Shapley Run Credits (SRC) and Offensive Shapley Win Credits (OSWC) improve our understanding of a baseball game when included in a box score.
Consider Table 1, which is a box score for the Los Angeles Dodgers 3-1 victory against the Tampa Bay Rays in game 6 of the 2020 World Series. The box score includes several well-known measures but is enhanced by the addition of SRC and OSWC in the last two columns.
TABLE 1: LOS ANGELES DODGERS BOX SCORE, GAME 6, 2020 WORLD SERIES
| PLAYER | AB | H | R | RBI | HR | BB | K | WPA | SRC | OSWC |
| M Betts (RF) | 4 | 2 | 2 | 1 | 1 | 0 | 2 | 0.148 | 2.00 | 0.667 |
| C Seager (SS) | 3 | 0 | 0 | 1 | 0 | 1 | 2 | 0.039 | 0.50 | 0.167 |
| J Turner (3B) | 3 | 0 | 0 | 0 | 0 | 0 | 2 | -0.065 | 0 | 0 |
| E Hernandez (2B) | 1 | 0 | 0 | 0 | 0 | 0 | 1 | -0.011 | 0 | 0 |
| M Muncy (1B) | 4 | 0 | 0 | 0 | 0 | 0 | 1 | -0.088 | 0 | 0 |
| W Smith (DH) | 3 | 1 | 0 | 0 | 0 | 0 | 1 | 0.000 | 0 | 0 |
| C Bellinger (CF) | 3 | 0 | 0 | 0 | 0 | 0 | 1 | -0.079 | 0 | 0 |
| C Taylor (2B-LF) | 3 | 1 | 0 | 0 | 0 | 0 | 1 | -0.011 | 0 | 0 |
| AJ Pollack (LF) | 2 | 0 | 0 | 0 | 0 | 0 | 0 | -0.082 | 0 | 0 |
| J Pederson (PH) | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0.007 | 0 | 0 |
| E Rios (3B) | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| A Barnes (C) | 3 | 1 | 1 | 0 | 0 | 0 | 0 | 0.064 | 0.50 | 0.167 |
| TEAM TOTALS | 29 | 5 | 3 | 2 | 1 | 2 | 11 | -0.078 | 3 | 1 |
The SRC column reports how the credit for the Dodgers’ 3 team runs is fairly distributed among the players on the team according to the Shapley Value calculation from cooperative game theory. Of the 3 runs that scored, Betts deserves credit for 2.00 runs, Seager and Barnes deserve credit of 0.50 runs each, and every other Dodger receives 0 credit. The SRC statistic distributes credit for all of the team runs, so the total SRC for the teammates always equals the total number of runs actually scored.
Notice that assigning credit for the runs that scored is not obvious from the standard box score information, so the SRC statistic provides meaningful and new information. It seems natural that Betts deserves more credit than the others. He scored twice and batted in a run, while Seager batted in a run but did not score, Barnes scored but did not bat in a run, and no other player was directly involved with the scoring of runs. However, it is not obvious how the credit for those 3 runs should be fairly distributed. In fact, only 2 RBI were credited for the team’s 3 runs, so some form of credit appears to be missing from a standard box score. By fully distributing the credit for all 3 runs, the SRC statistic reveals which players were responsible for scoring and how much credit they deserve.
The OSWC column reports how much credit each Dodger receives for outscoring the opponent according to the Shapley Value calculation. Betts deserves credit for 0.667 (i.e., two-thirds) of the win, Seager and Barnes each deserve credit of 0.167 (i.e., one-sixth), and every other Dodger receives 0 credit.
Again, the standard box score information does not reveal how much credit each player deserves for outscoring the opponent, so OSWC provides new and valuable information. It seems natural that Betts deserves more credit than the others, but it is not clear how much more. Seager and Barnes also seem to deserve credit, but it is not clear how much they deserve relative to each other and the other teammates. WPA could potentially reveal how much credit each player receives, but its interpretation for this purpose is unclear. The batters’ total team WPA is -0.78, which suggests that the Dodgers’ batters collectively did more to decrease their chances of winning rather than actually winning.
The players’ OSWC sum to 1 because exactly 1 game was won. As a measure of offensive contributions toward winning, the full credit of 1 is distributed among the batters. A combined measure of offensive and defensive credit is still in development. For now, only offensive credit is allocated.