2023 : Simulating the Final Ladder Before Round 1 - Fixed
/(NB This post replaces an earlier one in which I erroneously applied twice the mean regression used to convert end-of-season ratings into start-of-season ratings for the following year. That, understandably, significantly reduced the spread of Ratings.
Nothing is as reliable as making early season errors after 6 months off. Apologies if this has caused you any issues.)
For reasons outlined in a blog post over on the General Probability and Statistics journal, I’ll only be running - at least for now - hot simulations this season, which I’ll continue to refer to as Heretical Simulations for reasons of historical continunity and personal amusement.
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 exactly as if they were real ones.
The simulations suggest that the teams can now be roughly grouped as follows:
Geelong: 90% chance of being a finalist; 34% chance of being Minor Premier
Richmond, Collingwood, Melbourne, Port Adelaide, and Sydney: 59 to 64% chance of being a finalist; 6.5% to 9% chance of being Minor Premier
Western Bulldogs, Brisbane Lions, Carlton, and Fremantle: 49 to 53% chance of being a finalist; 4% to 6% chance of being Minor Premier
Gold Coast, St Kilda, GWS, and Adelaide: 31 to 39% chance of being a finalist; 1.5% to 2% chance of being Minor Premier
Essendon and Hawthorn: 22% chance of being a finalist; 0.5% to 1% chance of being Minor Premier
West Coast and North Melbourne: 5.5 to 10% chance of being a finalist; less than 0.5% 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 North Melbourne) to 73% (for Geelong). 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 the simulated rating across one replicate (although the individual lines are imopssible to differentiate).
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 -0.11 to +0.10)
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 St Kilda, Gold Coast, GWS, Adelaide, and Hawthorn.
Probably the most notably lower estimates for making Finals are for Melbourne, Brisbane Lions, Carlton, and maybe Richmond, Sydney, and West Coast.
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
HERETICAL METHODOLOGY
We can see that the vast majority of teams are currently effectively fighting for between 14 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 West Coast, North Melbourne, and Geelong, and on the ladder positions side, the exceptions are for 1st, 2nd, 3rd, 16th, 17th, and 18th.
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 14 positions, and the average ladder position has about 14 teams competing for it. These numbers confirm the relative conservatism of the Heretical simulation results at this point in the season.
WINS AND LADDER POSITION
With an extra game added to the fixture this season for every team, we’ll need to recalibrate the number of wins we think 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: 32% had 12 wins, 32% had 13 wins, and 9% had 12.5 wins
For teams finishing 4th in a replicate: 30% had 15 wins, 29% had 16 wins, and 8% had 15.5 wins (also 9% had 14 wins, and 5% had 14.5 wins)
For teams finishing win 11 wins: 7% made Finals
For teams finishing win 12 wins: 41% made Finals
For teams finishing win 13 wins: 83% made Finals
For teams finishing win 14 wins: 99% 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 9-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 3-in-20 chance that 1st will be decided on percentages
GAME IMPORTANCE
Unlike the Standard methodology, the Heretical methodology does not tend to push more distant games towards being 50:50 contests, so I feel a little more comfortable reinstating my game importance analysis this season.
To calculate a game’s importance for a particular team we first take the probability that this team plays Finals when the home team in that game wins. We then weight that probability by our estimated probability that the home team wins. Call that number H.
Next, we take the probability that this team makes Finals when the home team in that game loses. We then weight that probability by our estimated probability that the home team loses. Call that number A.
We then calculate the absolute value of H - A, which is a weighted measure of the importance of that game to that team’s Finals chances.
Lastly, we calculate this for all 18 teams and average the result to give us a measure of average weighted game importance across all teams. The higher the value, the more the result of that game affects teams’ Finals chances, and the more “important” it therefore is.
We could, of course, omit the weighting steps in the individual game calculations, but that can mean we rate a game as very important because of the Finals implications of an incredibly unlikely outcome. The weights are there to adjust for this and give us a “likely” impact for each team.
If we perform those calculations using the Heretical outputs, we find that the 30 most important games are as shown below.
We find that, for now at least, the early rounds are assessed as being relatively unimportant in the strict context of deciding who does or does not play Finals. It’s not until the Round 7 Sydney v GWS game that we get something in the Top 15, and there are also two other Round 7 games, and one Round 8 game.
Also in the Top 30 is the Dogs v Saints Round 2 clash, and the Crows v Dockers Round 4 matchup.
