Saturday, January 01, 2022
CoreWAR: Zero-point
When you win as many as you lose, your win differential is 0. When you score as many runs as you allow, your run differential is 0. Zero, in this case, however does not mean “no value”. Zero means average.
However, there is a math problem with zero = average. And that is this: the more you play, then you will maintain zero. Being average at 60 PA or 600 PA is still average. Being average at 20 IP or 200 IP is still average. Having a 1-1 record or an 11-11 record is both a win differential of zero, or average. But in terms of VALUE, 11-11 has far more value than 1-1. Quantity matters when you are .500.
But at some point below average, quantity does not matter. But how much below average? We've established it's around the .300 win%. So what does this mean? This means that whether you have 60 PA or 600 PA, being a .300 win% makes no difference, you have the same value. And that value is zero. So, unlike above, where a zero run or zero win differential means average, in our case, we literally mean zero meaning no-value.
This zero-point is what we call the replacement level. Now, while I say that the .300 win% is the zero-point, that is not set in stone. You can determine the zero-point replacement level however you think it should be. And it does not even have to be a static level. You can determine a dynamic level that hovers around your historical level.
For nonpitchers, I set the historical replacement level at 77% of league runs scored and 101% of league runs allowed. For pitchers, I set it at 122% of league average runs allowed (with a further split between SP and RP of roughly 130% and 108% respectively). There is flexibility as to where you personally can set it, but generally speaking, you'll land somewhere close to these figures.
Ultimately, because the replacement level is set such that zero = no-value, then wins above the replacement level defines value. And that value is paid proportionately (above the minimum).
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