nice job X- Act

just a question

we've seen that if all F = O we get 0, but does the same thing happen if all pokemon were used in an equal balance? (aka every pokemon from bulbasaur to Shymin minus UBERS) was used 5000 times each) this will never happen, but in theory if it did happen F and O just equal 0 right?

Let me think of this.

Suppose a metagame having P Pokemon is such that all of them are each used U times as you say. That would mean that the total number of usages would be PU.

F is the number of Pokemon having more than PU / 37.7113 usages. This number of Pokemon can either be 0 or P. If P > 37, then F = 0, else F = P.

O is the number of Pokemon having more than PU / 176.1407 usages. This number can also be either 0 or P. If P > 176, then O = 0, else O = P.

Hence, if the number of Pokemon in the metagame is between 38 and 176, then my formula would say that it would be a very uncentralised metagame. Otherwise it would say that it would be an infinitely centralised metagame, which is the incorrect value.

Thanks for the heads-up. I'll research this further, as this formula obviously does not work in the most extreme of cases.