Well then we need to define a new objective function.
This new objective function would define the tradeoff between elo variance (is that the standard deviation? The variance? Or the sum of absolute differences of team average and individual elos?) and team imbalance.
To illustrate this, consider these situations that share this (current) optimum:
- Elo difference 0, Elo variance 100
If you get to choose between the above and each of the following
individually (i.e. you're only comparing with one at a time), which one is to be taken in each case?
- Elo difference 1, Elo variance 0
- Elo difference 10, Elo variance 0
- Elo difference 100, Elo variance 0
- Elo difference 1, Elo variance 10
- Elo difference 10, Elo variance 10
- Elo difference 100, Elo variance 10
Note also that, as explained in posts
way back in the day, the current balance optimization function makes heavy use of the "simpleness" of the current objective function. By the sound of it, it would be prohibitively expensive to calculate something fancy like a standard deviation for every considered team composition. (Keep in mind that the problem we're solving is a variance of an
NP-hard problem.)
In other words, be prepared that even if we find an objective function that people agree on, it might still not be implementable.
Reverse TL;DR: This post summarized (in simpler terms) what
Brackman did/concluded
here.
PS: Well fuck it, zero-width spaces don't do the job for apostrophes after @<Playername> either. This stuff used to work fine!
