Re: The Top 25 College Hockey Teams of the NCAA Era
Technical commentary: this post will involve some subtle mathematics, so be fore-warned.
I had mentioned a distinction between independent variable and interdependent variable. This is an analogy to illustrate the difference, even though at first it will appear to have nothing to do with hockey.
Suppose you are lucky enough to have some money to invest, and you let a money manager handle part of it. She charges you a management fee. She places part of the money in a mutual fund, which charges an administration fee and an advisory fee. The question is, what do you have left after fees?
The initial impulse is to say, "my fees are F1 + F2 + F3, and so after fees I have (1 - (F1 + F2 + F3)) * initial amount.
However, the amount each person charges in fees actually depends upon what the others have already charged in fees. In other words, the mutual fund advisory fee is only charged on what is left after the administration fee has been charged; and the money manager's fee is only charged on what is left after the mutual fund advisory fee has been charged.
The actual formula is (1-F1)*(1-F2)*(1-F3). This will always give you a higher number than (1-(F1+F2+F3)), although the difference will not be very large. [footnote]
It seems to me that something analogous happens with your formula in the 16-team era. Several different components of your formula are all affected by that expansion, and it sounds like you made a linear correction when a non-linear correction would have fit better.
[footnote: as long as 0 < F1, F2, F3 < 1 and F1+F2+F3 < 1 are true, then (1-F1)*(1-F2)*(1-F3) will always be larger than (1-(F1+F2+F3)), or Result-NonLinear is always larger than Result-Linear. Since the analog of these components would be divisors, then 1/R-L is always greater than 1/R-NL, by a small amount, hence the inadvertant minor overweight of results for teams that played in the 16-team era relative to earlier-era teams].
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