I have a roster of entities which may compete in a competition that involves randomness . Generally if two entities directly compete and would have a win-loss-draw of about 50% (determined using monte-carlo simulation) with each other, we could consider them equivalent and give them the same arbitrary value.
Is there a set of mathematical functions that can determine this, more easily than say simulating varying ratios until you can achieve a 50% win rate (for example, if one entity is twice as valuably as another, that entity might have a 50% win rate paired against two of those opponents simultaneously).
If it is relevant, consider the competition might be similar to dodge-ball. Entities can be eliminated and take no further part in a game, and certain entities might be better at avoiding elimination, or at eliminating opponents. Ultimately, the aim is to fairly score two teams of entities, such that there is a relatively good balance of outcome, based on the sum value of the players compared.