Matter of Stats

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2023 : Simulating the Final Ladder After Round 23

Tony Corke

Things are a lot simpler after last weekend, at least as far as Minor Premier, Top 4, and Top 8 are concerned, and the simulations now suggest that the teams can be roughly grouped as follows:

  1. Collingwood: certain of finishing Top 4; and about 85% chance of being Minor Premier

  2. Brisbane Lions: certain of finishing Top 4; about a 15% chance of being Minor Premier

  3. Port Adelaide: certain of finishing Top 4; tiny chance of being Minor Premier (needs Collingwood to lose, Brisbane Lions to draw or lose, and to win by enough to lift their percentage above Collingwood’s. Roughly speaking, the sum of Collingwood’s losing margin and their own winning margin needs to be about 190 points or more)

  4. Melbourne: certain of finishing Top 4; no chance of being Minor Premier

  5. Carlton, St Kilda, and Sydney: certain of being finalists; no chance of finishing Top 4

  6. GWS: 70% chance of being finalists; no chance of finishing Top 4

  7. Western Bulldogs: 28% chance of being finalists; no chance of finishing Top 4

  8. Essendon, Geelong, Adelaide, Richmond, Gold Coast, Fremantle, Hawthorn, North Melbourne, and West Coast: no chance of being finalists

(For anyone who is curious about the precise methodology used for these simulations, please refer to this blog post over on the General Probability and Statistics journal)

LADDER FINISHES

The ladder projections using the Heretical outputs appear below.

The range of expected wins now runs from 3.1 to 17.8 (from 2.1 to 18.3 at the end of Round 22).

TEAM AND POSITION CONCENTRATION

The HHI figures for these pre-season simulation replicates appear below. These provide us with estimates of:

  • How many ladder positions a team is currently effectively fighting for

  • How many teams are currently effectively fighting for a given ladder position

Round 23 produced the highest single round overall decrease in the uncertainties around the final home and away ladder, but still left more than half of the teams currently effectively fighting for between about 2 and 4 ladder positions, and more than half the ladder positions having 2 to 3.5 teams effectively fighting for them.

There were particularly large decreases in uncertainty for Geelong, GWS, St Kilda, Adelaide, and Sydney, and for positions 7th and 10th through 13th.

On the teams side, those with least uncertainty are North Melbourne, West Coast, Collingwood, Melbourne, Carlton, and Hawthorn, and and, on the ladder positions side, those with least uncertainty are now 1st, 4th, and 5th, and 16th through 18th.

We see that the ladder positions with the most uncertainty remain those in the middle of the table, from about 6th to 12th.

We also see that the average team is effectively competing for about 2.2 positions, and the average ladder position has about 2.1 teams competing for it.

LIKELY IMPORTANCE OF PERCENTAGE

Next, we’ll use the simulations to investigate the estimated likelihood that any given pair of ladder positions will be determined after Round 24 based on percentage.

So, our new estimates are that:

  • There is now only about a 35% chance that 8th will be decided on percentages (which is down by about 30% points)

  • There is now no chance that 4th will be decided on percentages

  • There’s now almost a 1-in-5 chance that 1st will be decided on percentages (which is up by more than 5% points)

TOP X TEAMS

Top 2

In the latest simulations there were only three combinations of teams that finished 1st and 2nd in a given order at the end of the home and away season in at least 5% of replicates:

  • Collingwood / Brisbane Lions: 64%

  • Collingwood / Port Adelaide: 20%

  • Brisbane Lions / Collingwood: 15%

Top 4

In the latest simulations there were four combinations of teams that finished 1st through 4th in a given order at the end of the home and away season in at least 5% of replicates:

  • Collingwood / Brisbane Lions / Port Adelaide / Melbourne: 60%

  • Brisbane Lions / Collingwood / Port Adelaide / Melbourne: 14%

  • Collingwood / Port Adelaide / Brisbane Lions / Melbourne: 12%

  • Collingwood / Port Adelaide / Melbourne / Brisbane Lions: 8%

Top 8

In the latest simulations there were four combinations of teams that finished 1st through 8th in a given order at the end of the home and away season in at least 5% of replicates:

  • Collingwood / Brisbane Lions / Port Adelaide / Melbourne / Carlton / Sydney / St Kilda / GWS: 19%

  • Collingwood / Brisbane Lions / Port Adelaide / Melbourne / Carlton / Sydney / St Kilda / Western Bulldogs: 10%

  • Collingwood / Brisbane Lions / Port Adelaide / Melbourne / Carlton / St Kilda / Sydney / GWS: 9%

  • Collingwood / Brisbane Lions / Port Adelaide / Melbourne / Carlton / St Kilda / Sydney / Western Bulldogs: 6%

FINALS CHANCES

Finally we take another look at team’s chances all the way through to the Grand Final, making reasonable assumptions about where Finals will be played given the participants and week of the Finals.

GRAND FINALS

In the latest simulations there were six pairs of teams that met in the Grand Final in at least 5% of replicates:

  • Brisbane Lions / Melbourne: 16%

  • Collingwood / Brisbane Lions: 12%

  • Port Adelaide / Melbourne: 10%

  • Port Adelaide / Brisbane Lions: 9%

  • Collingwood / Port Adelaide: 7%

  • Collingwood / Melbourne: 6%

Altogether, there were 34 different Grand Final pairings across the 10,000 replicates.

POINT OF ELIMINATION

Melbourne are now slight Flag favourites according to the simulation results where we have:

  • Melbourne at about 24%

  • Brisbane Lions at about 21%

  • Collingwood at about 16%

  • Port Adelaide at about 15%

  • Carlton at about 11%

  • Sydney and St Kilda at about 5%

  • GWS at about 3%

  • Western Bulldogs at about 1%