This time last year the Australian Football League was under attack for the unfairness of its finals series.
This year it has changed the system slightly. The result is a completely fair finals system. Let me explain.
Last year the AFL had just moved from having a final five to having a final six.
The new final-six system was branded as unfair. It was unfair (for reasons which don’t matter now) and needed modifications. As a result of the changes no-one should complain. This is what happens:
The six finalists this year are in order: 1. Geelong, 2. Footscray, 3. Collingwood, 4. West Coast, 5. Hawthorn, 6. St Kilda.
In Round One of the finals, 4 plays 5 and 3 plays 6. The losers are eliminated. 1 plays 2.
The results determine a new final four. We’ll assume 1 and 4 win. The order of the final four depends on which of 3 v 6 wins.
If 6 wins, the order is 1, 4, 2 and 6. If 3 wins it is 1, 3, 4 and 6.
That final four plays in the traditional way. Let’s rename the final four as A, B, C and D. C plays D in the first semi-final. Let’s assume C wins. D is eliminated. A plays B in the second semi-final. Let’s assume A wins. B plays C in the preliminary final and the win of that plays A in the grand final.
In total there are seven games in the finals. This gives a total of 128 combinations. For the mathematically minded, 128 is two to the power of seven.
On its face, the system still seems unfair. How is it that the third-placed team can be eliminated by the sixth-placed? In the old final-five system, the third team got a second chance for its efforts. Now it can get the chop in the first game.
As a Collingwood supporter who remembers with some bitterness the 1966 grand final won by St Kilda, it seems especially irksome that St Kilda could do this very thing this weekend. That is why I sat down to prove how unfair the new system is. The result is quite the contrary. The system proves very fair.
The test of its fairness is that those higher up the ladder should have more chances of winning the grand final. Of course, it would be simpler to give the premiership to the side that tops the ladder at the end of the home-and-away series, like the British Football League Cup. But that would boring and would not yield any television dollars, nor huge gates.
Given a final series is necessary, as well as making for top spectator sport, it should be fair.
Let’s assume each team has an even chance of winning every game in the finals series. There are 128 games. The chances of each team winning the grand final are as follows: First and second each have 32 chances in 128, third has 24 chances, fourth and fifth have 16 chances and sixth has 8 chances. In summary, first and second each have four chances in sixteen (one in four), third has three in sixteen, fourth and fifth have two in sixteen and sixth has one in sixteen.
That is a very reasonable tailoring of winning chances to place on the ladder.
The top teams rightly get the easy run to the grand final.
Of course, all this is on paper. The quirks of game and the form of the sides can make a huge difference. The other finalists must be mightily pleased, for example, that Hawthorn has to travel to Perth where West Coast will do their dirty work for them. Hawthorn’s form belies its low place on the ladder. That quirk of placings alone will affect this final series more profoundly than the probability theorist’s paper summary.
Injuries, the weather and grounds more favourable to some teams will also affect the result.
That said, however, the AFL finals this year will be played on at least mathematically level playing fields.