Matter of Stats

View Original

2023 : Simulating the Final Ladder After Round 15

Tony Corke

There are still nine teams with about a 1-in-2 or better chance of playing Finals, seven teams with about a 1-in-9 or better chance of finishing Top 4, and three teams with about a 1-in-8 or better chance of finishing as Minor Premiers.

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

  1. Port Adelaide: almost certain of being finalists; 95% chance of finishing Top 4; and 50% chance of being Minor Premier

  2. Collingwood: almost certain of being finalists; 90% chance of finishing Top 4; and 30% chance of being Minor Premier

  3. Brisbane Lions: almost certain of being finalists; 80% chance of finishing Top 4; and about 10 to 15% chance of being Minor Premier

  4. Melbourne: 95% of being finalists; 70% chance of finishing Top 4; and about 5% chance of being Minor Premier

  5. Western Bulldogs: 65% of being finalists; 15 to 20% chance of finishing Top 4; and virtually no chance of being Minor Premier

  6. Essendon, Geelong, St Kilda,and Adelaide: about 45 to 55% chance of being finalists; about 7 to 11% chance of finishing Top 4; and virtually no chance of being Minor Premier

  7. Richmond, Gold Coast, and Sydney: about 30% chance of being finalists; about 2 to 3% chance of finishing Top 4; and virtually no chance of being Minor Premier

  8. Fremantle and Carlton: about 15% chance of being a finalist; about 0.5 to 1% chance of finishing Top 4; and no chance of being Minor Premier

  9. GWS: about 6% chance of being a finalist and virtually no chance of finishing Top 4 or being Minor Premier

  10. Hawthorn, North Melbourne, and West Coast: little to 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.

We see only small changes in Expected Win values again this week, the highest being +0.9 wins for Sydney, and the lowest -0.7 wins for Essendon and Hawthorn.

Sydney enjoyed the largest percentage point increases in their estimated finals chances and Essendon and St Kilda suffered the largest decline.

The range of expected wins now runs from 1.7 to 17.9 (from 2.1 to 17.9 at the end of Round 14).

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 15 did nothing to reduce the uncertainty around the final home and ladder and left just over half of the teams are now currently effectively fighting for between 9.5 and 11.5 ladder positions, and half the ladder positions having 10 to 11 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 11th.

We also see that the average team is effectively competing for about 7.6 positions, and the average ladder position has about 7.6 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 Sydney, St Kilda, Essendon, and Geelong, 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 only about 25% chances of playing Finals if they finish on 12 wins, although the figure is closer to 50% still for Adelaide, Geelong, Melbourne, and Sydney, We also see that teams have mostly better than 75% chances of playing Finals if they finish on 13 wins, with Port Adelaide the obvious exception.

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

Here we see more variability across the teams but find that 15 wins will still make most teams about even-money chances or better to finish Top 4. With 16 wins, the probabilities are all comfortably over 75%.

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: 36% had 12 wins (up 1%), 39% had 13 wins (up 3%), and 16% had 12.5 wins (no change). Also, 3% had 14 wins (no change), and 3% had 13.5 wins (down 1%)

  • For teams finishing 4th in a replicate: 44% had 15 wins (up 1%), 21% had 16 wins (down 5%), and 4% had 15.5 wins (no change). Also 20% had 14 wins (up 5%), and 5% had 14.5 wins (no change)

  • For teams finishing win 11 wins: 1% made Finals (down 1%)

  • For teams finishing win 12 wins: 29% made Finals (down 4%)

  • For teams finishing win 13 wins: 88% made Finals (down 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 now about a 4-in-9 chance that 8th will be decided on percentages (which is up by about 4% points)

  • There is still a slightly lower than 1-in-3 chance that 4th will be decided on percentages

  • There’s is still a slightly less than 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.

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

From that table we can see that the Round 16 games are likely to be of moderate to large importance to the Finals chances of Essendon, Fremantle, Geelong, Gold Coast, Richmond, Sydney, and Western Bulldogs. A pivotal round indeed, then.

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 now have four teams with fairly similar chances for the Flag: Port Adelaide and Melbourne around 1-in-5, and Collingwood and Brisbane Lions around 3-in-20. Thereafter comes Geelong at about 1-in-14, and then Western Bulldogs, Adelaide, Richmond, Sydney, and Essendon all in the 3% to 4.5% range.