With hockey playoffs upon us, I have been thinking about ways of modeling the results of athletic events.
Suppose team A wins 50% of its games against average teams, and team B wins 50% of its games against average teams (i.e. two average teams play). Then we expect team A wins 50% of the time and team B wins 50% of the time. That is, the game is a fair coin flip, a Bernoulli random variable with parameter $p = 0.5$.
Now suppose team A wins 60% of its games against average teams, and team B wins 50% of its games against average teams (i.e. team B is average). Then we expect team A wins 60% of the time and team B wins 40% of the time. This is again a Bernoulli random variable, but now $p = 0.6$.
Now suppose team A wins 60% of its games against average teams, and team B wins 30% of its games against average teams. I figure the outcome of this game should again be a Bernoulli random variable, but I am unsure of how to calculate $p$ in this case. Is my modeling framework too simplistic here? Do I need more information about team A and team B to draw a meaningful conclusion? I think I may need to assume how the team performances are distributed to come to an answer, but I'm not sure.
Apologies if my question is ill-posed or overly simplistic. I know lots of people do this kind of modelling professionally (albeit using much more complicated models), but it's a subject I don't know much about.