2019 : Simulating the Final Ladder After Round 4
/We’re four rounds in, so it must be time to start simulating the remainder of the home and away season to investigate, at this very early stage, how MoSHBODS sees the teams faring from here.
METHODOLOGY
Again this year, projections for the remaining games will be made using the MoSHBODS System.
Probability estimates will be derived using MoSHBODS' opinions in the following way:
Teams' offensive and defensive ratings as at the end of the most-recently completed round will be used, along with the most-recent Venue Performance Values, to calculate expected scores for both the Home and the Away team in every remaining game of the home and away season.
In that calculation for each contest, both teams' offensive and defensive ratings will be perturbed by a random amount based on drawing from a Normal distribution with mean 0 and a standard deviation that increases the further away the forecast is being made. This year, that standard deviation will increase with (4.5 times) the square root of the numbers of days between the game being forecast and the date of the next upcoming game. So, a game that’s 30 days away from the first game being simulated will use a standard deviation of 4.5 x sqrt(30) = 24.7. Both the choice of 4.5 as the multiplier and the square root as the appropriate functional form are somewhat arbitrary, although they were best amongst a number of options that I chose in reproducing the TAB bookmaker’s current Top 4 and Top 8 prices (assuming equal overround in each price).
The methodology here - which treats variability as increasing linearly with time - contrasts with the methodology used last year where we assumed it was constant over time. Last year, the standard deviation was 24 for games played next week and for games played in 20 weeks’ time. Incorporating a time-varying standard deviation reflects the reality of increased levels of uncertainty the further into the future we look, without the need to move to a “hot’ approach to simulation (ie one where we update ratings based on simulated results.)These expected scores will be converted into expected Scoring Shots using the average Scoring Shot conversion rate for all teams from 2018 (about 52%). If, when we make the random perturbations for a game, either team is then expected to register fewer than 10 Scoring Shots, their expectation is set to exactly 10 Scoring Shots
In turn, these expected Scoring Shots values will be used to simulate the outcome of each remaining game in the season, using a model similar to the one derived in this 2014 blog, which comprises a random draw for each team first for Scoring Shots and then for a Conversion rate.
In this latest set of simulations, the entire remaining season was simulated 50,000 times.
RESULTS
The table below should be fairly self-explanatory and it feels a little early to be making any meaningful comments about trends, so for this week I'll provide it without commentary other than to note that I think this year’s methodology is likely to be very conservative in terms of the range of expected wins at this point in the season because the high levels of uncertainty it assumes for games far off into the distance turns them into nearer 50:50 contests (see this related post to understand why additional uncertainty helps weaker teams).
That conservatism will only pay off if the season is appropriately unpredictable.
GAME IMPORTANCE
This year, as for the last few years, I'm going to use the results of the simulations to estimate the importance of each of the remaining games to the finals chances of every team. For this purpose I'll be first using a measure that I now know was proposed by Mark F Schilling and which defines the importance of game G to a team T as the change in that team's chances of achieving some goal - here, making the finals - if the Home team wins that game compared to if the Home team loses. (I'll be ignoring draws in this calculation).
To estimate this for a particular game and team using the simulation results we simply look at how often that team made the finals in all the simulation replicates where the Home team won the game being analysed, and compare this to how often it made the finals when the Home team lost that game.
The differences is those percentages are what's shown in the middle portion of the table below (which can be clicked on to access a larger version).
Shown here are the 25 games estimated as likely to have the greatest impact on the composition of the finalists - more on which in a minute.
The core of the table shows, for example, that Hawthorn’s estimated chances of making the finals differ by about 18% points depending on whether they win or lose their Round 10 clash with Port Adelaide (in which, Hawthorn are the Home team).
We can see that games generally have most impact on the finals chances of the teams directly involved in them, but that there can also be secondary effects for other teams expected to be in the race for finals spots. For example, for that same game, Richmond’s chances are reduced by just over 1% if Hawthorn prevail instead of Port Adelaide.
The first coloured column of the table is the Weighted Average Importance figure, which is the basis on which the 25 games shown here were determined and which is calculated for any game as follows:
Calculate the probability-weighted absolute change in a team's chances of making the final 8 across the three possible outcomes, Home win, Draw, Home loss. So, for example, if a team were a 27% chance of making the finals if the Home team won, a 26% chance if they drew, and a 22% chance if the Home team lost, and if the probabilities of those three outcomes were 70%, 1% and 29%, respectively, the calculation would be:
70% x abs(27% - 25.5%) + 1% x abs(26% - 25.5%) + 29% x abs(22% - 25.5%) = 2.1%
The 25.5% used in the calculation is the team's unconditional probability of making the finals, and the final number can be thought of as the expected absolute change in the team's finals chances after the result of this particular game is completed.Form a simple average of these expected absolute changes.
This final figure can be thought of as the average amount by which teams' finals chances will alter on the basis of the result of this game. Note that, in contrast to the 2015 methodology, I now form this average including all teams. That means there will be some teams whose contribution to the average is zero or nearly zero because their chances of making the finals are close to 0 or 1 regardless of the outcome of the game.
It's important not to read too much into small differences in Weighted Average Importance figures - and all of the differences here are very small. We are still early in the season, so there are a lot of probabilities being multiplied in estimating teams' finals chances, each containing its own uncertainty and potential bias. What’s more, because we are increasing the uncertainty we’re introducing into the simulations with time, games played towards the end of the season are drawn back towards being 50:50 contests, which tends to increase their estimated importance. As evidence for this, at the moment 8 of the 10 most important rounds are assessed as being the last 8 rounds of the season.
We’ll keep an eye on this factor as the season progresses, and hopefully get a much clearer picture of which games are most likely to influence the finals makeup as the season.
