OT: Making a Game System (part 2)

[Lokean]

Omnirizon, since you seem to be only vaguely familiar with the Pythagorean means, I'll give examples with the data set you gave earlier.

The Pythagorean means of the data set [1, 1, 1, 2, 10] are as follows:

The arithmetic mean is the sum of the members of the set divided by the population of the set.
μ = (1 + 1 + 1 + 2 + 10)/5 = 3

The Geometric mean is the product of the members of the set raised to the power of the reciprocal of the population of the set.
G = (1 * 1 * 1 * 2 * 10)^(1/5) = 1.82

The Harmonic mean is the reciprocal of the arithmetic mean of the reciprocals of the members of the set.

H = 1/((1/1 + 1/1 + 1/1 + 1/2 + 1/10)/5) = 1.39

It is vitally important to note that these functions only exist for positive, real numbers.

I think it essential that you realise how strongly the harmonic mean skews the results towards the low values and, quite importantly, the limit of the harmonic mean.
Consider a situation where a character's vitality cost for acting is the harmonic mean of 100 values, 99 of which are 10, one of which is 1. The harmonic mean is 9.17.
Consider the same thing, but now 99 of those values are one googolplex. The harmonic mean is 100.

This illustrates an important relationship with regards to the the population of a set, its smallest member and its harmonic mean. The maximum value of the harmonic mean of a data set is that of the smallest member multiplied by the population.