The problem with using bionominal in this account is that it can be used in flipping a coin. Right. So you have either heads or tails and that's it. So you can calculate what the probability of getting multiple heads (but probability is not odds. The odds don't change its still 50/50).
In baseball there are 1 of 2 outcomes win or lose. But, there are 12 teams, i.e. coins.
It also doens't take into effect other things that can impact the outcome. In a coin flip the only thing that's gonna change it is a wind which is random. baseball is a game of skill and has many more random factors. Those change those 50/50 factors in different ways.
Using bionominal does help calculate probability, but not the odds or chance you will win a championship by appearing in the playoffs more times. The previous year in a game of skill has no baring on the current. Maybe one of those other coins is heavily weighted to win. Maybe you keep getting brushed by the wind, i.e. a random bounce. Bionominal doesn't work in this situation.