In "Moneyball," Michael Lewis reported that former Oakland Athletics' assistant general manager Paul dePodesta believed that extra on base percentage (generated via walks) was worth three times as much as a similar amount of extra slugging percentage (a function of extra bases). The old wisdom was that the ratio was more like 1.50:1 or 3:2.
When I first read that, my reaction was "DePodesta can't be right." That would mean that a walk was worth as much as a triple, an obvious fallacy. Or else, three walks are worth three times as much as the triple. But the latter proposition (and similar ones) might actually be correct, depending on surrounding circumstances.
To do this analysis, I need to introduce some new terms. The first is "run expectation," where the raw data comes courtesy of FanGraphs. That is the expected number of runs that have historically resulted from different combinations of baserunners (up to three) and outs (maximum of three).
For instance, the run expectation at the beginning of an inning, with "none on and none out," is about half a run. That's just all the runs in the history of baseball divided by all the innings. If a man gets on first (by either hit or walk), the run expectation rises to 0.88, or about seven-eighths of a run.
More runners on base increase your run expectation. More outs decrease this metric.
I'll also introduce a term that I call "base capture." That is similar to the more commonly used "total bases," except that walks are included. A walk represents a capture of one base. So does a single. But a double represents TWO total bases, or bases captured, a triple, three, and a home run four.
Using these concepts, an example will illustrate how useful walks are.
Suppose you have two clones for your first four batters. The first clone bats .250, and never walks, but every hit is a home run. The second clone walks every time. After four plate appearances, both sets of clones have captured four bases, using our terminology. The rest of your lineup is drawn at random from all of baseball.
The first clone will hit one home run and make three outs in an inning, for a total of one run per inning. That's a lot. (There will be a few innings with two home runs, and others with three outs before the fourth batter hits a home run, but they'll cancel out.)
The second clone will load the bases, and then walk a man home, thereby scoring one run. But the inning isn't over. Most likely, there will be followup runs.
The run expectation with loaded bases and no outs is 2.33, using random followup batters (our assumption). With the one run in the bank, a lineup headed by the second clone will contribute an average of 3.33 runs in an inning, more than three times as many as the first one.
If two batters walk, capturing two bases, so that you have men on first and second, the run expectation rises to 1.49 from 0.88 for a man on first. A double that captures two bases has a run expectation of only 1.12, because you have only one man on base. The ratio of the first to the second is 1.34, a bit less than 50 percent higher.
But there's another wrinkle. The two walkers have made two plate appearances while the doubler has made only one. What do we do about the second plate appearance? In order to make a valid comparison and hold the bases captured constant at two, we need to assume that the batter behind the double makes an out.
This one fact hugely changes things in favor of the walkers.With a man on second and one out, the run expectation drops to 0.68, less than one-half of the value of two walks.
You can do the exercise with triples and three walks. Loaded bases with none out have a run expectation of 2.33 runs. An inning with a man on third and no outs has a run expectation of 1.40, of which 2.33 is 1.66 times. But add two outs to the equation, to equalize plate appearances, and the run expectation drops to 0.35, a small fraction of 2.33 runs.
Basically, the walkers do two things for the same base capture: 1) They get more men on base for the same number of captured bases. 2) They fail to make outs that lower your run expectation.
The old sabermetricians took into account only the first effect in estimating the extra value of extra walks over extra bases. DePodesta also took into account the second effect, which makes extra walks worth between two to three times an equivalent amount of extra bases.
The A's Jason Giambi was an example of the value of on base percentage (OBP). At his peak, his OBP was .470, twice his mediocre batting average, which means that he got on base, through hit or walk, nearly half the time he showed up at the plate.
Add a certain number of successful sacrifices, and maybe half his plate appearances were "productive." Forget that he also had considerable power—gotten in a dishonorable way (steroids)—by assuming that every hit was a single, and just think about the value of his keen eye.
The Pittsburgh Pirates, on the other hand, tend to trade away players like Rajai Davis, Nate McLouth, and Jose Bautista who have high OBPs and low batting averages (at the time of trade). Forget about the fact that Davis, at least, improved his batting average significantly. All three get on base more than usual, while many member of the existing team do not.
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