from Amazon
Wednesday, September 16, 2009
More math nonsense
In addition to my problem with ”seasonal age” is my problem with “GB/FB ratio”. Dave points out how ridiculous it is to ignore line drives. That is a great point. I wish I would have thought about that part more.
My bigger problem is the non-symmetry of a ratio. For example, if the “average” GB/FB ratio is 1.1, then if you have a linear equation that uses GB/FB ratio, it will give equal impact to a ratio that is 2.0 or 0.1 (both are 0.9 “ratios” from the average). As you can see, this is mathematical nonsense. If the average GB/FB ratio is 1.1, then the GB/(GB+FB) percentage is 52.4%. And a 2.0 GB/FB ratio is a 66.7% percentage. Symetrically, that’s a GB/(GB+FB) percentage of 38%, or a GB/FB ratio is 0.6. That is, a 2.0 GB/FB ratio is as far away from 1.1, as 0.6 is from 1.1.
Indeed, imagine instead of using GB/FB ratio, you use FB/GB ratio. If you have an equation that is based on using the ratio, you should be able to simply change the coefficient, and get back the exact same results from your equation. This cannot happen if you use a ratio. Suppose, for example, instead of on base percentage, you use outs percentage. That is, 1-OBP, which I’ll call OP. If you have a metric that is 1.8*OBP+SLG, then the equivalent using OP is SLG-1.8*OP+1.8.
I talked about it three years ago.