Saber-Slant #3: How do players score runs?

Let’s begin with this hypothetical. Florida Marlins left fielder Chris Coghlan starts off a game as the leadoff man and gets on base via a walk. Hanley Ramirez soon steps up to the plate with Coghlan on first base and hits a double, moving Coghlan to third base. Jorge Cantu follows up with a single, driving in both runners.

Now, remember that we want to measure our players in terms of runs. Who would get the credit for runs here using traditional stats? Well, Coghlan and Ramirez scored the runs, so they each got credit for one, while Cantu drove in both of them, giving him credit for two runs. So in terms of traditional run-based stats, we would say that Cantu’s contribution was worth twice that of Coghlan’s or Ramirez’.

But let’s think about this. Take those batting events on their own, away from the situation on the bases. Which event would be worth more? Logically, the double would be worth the most, followed by the single, then the walk. But in our case, using RBI and runs scored, we are weighing the single twice as much as the walk and the double. How can that be?

Intuitively, of course, we know why that single was worth twice that walk and double. That’s because the single came up in a more important situation, and it directly led to more runs. The walk was just the beginning of the inning, as it came up with the bases empty and no one out, a situation holding far less potential. The double brought up a lot of additional potential to that inning, and Cantu simply cashed in on that potential with his bases clearing single.

In other words, the context (remember how that’s everything?) of the situation surrounding Cantu’s plate appearance inflated the value of his single. But the context that was built around Cantu’s PA was based on work done by Coghlan and Ramirez. So I now pose this second question:

Why are we giving credit to a player for things he did not do?

Think about that for a second. An RBI is a function of two things:

1) Your ability as a hitter to advance runners

2) The opportunities provided to you with runners on base

Similarly, a run scored is a function of two things:

1) Your ability to get on base and advance yourself with baserunning

2) Your teammates’ abilities to advance you while hitting

In the example above, it seems ridiculous to hand out credit the way we did with runs and RBI when not one of those players produced the run credited to them on their own. Coghlan advanced not only on Cantu’s single, but on Ramirez’ double as well; you would figure some part of the RBI (the advancement aspect of the credited runs) would be given to Ramirez. Ramirez also advanced himself a good deal before Cantu’s single, but he got just as much credit as Coghlan, who did far less by reaching first base on a walk. Cantu received twice the credit as either of those players, even though runners advanced just as much with Cantu’s single as with Hanley’s double.

This basic example gets to the heart of the problem with using runs and RBI as our run metrics for evaluating offense. As individual a game as baseball is, run scoring is still dependent on a group effort through the lineup. Runs scored is quite telling when applied at a team level, but applying those team runs individually brings a lot of team interactions into play that would be muddled if viewed as individual stats. Chances for runs and RBI are dependent not only on the players surrounding a hitter, but the placement of a player in the lineup as well. Should an individual hitter be given credit for hitting fourth behind Chase Utley rather than Casey Kotchman?

In short, the context-dependence of runs scored and runs allowed makes using them for players essentially worthless. But what should we do if we want to find an individual player’s offensive value, stripped away from the context in which he is placed? There are a few ways to do this, and I’ll get into them in the next few Saber-Slants. For now, however, think about this: Cantu’s single in that situation may have been worth around two runs, but what if we gave him credit for just the average single?

Tags: Chris Coghlan Hanley Ramirez Jorge Cantu

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