calculations for OSWC you must first create something called the value function which is a mathematical, game-theoretic representation of how the different offensive events combine in different ways to win the game. The second is computational: the number of calculations required to create the value function and then calculate each player’s OSWC increases exponentially in the number of players. Any person with enough motivation can overcome these challenges, but it is often more fun just to use the statistics rather than go to the trouble of calculating them. My calculations required hours of coding and machine learning.
Note also that a degree of judgment is exercised when constructing the value function. Just like different versions of wins above replacement (WAR) make different assumptions about what is the best way to measure a player’s effectiveness (such as using FIP instead of ERA or using ERA instead of FIP) that result in slightly different WAR calculations, two people may produce slightly different versions of OSWC if they make different assumptions in the value function. There is only one way to calculate a Shapley Value once you have the value function, but there can be more than one way to construct a value function. In most cases, any two persons will agree on the value function, but just like scorekeepers might disagree on whether a fielder deserves an error, there can also be honest disagreement about the value function that produces slight differences in OSWC.
6. HOW DOES OSWC COMPARE WITH OTHER WIN MEASURES?
On average, a team wins one more game a season for about every 8-10 additional runs it scores, and the simplest estimate of a player’s win contribution is to estimate their run contribution and divide by 8 or 10 or another runs-per-win ratio. The resulting number is an estimate of the player’s contribution to wins in win units. Thorn and Palmer (1984) and various measures of WAR follow this procedure. This direct linkage from batting and base-running inputs to runs and wins is not present in OSWC because the impact of a particular offensive event on OSWC depends on how it is combined with teammates’ events. Consequently, the relationship between SRC and OSWC varies widely from game to game, although over the course of many games the SRC-per-OSWC ratio should approximate the runs-per-win ratio.
Win Probability Added (WPA) is the change in win expectancy resulting from a player’s plate appearance as derived from averaged historical data. The winning players’ WPA sum to 0.5 because the team went from 50% winning at the game’s start to 100% winning at the end, while the losers’ WPA sum to -0.5. WPA thus respects a strict accounting of credit that aggregates across games and seasons. Because WPA and OSWC consider context explicitly, both will be less predictive of future performance than context-neutral statistics, yet context matters differently for each. WPA awards more credit to players who performed well in later innings of close games, while OSWC does not treat performance differently based on the inning. WPA thus captures the emotion of the game, while OSWC captures team collaboration. Moreover, WPA’s credits changes in win expectancy, not winning per se. A player who hits a late-inning home run that ties the game will receive a large WPA even if his team loses. OSWC does not credit improved chances of winning; it credits players for actually winning. These similarities and differences also apply to WPA derivations.
Win Shares (WS) is a hybrid approach to crediting wins that transforms individual skill-based statistics into win credits based on the team’s season wins. The player’s run contribution for the entire season is estimated, and his WS (after controlling for defense) is the proportion of the team’s season win total that equals the proportion of his run contribution to the team’s runs (scaled to three win shares per win), The sum of WS on a team thus equals the team’s actual season wins (times three). WS is efficient and symmetric. However, by averaging over context-neutral inputs when calculating shares, WS does not aggregate from game to game throughout the season thereby failing to meet one of the conditions of Shapley value-based measure.