2023 : Simulating the Final Ladder After Round 13
/There are now nine teams with about a 5-in-9 or better chance of playing Finals, nine teams with about a 1-in-9 or better chance of finishing Top 4, and three teams with about a 1-in-7 or better chance of finishing as Minor Premiers.
Those simulations suggest that the teams can now be roughly grouped as follows:
Port Adelaide and Collingwood: almost certain of being finalists; 85 to 90% chance of finishing Top 4; and 35 to 40% chance of being Minor Premier
Melbourne: almost certain of being finalists; 75% chance of finishing Top 4; and about 15% chance of being Minor Premier
Brisbane Lions: about 90% chance of being finalists; 60% chances of finishing Top 4; and 8% chance of being Minor Premier
St Kilda and Essendon: about 65 to 70% chance of being finalists; about 20 to 25% chance of finishing Top 4; and 2% chance of being Minor Premier
Western Bulldogs, Adelaide, and Geelong: about 55 to 60% chance of being finalists; 10 to 15% chance of finishing Top 4; and about 0.5% chance of being Minor Premier
Gold Coast and Fremantle: about 30% chance of being finalists; about 4% chance of finishing Top 4; and virtually no chance of being Minor Premier
Richmond and Sydney: about 20% chance of being a finalist; 1.5% chance of finishing Top 4; and virtually no chance of being Minor Premier
Carlton: roughly 7% chance of being finalists; and little to virtually no chance of finishing Top 4 or being Minor Premier
GWS: about 3% chance of being a finalist and virtually no chance of finishing Top 4 or being Minor Premier
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 +1.1 wins for Hawthorn, and the lowest -1.1 wins for Brisbane Lions.
Adelaide enjoyed the largest percentage point increases in their estimated finals chances, though Essendon and St Kilda enjoyed similar gains. Fremantle suffered the largest decline, but there were also significant drops for Western Bulldogs, Sydney, and Carlton.
The range of expected wins now runs from 2.1 to 17.4 (from 2.5 to 17.8 at the end of Round 11).
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 13 results left us with the lowest level of overall uncertainty we’ve had this year, with that around teams falling by about 0.3 positions per team, and that around ladder positions falling by about 0.3 teams per position. Half of the teams are now currently effectively fighting for between 10 and 12 ladder positions, and half the ladder positions have 9.5 to 11.5 teams effectively fighting for them.
On the teams side, those with least uncertainty are 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 12th.
We also see that the average team is effectively competing for about 7.8 positions, and the average ladder position has about 7.9 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 St Kilda, Fremantle, Geelong and Gold Coast, 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 most teams are still only about 25% chances of playing Finals if they finish on 12 wins, but mostly better than 75% chances 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 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 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: 27% had 12 wins (no change), 46% had 13 wins (up 1%), and 11% had 12.5 wins (no change). Also, 8% had 14 wins (no change), and 4% had 13.5 wins (down 1%)
For teams finishing 4th in a replicate: 44% had 15 wins (up 1%), 27% had 16 wins (no change), and 5% had 15.5 wins (no change). Also 14% had 14 wins (no change), and 5% had 14.5 wins (up 1%)
For teams finishing win 11 wins: 1% made Finals (no change)
For teams finishing win 12 wins: 25% made Finals (no change)
For teams finishing win 13 wins: 80% made Finals (no change)
For teams finishing win 14 wins: 99% 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 remains a slightly higher than 35% chance that 4th will be decided on percentages
There’s still about a 1-in-5 chance that 1st will be decided on percentages
GAME IMPORTANCE
Having done further analysis, I think I might have been too hasty in rejecting my weighted game importance metric as being too prone to sampling error, especially if we use it solely to order the remaining games by importance for each team, and to get a sense of relatively how important each game is. That is what has been done in the table below.
The metric provides an estimate of how much the result of a particular game is likely to change a team’s Finals chances, relative to their overall unconditional chances. The calculation for each game involves:
calculating the proportion of replicates in which the team we’re interested in makes the Final 8 given a home team victory in the game in question (call this PH)
calculating the proportion of replicates in which the team we’re interested in makes the Final 8 given a draw in the game in question (call this PN)
calculating the proportion of replicates in which the team we’re interested in makes the Final 8 given a home team loss in the game in question (call this PA)
calculating the overall proportion of replicates in which the team we’re interested in makes the Final 8, ignoring the result of the game in question (call this PU)
calculating the overall proportion of replicates in which the home team wins the game in question (call this PW)
calculating the overall proportion of replicates in which the game in question finishes as a draw (call this PD)
calculating the overall proportion of replicates in which the home team loses the game in question (call this PL)
The weighted game importance metric is then:
GI = PW x abs(PH - PU) + PD x abs(PN - PU) + PL x abs(PA - PU)
As you would expect, this metric tends to be highest for games in which the team in question is playing, as you can see in the table above.
From that table we can see that the Round 14 games are generally of small or no importance to teams, the exceptions being Fremantle, Geelong, and Gold Coast. Whilst the Round 14 clash is second on the list for Port Adelaide, its relative importance is quite small.
(I have a strong suspicion that GI can be expressed in a simpler form by recognising that PW + PD + PL =1 and PU = PW x PH + PD x PN + PL x PA).
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 three near equal favourites for the Flag with Melbourne highest at 2-in-9 followed by Colingwood at 1-in-5, and then Port Adelaide at 1-in-6. Thereafter comes Brisbane Lions at 1-in-9, Geelong at 2-in-25, and then St Kilda, Western Bulldogs, Essendon, and Adelaide all in the 1-in-33 to 1-in-20 range.
