1. WHAT IS THE BEST WAY TO INTERPRET SRC?
SRC distributes credit for each run that scores among the offensive players who deserve direct credit for the scoring of that run. The calculation of SRC 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 SRC allocated among the players must exactly equal the number of runs that score, so credit is fully distributed with none left over.
2. HOW DOES SRC COMPARE TO OTHER CREDIT STATISTICS IN BASEBALL?
SRC is a credit statistic, that is, it assigns credit to a player for something accomplished during the game. Other common credit statistics are hits (H), runs scored (R), runs batted in (RBI), stolen bases (SB), sacrifice fly (SF), walk (BB), and so on. Like these credit statistics, SRC can be meaningfully added up across innings, games, series, and seasons for a player.
However, SRC differs from these standard credit statistics in several important ways.
First, SRC distributes shares of credit. When a run scores, SRC divides the credit for that 1 run among all of the players who deserve credit. This differs from, say, the R statistic which gives full credit of 1 to the player who reached home or the RBI statistic which gives full credit of 1 to the player who batted in a run.
Second, SRC distributes credit according to mathematical fairness axioms. Standard baseball credit statistics are not grounded in theoretical notions of fairness, but SRC is calculated using the Shapley Value concept from coalitional game theory (see Shapley Value Learning Page).
Third, SRC is a holistic measure that captures all types of direct contributions to run scoring, including hits, walks, hit-by-pitches, stolen bases, sacrifice flies and bunts, advances on wild pitches, or any other offensive contribution. Other credit measures are not holistic measures.
Fourth, SRC explicitly accounts for teamwork in its calculation. Run-scoring collaborations among a group of players will result in those players splitting the credit in proportion to their importance in the run scoring.
3. CAN A PLAYER HAVE NEGATIVE SRC?
Yes, a player can receive negative credit if their offensive event prevented their team from scoring. This can happen, for example, when a player hits into a double play but is then followed in the same half-inning by several players reaching base safely. The player who hit into the double play may have actually led to a lower number of runs scored in the half-inning than if that player had not had a plate appearance. Thus, SRC assigns credit for runs that score in an inning, but it also assigns blame (i.e., negative credit) for runs that could have scored in that inning but did not.
4. IT SOUNDS LIKE THE CALCUATION OF SRC REQUIRES AN ASSESSMENT OF HOW AN INNING MIGHT HAVE PLAYED OUT DIFFERENTLY. IS THAT CORRECT?
Yes, that is correct. These kinds of assessments are a standard part of scorekeeping in baseball, e.g., when deciding whether not a run that scores is an earned run or unearned run, the scorekeeper imagines how the inning would have played out had an error not been made. The calculation of SRC requires that similar hypotheticals be made, but for SRC the hypotheticals consider different combinations of an inning’s actual offensive events.
5. CAN I CALCULATE SRC MYSELF?
If you understand how to construct a value function and then do the Shapley Value calculations, then, yes, you can calculate a version of SRC yourself. You can actually calculate SRC by hand on a single piece of paper if the inning that has only a few offensive players. In general, however, it is best left to a computer.
There are two main challenges with calculating SRC. The first is conceptual: before making the final calculations for SRC 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 score runs in an inning. The second is computational: the number of calculations required to create the value function and then calculate each player’s SRC 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 SRC 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 SRC.
6. FOR WHAT KINDS OF OFFENSIVE EVENTS CAN A PLAYER RECEIVE POSITIVE SRC?
A player can receive positive SRC for any offensive event that contributes to the team scoring a run. This could be a hit, walk, hit by pitch, sacrifice bunt, fly ball that advances a runner, stolen base, base advancement on defensive indifference, etc. This feature of SRC is necessary because a credit statistic that does not account for these types of contributions would not be fairly distributing credit.
7. WHAT STATISTICS ARE MOST CLOSELY RELATED TO SRC?
SRC is most closely related to R and RBI because they are credit statistics that always capture an element of runs being scored. Indeed, there is a correlation between SRC and two lesser-known statistics that are derived from R and RBI.
The first is called Runs Participated In (RPI):
RPI = R + RBI – HR.
RPI is an inferior credit measure for multiple reasons. For example, except in the case of HR, the sum of credit for any particular run will sum to greater than 1. Moreover, credit for advancing a runner is ignored, with credit only given to the player who scored or batted in the run. However, assuming that each run-scoring coalition has three players, and being in one of these run-scoring coalitions equally likely, then the following Weighted Runs Participated In (wRPI) can be derived mathematically from a credit-based argument that accounts for runner advancement:
wRPI = HR + 0.5*(R – HR) + 0.5*(RBI – HR).
The player gets full credit for a HR, half credit when batted in by another player, and half credit for batting in another player. Different assumptions can yield other weights, or the weights can be estimated to better fit SRC (e.g., one linear regression yielded 0.567*R + 0.453*RBI). Yet, this simple wRPI provides a rough but quick estimate of SRC that is less accurate for a single inning but a reasonable shadow statistic for SRC over several games.
The second related statistic is Run Shares (RS):
RS = (R + RBI)/2.
By canceling the HR terms in the wRPI calculator, we see that wRPI equals wRPI. Thus, RS also serves as a shadow stat for SRC.
SRC is superior to RPI and wRPI/RS because it more accurately distributes credit. However, for a rough estimate of SRC, you can use wRPI/RS.
8. WHAT ARE DIRECT CONTRIBUTIONS?
SRC distributes credit for direct contributions. A batter who, for example, strikes out after a twenty-pitch plate appearance may be thought to have contributed to wearing down a pitcher who later gives up a hit that wins the game. This type of indirect contribution is not captured by SRC, nor is it captured in any other standard credit measure.
9. DO EXTRA-BASE HITS RECEIVE LARGER SRC THAN SINGLES?
On average, an extra-base hit will receive more SRC than a single, not because an extra-base is inherently better than a single but rather because, conditional on happening, an extra-base hit will more often be involved in run-scoring collaboration than a single. However, it depends on what the teammates do. A player who doubles and is stranded in a scoreless inning will receive less SRC than another player who hits an RBI single.
This is a key feature of SRC. Over the course of a season a player who hits more extra-base hits than another will, all else equal, amass more SRC over the season. But in any particular inning, the credit will depend on particular events of that inning. This logic extends to all offensive events. Stolen bases, sacrifice bunts, and other “lesser” offensive events can be awarded more credit according to SRC if they happen to work well in collaboration with other teammates’ offensive events.
A special extra-base hit is a HR. A player who hits a HR will always receive 1 SRC for scoring themselves, i.e., they receive full credit for scoring themselves. How much credit they receive for scoring other players who scored as part of the HR will depend on what else happens in that inning. A common distribution of credit is for the HR hitter to get 1 SRC for their own run and half of the SRC for any other run that scored, however the HR hitter can also receive less than 0.5 of the credit for any particular run depending on the contributions of other batters.
10. HOW DOES SRC COMPARE WITH BA, OPS, SLG, AND OTHER SKILL STATISTICS?
Standard skill statistics in baseball such as BA, OPS, SLG, OPS, wOBA, and others attempt to isolate the player’s performance outside of the team context and their direct role of scoring runs in any particular game. For this reason, standard skill statistics will also typically always give the same weight to a particular type of hit. For example, the SLG calculation always gives weight 1 to singles, 2 to doubles, 3 to triples, and 4 to HR.
SRC intentionally keeps the player within the team context to account for how well the player collaborated with teammates. As such, the credit attributed to any particular hit by SRC will vary from inning depending on whether that hit was a part of a run-scoring coalition.
Although more skilled offensive players will likely accrue larger SRC over the course of many games, SRC is not intended to be a measure of skill. A player’s SRC, like R and RBI, will depend on the contributions of that player’s teammates, and so it will not predict future performance as accurately as skill statistics. SRC will, however, provide an accurate accounting of credit during an inning or game. SRC looks back at what happened rather than projecting forward what will happen.
11. HOW DOES SRC COMPARE WITH RUN ESTIMATORS?
Run estimators approximate the batter’s contribution to runs scored in run units. Linear run estimators, such as Batting Runs (BR) and Weighted Runs Created (wRC), estimate a player’s run contribution via a linear formula. They differ from one another by the set of inputs used, the weights placed on each input, and the method by which the weights are derived. Multiplicative run estimators, such as Runs Created (RC) and Base Runs (BsR), combine offensive inputs to mimic the getting on base and advancing runners. Unlike SRC, run estimators decontextualize batting data and give every instance of a type of offensive input the same weight irrespective of whether a run scored.