Matter of Stats

View Original

2023 : Simulating the Final Ladder After Round 17

Tony Corke

The latest simulations suggest that there are 11 teams with a 1-in-3 or better chance of playing Finals, seven teams with about a 1-in-10 or better chance of finishing Top 4, and three teams with about a 1-in-9 or better chance of finishing as Minor Premiers.

Those simulations suggest that the teams can now be roughly grouped as follows:

  1. Collingwood and Port Adelaide: almost certain of being finalists; 99% chance or better of finishing Top 4; and 40 to 50% chance of being Minor Premier

  2. Brisbane Lions: almost certain of being finalists; 95% chance of finishing Top 4; and about 10% chance of being Minor Premier

  3. Melbourne: about 95% of being finalists; 65% chance of finishing Top 4; but virtually no chance of being Minor Premier

  4. Western Bulldogs. Essendon, and Geelong: 65 to 70% of being finalists; 10% chance of finishing Top 4; and no chance of being Minor Premier

  5. St Kilda, Adelaide, and Carlton: about 40 to 50% chance of being finalists; about 3 to 4% chance of finishing Top 4; and no chance of being Minor Premier

  6. Richmond: about 33% chance of being finalists; virtually no chance of finishing Top 4; and no chance of being Minor Premier

  7. Sydney, GWS, and Gold Coast: about 8 to 16% chance of being finalists; virtually no chance of finishing Top 4; and no chance of being Minor Premier

  8. Fremantle: about 3% chance of being a finalist; virtually no chance of finishing Top 4; and no chance of being Minor Premier

  9. Hawthorn, North Melbourne, and West Coast: no chance of being finalists, finishing Top 4. or being Minor Premier

(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.

As the home and away season wanes, we again see mostly small changes in Expected Win values this week, the highest being +0.8 wins for Carlton, and the lowest -0.8 wins for Fremantle.

Essendon, Carlton, and Richmond enjoyed the largest percentage point increases in their estimated finals chances, and Adelaide and Sydney suffered the largest declines.

The range of expected wins now runs from 1.7 to 18.4 (from 1.8 to 18.2 at the end of Round 16).

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 17 saw more large reductions in the uncertainty around the final home and away ladder, and left half of the teams currently effectively fighting for between 7.5 and 10.5 ladder positions, and half the ladder positions having 7.5 to 10.5 teams effectively fighting for them.

On the teams side, those with least uncertainty remain West Coast, North Melbourne, and Hawthorn and, on the ladder positions side, those with least uncertainty are still 1st, 16th, 17th, and 18th.

We see that the ladder positions with the most uncertainty remain those in the middle of the table, from about 5th to 13th, though especially 6th through 12th.

We also see that the average team is effectively competing for about 6 positions, and the average ladder position has about 6 teams competing for it.

WINS AND LADDER POSITION

The charts below investigate the relationships between ladder position and number of wins.

Firstly, we show the relationships by team, which illustrate the comments from the previous section about the teams with least uncertainty about their final home-and-away ladder finishes (viz West Coast, Hawthorn, and North Melbourne). Contrast the results for those teams with, say, those for Carlton, St Kilda, Richmond, and Adelaide, which are the teams with the most uncertainty according to the HHI.

In the next chart we look at the probability that each team plays Finals given that it finishes with a specified number of wins.

We see that many teams are still about 25% chances of playing Finals if they finish on 12 wins, although the figure is closer to 50% for Adelaide, Carlton, Geelong, Melbourne, and Sydney, We also see that all teams have better than 75% chances of playing Finals if they finish on 13 wins.

Next, let’s look at what’s required for a Top 4 finish.

Here we see more variability across the teams and find that 14 wins will make Melbourne about 50:50 chances for a Top 4 spot, but will give most other teams only about 25% chances. Fifteen wins will make all teams except St Kilda all least even-money chances or better to finish Top 4, but makes Adelaide, Brisbane Lions, Collingwood, Geelong, Melbourne, and Port Adelaide 75% chances or better. With 16 wins, the probabilities are all comfortably over 75% for every team.

Next, we show the relationships between ladder position and wins after aggregating across teams.

Based on the simulations, we can say that:

  • For teams finishing 8th in a replicate: 34% had 12 wins (no change), 23% had 13 wins (down 2%), and 33% had 12.5 wins (up 4%). Also, 3% had 13.5 wins (no change)

  • For teams finishing 4th in a replicate: 39% had 15 wins (down 2%), 18% had 16 wins (down 1%), and 4% had 15.5 wins (no change). Also 21% had 14 wins (up 1%), and 11% had 14.5 wins (up 1%)

  • For teams finishing win 11 wins: 0.5% made Finals (no change)

  • For teams finishing win 12 wins: 34% made Finals (down 1%)

  • For teams finishing win 13 wins: 95% made Finals (up 1%)

  • For teams finishing win 14 wins: almost 100% made Finals (no change)

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 still about a 2-in-5 chance that 8th will be decided on percentages

  • There is only now a slightly lower than 1-in-4 chance that 4th will be decided on percentages (which is down by about 2 to 3% points)

  • There’s is about a 1-in-5 chance that 1st will be decided on percentages

GAME IMPORTANCE

Here is an updated list of the Top 10 most important remaining games for each team. Note that teams no longer have 10 games left to play, so matches involving other teams will make it onto their list. Note also that I have ignored games with weighted importance values below 0.01.

(For details on how this metric is calculated, see this blog)

From that table we can see that the Round 18 games are likely to be of:

  • High Importance for: Adelaide, Carlton, Essendon, Geelong, and St Kilda

  • Moderate Importance for: GWS, Sydney, and Western Bulldogs (although bordering on high for Western Bulldogs)

  • Low Importance for: Fremantle, Gold Coast, and Melbourne

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.

We still have four teams with fairly similar chances for the Flag: Collingwood at just above 11-in-50, Port Adelaide and Brisbane Lions at about 9-in-50, and Melbourne at around 1-in-6. Thereafter comes Geelong at about 1-in-14, and then Western Bulldogs and Essendon at about 1-in-25 to 1-in-33.