May 2, 2017
Is the Whole the Sum Of Its Parts?
We live in a statistical ecosystem that is dominated by WAR, a statistic that for all its perks does contain some weaknesses. WAR–in an attempt to compare all players to a common baseline–specifically assigns a value to players with the intention of stripping away all of the context of his teammates. There’s no secret here. This is celebrated as the great triumph of WAR. Where RBI or runs scored were decent indicators of a hitter’s abilities, they were also dependent on the abilities of his teammates. As an individual measure, WAR makes sense as a way to compare everyone to the same baseline.
Problem: the big trophy at the end of the year goes to the team that won the World Series. Sure, the more individual talent that a team has on its bench, the better. However, is the way to evaluate a team to simply add up all the WAR?
I think at this point, we have enough evidence to say that the answer is “no.” We know for example that WAR doesn’t do a great job valuing relievers, mostly because the actual amount of value that a reliever will produce has a bit more to do with what role he’s used in, purposely or accidentally, than strictly his stats. The more interesting question is how much of a difference that makes. If the answer is “the whole is greater than the sum of its parts, but the effect size is only half a run,” then it’s not something that we should worry about.
I don’t think we’re going to solve this question today, because for one, there is going to be variance between a team’s talent (in the sense of “add up all the WAR”) and their results because of timing and random chance. But what if there are provable ways in which a team can generate value by putting its players together in a certain way?
Warning! Gory Mathematical Details Ahead!
In 2016, there were 21,744 runs scored, MLB-wide. There were 5,610 home runs hit. That means that about three quarters of all runs scored were, by definition, the work of at least two players. A hitter got on base and someone else knocked him in. Baseball might be a game where the atomic unit is the pitcher-batter confrontation, but the way that runs are scored is a matter of interaction.