Earlier in the week I posted the results for the latest set of Finals simulations and explored the interdependencies amongst team Finals fates, estimating how likely it was that Team A would make the Finals if Team B did or did not. In today's blog I'm going to analyse other dependencies, not between Team A's and Team B's Finals chances but instead between Team A's Finals chances and the results of each of the remaining games.
Specifically, what I'm going to estimate is how each team's probability of making the Finals varies with the outcome of each of the remaining games, including those games in which it is not a participant, because these games can alsohave an effect albeit a smaller one. I'll do this by running 10,000 replicates of my simulation using exactly the same methodology as I've been using to simulate the remainder of the competition previously, and then compare the proportion of times that a team makes the Finals when the home team wins a particular game versus the proportion of times it makes the Finals when the home team loses that same game. I'll ignore draws.
The table below contains the results.
The first row, as an example, tells us that the Roos v Dons game finished as a Roos loss about 25% of the time, a draw about 1%, and a Roos win about 75% of the time. A Roos victory, everything else being equal in all other games, dropped the Crows' chances of making the Finals by 5% points. It also dropped the Pies' chances by 4%, the Cats by 2%, and so on.
This game has, of course, largest impact on the participants with Finals aspirations - here only the Roos, whose chances are 27% points higher if they win than if they lose - but you can see that it also affects the chances of the seven other teams still in the running for a Finals berth. The sum of the impacts on all teams is, of mathematical necessity, zero, but we can get a measure of the game's overall impact on the ultimate composition of the 8 by summing the absolute impacts it has on each team's chances. For this game that sum is 55% points, which ranks it 15th amongst all remaining games in terms of impact as reflected by this metric.
Other lines for other games can be read in the same manner, and I'll leave it as an exercise for you to review and take out from the entire table whatever interests you.
Here though are a few things I've noted:
- This week includes the game with the greatest impact on the composition of the final 8: the Port Adelaide v Adelaide game. For Adelaide, the difference between a win and a loss is a 32% point swing in their Finals chances, the largest difference for any team in any of the remaining contests.
- Next week includes three games from the dozen most-impactful contests, including particularly important games for GWS, the Roos, Pies and Dogs.
- The Gold Coast v GWS game this week will affect every aspirant's Finals chances by at least 3% points. The Lions v Roos game next week will do the same. No other game will have such a widespread impact.
- The Dees v Roos game in four weeks time will alter the Finals chances of four of the aspirants by more than 5% points. No other game will have this large an effect on so many teams.
This same approach could also be used to estimate the impacts of varying the result of each remaining game on other competition outcomes, for example on team chances of winning the Minor Premiership, finishing in the Top 2, or finishing in the Top 4. I'll take a look at some of these in future weeks.