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Thursday, June 21, 2007
Translating homeruns
Patriot gives us a good introduction on translating (rescaling) stats, focusing on the HR, which if you cut right to the chase is based on this:
New HR = HR/(PF*RPG)*9
In essence, Patriot is scaling it linearly to runs per game. So, 25 HR in a 2.5 RPG environment would scale to 50 HR in a 5.0 RPG environment. If we run the Markov calculator:
http://www.tangotiger.net/markov.html , we see that 0.66 HR hit in a 2.5 RPG environment (set AB=51, or multiply all the default numbers by 27/41) would be equivalent to 1 HR in 5.0 RPG. (Note: the run value of a HR, while fairly stable, drops by about 5%.)
What if we go to win values instead? Using PythagenPat, the win value of a HR is .133 wins in a 5.0 RPG and .21 wins in a 2.5 RPG environment. That 1 HR in a 5 RPG environment is worth .133 wins. And, how many HR in a 2.5 RPG would be worth .133 wins? 0.63 HR.
As you can see, both approaches give a fairly similar number, and is a bit different from the 0.50 HR that Patriot would propose. However, I chose rather extreme environments, and perhaps in more realistic extreme environments, we won’t find such differences. Trying a 3.5 RPG environment, Markov gives the equivalency as 0.82 HR, and PythagenPat says 0.79 HR. Patriot’s approach would have said that 0.70 HR in a 3.5 RPG environment would translate to 1.00 HR in a 5.0 RPG environment.
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