A Run Scored is the Same as a Run Prevented – or is it?
One of my earliest criticisms of baseball sabermetrics had to do with the way that player defensive value was shrugged off as merely being a matter of position and scarcity. Defensive stats have come a long way, possibly to the point where this criticism is no longer relevant. A run prevented is pretty much treated the same as a run scored.
Is this the case though? In the most literal sense, of course it’s true — either way, you’re one run closer to winning a game. It also makes for a nice way of promoting defense: a player who saves a run with the glove is just as valuable as a player who creates a run with the bat.
Defense is of paramount importance to baseball teams because much of what is perceived as pitching success or failure is probably defensive success or failure. There is a reason that many “stats” guys feel like MLB teams overvalue the negative effect of a pitcher who gives up too many home runs, but I’m siding with the baseball execs here: keeping the ball in the park needs to be the number one concern for pitchers: it’s far more devastating to give up the long ball at an above average rate than whatever the linear weights equivalents of reduced strikeouts or increased walks may be. For pitchers, a high HR rate represents a lack of command similar to that of an increase walk rate, only with a more devastating result. “Wild” pitchers can see an uptick in both walks and strikeouts, without having their HR rates change whatsoever.
When we talk about defensive runs prevented we talk about a denominator of the expected value of runs on total balls in play. But offensively, the denominator is different. It’s not all balls in play, it’s the outcome of every at bat in a sample. The difference between the two is known as defensive independent pitching. But DIPS come with a caveat that batted balls aren’t totally independent of pitching, only mostly independent. The quality and type of pitcher can affect the difficulty of turning batted balls into outs. This would certainly imply that a defensive run saved would somehow be different than an offensive run created, and that pitchers are the primary variable. Though this is widely accepted, it’s also counter-intuitive to how modern statistical writers perceive baseball.
The other thing is that the score and game situation matters. Teams attempt to maximize win probability, not always run probability. The hottest area of debate over this principle is the strategic value of sacrifice bunting (usually both run- and win-probability deflating), but I want to focus on outs. An offensive out is, in theory, always of the same value: one out closer to ending an inning/the game. They are baseball’s independent variable. The third out is usually more costly to an offense than the second or first out, but all progress the game in exactly the same fashion. Defensively, however, this isn’t always the case. If the outs/runs matrix was identical in all game situations, there would be a universal optimal choice on this game situation:
Runners on 1st and 3rd, 0 outs. Ground ball to third base, with all runners trying to advance. The ball is cleanly fielded.
In perfectly normal game situations, it makes more statistical sense to go to second to attempt a double play, so long as the team plays at a level where the double play would be executed routinely. As soon as the third baseman goes to second for the first out, the run is going to score. It is, by definition, not run preventing because a run is scoring on this play by fielder’s choice (literally, the official scorer rules the play a fielders choice, no matter where the ball is thrown or what the outcome is). If I give you more information about the play, telling you that the game is tied in the bottom of the ninth inning, then throwing to second is the right choice 0% of the time. Two outs are meaningless, because the game ends when the run is scored.
This is a much more telling “strategic” dilemma than the sacrifice bunt matrices because both strategies are made with the abstract idea of preventing runs, but once again, that brings me back to the original point: not all runs are created equal, and because there are two strategic players in baseball (the teams, and specifically the managers), game theory indicates that even in normal game situations, no run can be perceived precisely the same way by both teams. This means that a run scored and a run prevented are, in the most strategic sense, not identical, nor are they of identical value.
This revelation is probably meaningless, because even though I have argued that scored runs and prevented runs are not of identical value, it’s not clear if or why one should be considered inherently more valuable than the other. I suspect — with no numbers to back this up — that scored runs are slightly more valuable than prevented runs. Obviously, this whole post is a case of abstract nitpicking. When building a baseball team, it makes perfect sense to try to improve the team by both adding runs and preventing runs, and not simply deciding to become proficient at one or the other and let the chips fall where they may. I do think there is an inherent strategic advantage to having a high total of runs scored with regard to winning games, because it would seem easier for a manager to pull a couple strings with his bullpen and defense to stop the bleeding than for the same manager to try to create “just enough” runs to beat a pitcher that could easily dominate his offense.
What does all of this mean? Probably not very much. It just means that runs scored and runs prevented are not of inherently identical value. It doesn’t mean that MLB defense or pitching or offense are overvalued or undervalued. I did not discover any market inefficiencies in this post. If anything, I went well out of my way to loosely agree with the baseball establishment, and the way they do things. But just like football analysis gets raked for not properly considering weather, opponent, and injury context, baseball analysis probably has a bit of work to do before properly assessing the value of defensive runs in, well, player value, but much more significantly, team and division projections.