The "contest success function" between two adversaries is a sigmoid.

The curve is the success rate given the relative amount of resources between the adversaries.

If you have far fewer resources than your adversary then a bit more won't help.

If you have far more than your adversary already then a bit more won't help.

But if you are roughly equally matched, a bit more can make all the difference

Systems in dynamic equilibrium are often on the cusp of a phase transition.