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Wednesday, July 28, 2010
SABR 111 - Out value
The good news is that we got the bases and outs to add up exactly to the number of runs scored. The bad news is… it doesn’t work like that.
The base-value of the outs is simply to count the number of bases left on base. Make the final out, stranding the runner on 3B? That’s minus 3 bases. Imagine therefore you have a high run environment where the average number of runners left on base is 1.6 runners (say a total of 3.0 bases). Let’s call this a 10 runs per game environment. Imagine a far higher runs per game environment, say 20 runs, where you leave 2.0 runners on base (say a total of 3.75 bases). Imagine an even much much higher run environment, say 40 runs, where you leave 2.5 runners on base (say a total of 4.8 bases). And imagine the biggest run environment, like ever, a gazillion runs, where you leave the bases loaded every time (for a total of just 6.0 bases).
So, making the third out removes 3 bases in one reasonably extreme situation, and it removes 6 bases in the other most extreme situation. Hardly seems to make sense that an out’s impact can be capped like that.
Well, it doesn’t make sense. The out serves two functions: one is to remove the base-value of the runners on base, which is what we’ve been discussing so far. The other is to extend the inning. By making an out, you are turning a 3-out inning, into a 2-out inning. As you can imagine, an out in a run environment where 10 runs are scored is far more damaging than in an environment where 3 runs are scored. You can afford to give up an out to get a base when you are facing Pedro. You can’t afford to play small ball when runs are so easy to come by.
But, waitaminute, we already were able to exactly add up bases and out to runs. If we have to apply an extra penalty to outs, then we’re going to get a number that is less than total runs scored.
Right, exactly. Because it’s important to know the run environment you are in, the correct thing to match on is not total runs scored, but runs scored relative to average. And so, bases and outs have to add up to zero.
That’s why Linear Weights works.
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