Matter of Stats

View Original

2024 : Simulating the Final Ladder After Round 9

Tony Corke

This year’s post Round 9 simulations suggest that the teams can be roughly grouped as below:

(For anyone who is curious about the precise methodology I’ve employed, see this blog post over on the General Probability and Statistics journal)

  1. Sydney and Geelong: 95% chances of being finalists; 70-80% chances of Top 4; 20-40% chances of being Minor Premier

  2. Melbourne: 85% chances of being finalists; 50% chances of Top 4; 10% chances of being Minor Premier

  3. Carlton, GWS, Collingwood, Port Adelaide, and Essendon: 65-75% chances of being finalists; 25-35% chances of Top 4; 5% chances of being Minor Premier

  4. Brisbane Lions, Fremantle, Gold Coast, and Western Bulldogs: 35-45% chances of being finalists; 10% chances of Top 4; 0.5-1% chances of being Minor Premier

  5. Adelaide, St Kilda, and Hawthorn: 5-10% chance of being finalists; tiny chance of Top 4; none or virtually no chance of being Minor Premier

  6. West Coast, Richmond, and North Melbourne: none or virtually no chance of being finalists; none or virtually no chance of Top 4; no chance of being Minor Premier

There is now, then, an emerging gap between a clear Top 8 and the rest of the teams, and also a clear Top 2.

LADDER FINISHES

The ladder projections using the Heretical outputs appear below.

There were a few large movements in teams’ Final chances this week, with Fremantle’s and GWS’ Finals chances falling most substantially (c 10 to 20% points), and Port Adelaide’s, Essendon’s and Western Bulldogs’ rising most substantially (c 13% points).

There are now only 8 teams with a 50% or better chance of playing Finals, and eight teams with a 25% or higher chance of finishing Top 4. There are also three teams with about a 10% or better chance of taking the Minor Premiership.

TEAM AND POSITION CONCENTRATION

The HHI figures for the latest 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

Overall ladder uncertainty fell only a little this week, with the nine least certain teams now effectively fighting for between 12 and 13 ladder positions, and the nine least certain ladder positions having 11 to 13 teams effectively fighting for them.

On the teams side, the largest exceptions are North Melbourne, Richmond, Sydney, and West Coast, while on the ladder positions side, the largest exceptions are 1st, 16th, 17th, and 18th.

Tthe ladder positions with the most uncertainty remain those in the middle of the table, from about 3rd to 13th.

We also see that the average team is effectively competing for about 9.2 positions, and the average ladder position has about 9.1 teams competing for it.

WINS AND LADDER POSITION

Let’s look at the number of wins MoSHBODS thinks will be sufficient for given ladder positions.

Based on the simulations, we can say that:

  • For teams finishing 8th in a replicate: 13% had 12 wins (down 9%), 38% had 13 wins (down 1%), and 17% had 12.5 wins (also, 0.5% had 11 wins, and 17% had 12.5 wins).

  • For teams finishing 4th in a replicate: 32% had 15 wins (no change), 26% had 16 wins (down 2%), and 16% had 15.5 wins (also, 6% had 14 wins, and 9% had 14.5 wins).

To me, it still looks like 12.5 or 13 wins will be needed to play Finals, and possibly 15 will be good enough for Top 4.

Looked at another way:

  • For teams finishing win 11 wins: 0.5% made Finals (down 1.5%)

  • For teams finishing win 12 wins: 15% made Finals (down 9%)

  • For teams finishing win 13 wins: 69% made Finals (down 7%)

  • For teams finishing win 14 wins: 98% made Finals and 6% finished Top 4 (down 1%)

  • For teams finishing win 15 wins: 46% finished Top 4 (up 1%)

  • For teams finishing win 16 wins: 89% finished Top 4 (up 1%)

Here’s what it looks like on a team-by-team basis:

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 current estimates are that:

  • There’s now a bit less than a 1-in-3 chance that 8th will be decided on percentages (down by about 2% on last week)

  • There’s still only about a 3-in-10 chance that 4th will be decided on percentages (up by about 1% on last week)

  • There’s still about a 1-in-6 chance that 1st will be decided on percentages (down by about 0.5% on last week)

FINALS CHANCES

Finally, here’s what the simulations provide by way of finals-related probabilities.

Melbourne continues to fare well in Grand Finals because of the likelihood that it will meet an interstate team and because of its relatively high VPV there.