As winrate can be though of as EV which will give us linear operators, without getting into anything too abstract with degrees of freedom, we are fundamentally determining the values in a system of linear equations.
In our simple example we have 3 variables that can change. Then we expect any 3 pieces of different information to determine our system of equations.
If we allow populations for each strategy to also vary, then for each population that is allowed to vary we must add another piece of information to determine our system. So if we had exactly three strategies that can each be played by a variable amount of players we would need 6 pieces of information to determine our system.
As we add more strategies and players the information to fully determine the system will grow. However, since in this example we only care about strategy A wrt B, we can lump all other strategies together into strategy C and we will only need 6 pieces of information to determine our system regardless of how many strategies that are lumped into C.
An example of the information that would sufficiently determine our system would be:
The population of A
The population of B
The total number of players in A, B, & C
The winrate of A vs the field
The winrate of B vs the field
The winrate of B vs C