0-16 and on track for the finals

When Andrew Demetriou wakes up in the middle of the night – and seriously, that’s gotta be happening pretty regularly – he’s probably worrying about racism, bizarre behaviour by officials, or some combination of the two. From time to time he might even worry about competition equalisation. It’s even been suggested that the AFL might be on the way to becoming a de facto two-tier league, so much so that the AFL is off on a jaunt to the home of the fair go, America, to take a sneak peek at how they do it.

But why worry when, as I promised at the end of the last post, even a team that gets to 0-16 has a chance of making the finals? (Microscopic font: in ridiculously unlikely circumstances.) First, to set the scene: the league currently has 18 teams, who each play 22 games (cumulative research time: 30 seconds). This means the home and away season features 22×9 = 198 matches, needing 198 winners (cumulative research time: 1 minute). For the purposes of this experiment, I’m ignoring draws, docked points, Waverley Park lights-off scenarios, alien invasion, etc.

To create a scenario for the eighth-placed team to have a low number of wins, the top 7 teams need to dominate the league, leaving only relatively few matches available for winning by the other 11. They need to beat the other 11 teams all the time, and not play each other twice; therefore they play only 6 matches against other dominant teams, for 3 wins and their only 3 losses of the season. 3 losses means 19 wins; 7 teams with 19 wins is 133 wins, leaving just 65 wins to divide amongst the remaining 11 teams at an average of less than 6 each (cumulative research time: 5 minutes).

So, what’s the easiest and clearest way to show all this? (Cumulative research time: ever since last post.)

Below is an 18-team football league schedule shown in a matrix. The greyed-out boxes stop teams from playing against themselves (although I’m sure the AFL would schedule Collingwood vs Collingwood if they thought it’d draw a crowd), the part of the matrix below the grey boxes is where every team initially plays every other team.

So, in the 0-16 scenario, here are the league results for the first 17 games, and the league ladder. The letters in the grid represent, with suspiciously alphacentric convenience, the winners of each contest.

Rounds 1-17

Schedule rounds 1-17

It takes little imagination, I hope, to picture Healesville winning its seventeenth game (little more than picturing this league at all, anyway) after starting 0-16.

The remainder of the schedule is at the discretion of the league administration. In the AFL, this means balancing the needs and requests of the clubs; in this instance it means rigging it to prove my point.

Schedule rounds 1-22

Schedule rounds 1-22

And with percentage the standard tie-breaker, there are plenty of result combinations leading to Healesville claiming eighth, and no doubt drafting their email to the Guinness Book of Records before the post-match ales are poured.

Assuming that you don’t find the whole thing unlikely enough already, keep in mind that a team with the ability to win 6 games in a season (approximately 27%), the probability of losing 16 games in a row is around 1 in 163. (There are a lot of assumptions built into that statement. But still.)

So the question for Demetriou is, what’s worse? A somewhat uneven competition where some teams get regularly belted and repeat finalists abound… or two unambiguously different sets of teams, who put on an “any team can make it” round 22 race for eighth place? And seventh, sixth, fifth…

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