I was thinking about Age of mythology board game recently which have different unit types with bonus against other unit types. Creating a sort of Rock-Paper-Scissor system.
How can that pool of units be signed to be balanced across all factions? The objective is to find units too weak/strong, for find overused/underused unit types, or attack bonus.
Solutions I came up so far:
1.First way to analyze this is to count the number of units of each type. Some units can have multiple types, therefore being weaker.
2.Create a graph of unit types targeting unit types. See the number of arrows targeting each type. The more, the weaker units in that category should be.
3.Same thing for exiting arrows, the more arrows, the stronger is that type.
4. A matrix could be used. You sum the modified strength of units for each possible combinations. The units with the biggest sums are stronger.
4. Again using a matrix, but instead of summing combat strength, you sum up probabilities to kill, the target.
Do you have other suggestions?
It does not have to be a strict X-way RPS. There can be multiple systems which are not symmetric.
Age of mythology use a binomial system: Roll X dices > Y. You get additional dices against certain unit types. Some units can have multiple types (therefore weakness).
Here is a picture of the reference sheet I made for all the units in Age of Mythology. The number in square is the unmodified nb of dices rolled.
http://bgd.lariennalibrary.com/uploads/Mainsite/Variants/Variants2009072...
X3M: Can you elaborate on your embedded matrix idea. Give an example if possible. Right now, I do not see how I can embed the results of one matrix into another.
***
As discussed on BGG, the main difficulties are if there are external factors involved than the duel itself. For example, is there synergies between units that makes units on paper weaker, but stronger when a specific pair is combined. In advance wars, artillery units are considered weaker (they can be easily killed), but they ignore the fact that they can attack at long range.