2024 : Simulating the Final Ladder Before Round 0
/For reasons outlined last year in a blog post over on the General Probability and Statistics journal, and because I feel as though the simulations last year were fairly reasonable, I am now running only hot (aka Heretical) simulations.
For anyone who is curious about the precise methodology I’ve employed, there are also some details about this in that blog post. The short version though is that, within each simulation replicate, the results of a simulated game are used to update the teams’ Ratings and Venue Performance Values, which are then used for the following game. In other words, we treat the simulated results as if they were real ones, and alter the relevant parameters accordingly.
This year’s pre Round 0 (sic) simulations suggest that the teams can be roughly grouped as follows (although such grouping is much harder this year, such is the apparent evenness of the competition):
GWS and Adelaide: 70%-75% chances of being finalists; 13-17% chances of being Minor Premier
Melbourne, Brisbane Lions, Sydney, Collingwood, and Port Adelaide: 55-65% chances of being finalists; 6.5% to 10% chances of being Minor Premier
Fremantle, Carlton, St Kilda, Western Bulldogs, and Geelong: 40-50% chances of being finalists; 4% to 6% chances of being Minor Premier
Gold Coast, Richmond, and Hawthorn: 30-40% chances of being finalists; 2-3% chances of being Minor Premier
North Melbourne and Essendon: 15% chances of being finalists; 0.5% chances of being Minor Premier
West Coast: 5% chance of being a finalist; 0.1% chance of being Minor Premier
LADDER FINISHES
The ladder projections using the Heretical outputs appear below.
The Heretical simulation methodology is quite conservative in that expected win percentages range from only 27% (for West Coast) to 64% (for GWS). As I also discussed last season, to understand why this might be the case, let’s first look at the different rating trajectories that each team follows across the 2,500 Heretical simulations. Each line on the chart below tracks a quantile for the simulated rating across all replicates for a given team. For example, the purple line for Adelaide tracks the median rating for Adelaide across each round of the home and away season.
We see that the distribution of ratings for each team spreads out as the season progresses in what looks like a symmetric fashion around the team’s initial rating. Indeed, if we just check the distribution of ratings after the final round, the symmetry is apparent (the skewnesses range from -0.08 to +0.05)
In summary then, a team is as likely to be above its initial rating by some amount as below it by that same amount at any point in the season.
Consider, then, a team that started out rated +10 and imagine it facing a team rated 0 in, say, Round 5. For illustrative purposes, let’s use for the game a margin the Normal distribution with a standard deviation of 37. The probability of victory of the +10 team would then be given in Excel by NORMDIST(10,0,37,TRUE), which is 61%.
Now let’s say the team that started +10 has, instead, dropped to +0 by Round 5. It’s chances against another +0 team are 50%, which is an 11.2% reduction. If, instead, its rating has climbed 10 points to +20, it’s chances against a +0 team would be given by NORMDIST(20,0,37,TRUE), which is 71.6%, or only a 10.6% increase.
In summary, a 10 point rating drop will reduce its victory probability by 11.2%, but a 10 point rating gain will increase its victory probability by only 10.6%.
If we do the same calculations for a team whose initial rating is -10, we find that a decline to -20 moves the victory probability from 38.8% to 28.4% (a 10.4% decline), and an increase to +0 moves the victory probability from 38.8% to 50% (an 11.2% increase).
There is, then, an asymmetry here, which tends, across a suite of replicates, to push average victory probabilities closer to 50%. That is the phenomenon we’re seeing in the Heretical simulation outputs.
In practical terms this has meant that the Heretical simulations provide higher estimates of some of the lower-rated teams’ finals chances than are implied by current market prices. This is the case for North Melbourne, Hawthorn, Richmond, Fremantle, and St Kilda.
Conversely, it also means that the Heretical simulations provide lower estimates of some of the higher-rated teams’ finals chances than are implied by current market prices. This is most notably the case for Collingwood, Brisbane Lions, Port Adelaide, Sydney, and Carlton, although it’s also likely that MoSHBODS’ underlying ratings of some of those teams is lower than the bookmakers’ estimates.
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
We can see that the vast majority of teams are currently effectively fighting for between 15 and 17 ladder positions, and that most ladder positions have 15 to 17 teams effectively fighting for them.
On the teams side, the exceptions are Adelaide, North Melbourne, GWS, Essendon, and West Coast, and on the ladder positions side, the exceptions are for 1st, 2nd, 3rd, 16th, 17th, and 18th, as is tradition (and common sense if you think about it).
We see, as we do every year, that the ladder positions with the most uncertainty are those in the middle of the table, from about 5th to 14th.
We also see that the average team is effectively competing for 15 positions, and the average ladder position has about 15 teams competing for it. These are about 1 position/team higher than last season, which implies that MoSHBODS, at least, is even less certain about this year than it was about last year.
WINS AND LADDER POSITION
With 23 games per team again this season, let’s look at the number of wins MoSHBODS thinks will be sufficient for given ladder positions.
The chart below reveals what the simulations suggest about that recalibration.
Based on the simulations, we can say that:
For teams finishing 8th in a replicate: 29% had 12 wins, 35% had 13 wins, and 10% had 12.5 wins (also, 6% had 11 wins and 10% had 14 wins)
For teams finishing 4th in a replicate: 29% had 15 wins, 30% had 16 wins, and 8% had 15.5 wins (also, 10% had 14 wins, and 5% had 14.5 wins)
Looked at another way:
For teams finishing win 11 wins: 6% made Finals
For teams finishing win 12 wins: 37% made Finals
For teams finishing win 13 wins: 82% made Finals
For teams finishing win 14 wins: 98% made Finals
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 initial estimates are that:
There’s about a 7-in-20 chance that 8th will be decided on percentages
There’s about a 3-in-10 chance that 4th will be decided on percentages
There’s about a 1-in-6 chance that 1st will be decided on percentages
