League of 10 teams
For all matches between teams i and j (except possibly those involving team A),
P ( team i wins ) = P ( team j wins ) = 0.4
P ( draw ) = 0.2
This diagram shows that a simulation can give insight into a fairly complex situation.
Click Accumulate and simulate the league several times. Explain that Team A is almost equally likely to be in any position at the end of the season (as expected since all teams are equal). Since first-equal is counted as rank 1, the probability of having rank 1 is actually slightly more than 0.1.
Use the slider to give Team A a probability of 0.55 of winning each match (and 0.25 of losing) then repeat the simulation.
Observe that Team A only tops the league in about half of the simulated
seasons, despite having more than twice the chance of winning than losing each match. It even ends in the bottom half of the league occasionally.
Even a simple probability model can give valuable and perhaps surprising insight into a system through a simulation.
In this league simulation,
Points from a match = | 3 if team wins 1 if team draws 0 if team loses |
Each team plays each other twice (once home and once away).