# The probability of winning the AFL premiership

I realise this as nothing to do with hydrology…

What is the probability that any particular team will win the AFL premiership?  One important factor is ladder position at the end of the home and away season.   The AFL has a final 8, but the teams in positions 1 to 4 have the advantage of being able to lose one game but stay in the competition.  For the teams in positions 5 to 8, one loss and you are out.  This has a big impact on the probability of winning the flag.

Consider a final series of 8 equal teams.  To win from positions 1 to 4 you have to win three in a row or lose 1 and win three. So if there is a 50:50 chance of winning each game the probability of winning the premiership is:

P(win from 1:4) = 0.5^3 + 0.5^4               (1)

To win from 5:8 you need to win 4 in a row so the probability is:

P(win from 5:8) = 0.5^4                            (2)

The ratio of these two equations quantifies the advantage of being in the top half of the ladder.

P(win from 1:4)/P(win from 5:8) = 3

So for equal teams, the probability of winning from positions 1 to 4 is three times that of winning from 5 to 8. Actually, the odds favouring the top 4 are even higher than this because they are generally stronger teams.

Lets look at the data.  The final 8 started in 1994 so we’ve had 20 premierships since then.  If all the teams in the top 8 were equal we would expect teams in positions 1 to 4 to have won 75% of the time.  In fact they have won 95% of the time.  The single exception is Adelaide winning from 5th in 1998.  The graph below shows that in most years, teams finishing in positions 1 and 2 are clearly ahead of the rest; 75% of finals have been won by these teams.

The upshot is that Tigers fans (I’m one) shouldn’t be getting too excited just yet.  Any team that wins from positions 5 to 8 has to be very strong, and and very lucky.

Number of premierships v ladder position at the start of the finals