This year I'll be running a special competition in which participants will be asked to predict how the teams will finish on the ladder at the end of the home and away season. Entries will need to be in before the first game of Round 7. More details will be provided in a few weeks time.
In the meantime, here are a few permutations and combinations relating to the ladder, assuming that each team has a 1/16th probability of finishing in any given ladder position:
- How many different ways are there in which the 16 teams could finish this year? Almost 21 billion.
- How many different final 8s are there, including different orderings of the same set of 8 teams? Over 500 million.
- How many different final 8s are there if we ignore different orderings of the same set of 8 teams?12,870.
- How many different top 4s are there, including different orderings of the same set of 4 teams? 43,680.
- How many different top 4s are there if we ignore different orderings of the same set of 4 teams? 1,820.
- How many different Grand Final match ups are there? 120.
Those first two numbers neatly explain why there's no market for predicting the finishing order of all teams or for predicting the 8 finalists in order. By way of context, correctly selecting the finishing order of all 16 teams (under the assumptions I've made) is almost 400,000 times more difficult than winning Powerball.
So, predicting the correct finishing order for all 16 teams seems a bit hard. How many could you reasonably expect to get right? Well, again making the assumption that any given team is equally likely to finish in any given ladder position, you should expect to correctly predict the finishing order of just one team (and, you should expect almost 37% of the time to get none at all correct).