A fair crack of the whip

by Burkard Polster and Marty Ross

The Age, 3 September 2007

What is a fair finals system for the AFL? Obviously, one that allows our beloved Saints to win! Apart from that, it is clear that the higher finishing teams should receive some advantage. But exactly how much advantage?

At one extreme, we could copy the English Premier League and simply declare the league leader to be the Premiership winner; this would delight current Cats fans, but no one else. At the other extreme, we can use the ladder only for the seeding of selected teams in a knockout competition, as is used in most American sports.

Since 1897, the AFL-VFL has used many different systems, lying between the above extremes. What is distinctive about most of these systems is the granting of the "double chance”: the systems are essentially knockout, but one or more teams are permitted to lose a game. How much advantage does the double chance give? To simplify things, we'll assume all the teams are of equal strength and we’ll ignore home ground advantage. So, we’ll regard every game as 50-50 (yes, even the Cats versus the Saints).

For most years up to 1930, the VFL used the "Argus System". The top four teams played in a knockout competition beginning with - for Heavens knows what reason - the pairings 1 v 3 and 2 v 4. The winners then played off in a Final. However, if the league leader failed to win, then the leader could challenge. So, the leader had a 1/4 chance of winning in the original competition, but if they lost (a 3/4 chance), they still had a 1/2 chance of winning the Challenge Final. It then works out that the leader had a 5/8 chance of winning the Premiership, and the other finals teams each had a 1/8 chance.

Rightly or wrongly, the Argus system was seen as giving too much advantage to the leader – the Saints were cruelly robbed by the Challenge in 1913 - and in 1931 the Page-McIntyre System was introduced. Here, the pairing was 1 v 2, with the winner going on to Grand Final. The loser received the double chance, playing the winner of 3 v 4 in the Preliminary Final, for the right to also go on to the Grand Final. This system gave 1 and 2 a 3/8 chance of winning, with 3 and 4 having again a 1/8 chance.

From 1972 to the present, the AFL finals have expanded to include five teams (1972), six teams (1991), and finally, since 1994, to eight teams. With the increasing number of teams, the balancing of probabilities is very difficult: there needs to be sufficient incentive to finish high on the ladder, but the other teams in the finals can expect some decent chance as well.

Arguably the fairest system was the McIntyre Final Eight system, used from 1994 to 1999. Here the parings were 1 v 8, 2 v 7, and so on. The two lowest placed losers were eliminated, and the two highest placed winners gained entry to two Preliminary Finals. The remaining teams played in semifinals, to qualify for the Preliminary Finals. Finally, the winners of the two Preliminary Finals played in the Grand Final. The probabilities of winning descended slowly: 6/32 for 1 and 2, 5/32 for 3, 4/32 for 4 and 5, 3/32 for 6, and 2/32 for 7 and 8.

It may have been popular with mathematicians, but the McIntyre Final Eight System was widely criticized by footy fans. In particular, it was possible for 3 and 4 to be eliminated in the first week, and this was considered unfair.

Consequently, in 2000 the finals system was revised to its current form, where the double chance was guaranteed to the top four teams. This gives those teams a 3/16 chance, with 5 through 8 having a 1/16 chance. This might now be very annoying for Collingwood fans, perhaps watching their team fall into 5th place. But, it can be argued that the top four teams have earned their significantly greater chance. And anyway, any finals system that annoys Pies fans can’t be all bad!