2018 : Simulating the Final Ladder After Round 21
/Updated final home and away ladder simulations appear below.
(For details on the methodology, see this post from earlier.)
Five teams gained one half of an Expected Win or more this week:
- Sydney (+0.7, making it +1.2 over the past two weeks)
- Western Bulldogs (+0.7, making it +1.4 over the past two weeks)
- Hawthorn (+0.5, making it +1.5 over the past three weeks)
- West Coast (+0.5)
Four more saw their Expected Win count drop by half a game or more:
- Melbourne (-0.7)
- North Melbourne (-0.7)
- Port Adelaide (-0.5, making it -1.1 over the past two weeks)
- Geelong (-0.5)
In terms of likelihood of making the Finals, the week's big gainers were:
- Sydney (+41% points)
- Hawthorn (+11% points, making it +47% points over the past four weeks)
The week's big losers were:
- North Melbourne (-23% points)
- Port Adelaide (-16% points, making it -31% points over the past two weeks)
- Melbourne (-10% points)
- Geelong (-10% points)
Nine teams are now assessed as better than even-money chances for a spot in the Finals.
In the quest for a Top 4 spot, the largest changes were:
- Hawthorn (+16% points, making it +32% points over the past four weeks)
- GWS (+14% points, making it +29% points over the past two weeks)
- Collingwood (+13% points)
- Sydney (+10% points)
- West Coast (+9% points, making it +19% points over the past two weeks)
- Melbourne (-34% points)
- Geelong (-15% points)
- Port Adelaide (-11% points, making it -26% points over the past two weeks)
Four teams have estimated better than even-money chances for a place in the Top 4. Four other teams have between 5% and 44% chances.
The weekend's results made percentage slightly less likely to be required as a tie-breaker for a number of key ladder positions. There's now an estimated 61% chance (down 7% points from last week) that the team in 9th will be separated only on percentage from the team in 8th at the end of the home-and-away season.
There's also about a 17% chance that 6th and 9th will all be equal on wins, and about a 42% chance that the teams in 4th and 5th will finish equal on wins.
MOST LIKELY TOp EIGHT
According to the latest simulations, there are still 2,986 possible final Top 8s, 227 of which occurred in at least 50 (0.1%) of the replicates.
The 10 most common, and their estimated probability of occurrence, appear at right.
Richmond and West Coast finish 1st and 2nd in all 10, and GWS 3rd in seven. Hawthorn finishes as high as 3rd and as low as 6th, as does Collingwood.
Melbourne makes the Top 4 in only the last of the 10, while Sydney and Port Adelaide never do so.
TEAM AND POSITION CONCENTRATION
This week's Gini concentration measures appear below, and reflect the level of certainty in our knowledge about which teams will finish where at the end of the home and away season.
For information about how to interpret these measures, you can see this blog, but the table at right might also help. It shows the Gini coefficient that a team would have if it were equally likely to finish in any of a specified number of ladder positions (and in no other position).
So, for example, a team that was equally likely to finish in any of six ladder positions would have a Gini coefficient of 0.667. This week, as we'll see in a moment, North Melbourne has a Gini coefficient of 0.643, so we can think of the level of uncertainty it has about its final home-and-away ladder position as roughly equivalent to that for a notional team that found itself equally likely to finish in any of six ladder positions. Note that we're not saying that North Melbourne is only capable of finishing in six different ladder positions (it can actually finish in any of 15 different positions, 11 of them with an estimated probability of 1% or more), just that the uncertainty it faces it roughly equivalent to a team in that situation.
You'll note that a team equally likely of finishing in any of the 18 ladder positions will have a Gini coefficient of 0, but one that is absolutely certain of its final ladder position will have a Gini coefficient of 0.944, not 1. There's a technical reason for this - and a 'bias correction' we could apply to all coefficients to force the range to be (0,1) - but for our purposes, the uncorrected coefficients are fine.
(Note that, when we're looking at the Gini coefficients for ladder finishes rather than teams, we can substitute "Number of Equally-Likely Finishes" for a team with "Number of Teams Equally-Likely to Finish in the Position".)
Every team except Essendon became more certain about their final home and away ladder position this week.
Port Adelaide remain the team with most uncertainty. They have an estimated 8% or greater chance of finishing in any of the positions 5th through 11th, and an estimated 12% or greater chance of finishing in any of the positions 7th through 10th
Overall certainty increased substantially this, with the average Gini coefficient rising by almost 7.0%.
The largest increases in certainty came for Geelong and Hawthorn, but Richmond and Carlton remain most certain about their final ladder finishes. Richmond are 97% chances to finish 1st, and Carlton 96% chances to finish last.
The only ladder position for which uncertainty increased this week was 12th where we now find six teams with non-zero chances, and three with chances of between 22% and 45%.
The position with least certainty though is now 9th, which has nine possible final occupants, five of them with chances of between 11% and 22%. Next-most uncertain is 8th spot, which any of 10 teams could occupy, four of them with chances ranging between 14% to 26%. Positions 3rd through 10th remain the seven most-uncertain ladder positions of all.
Least uncertainty is associated with 1st position, which, as just noted, Richmond has a very high chance of occupying.
Across all 18 ladder positions, the average decrease in uncertainty this week is similar to that we saw for the team-based view (viz about a 7% increase in the average Gini coefficient).
WINS REQUIRED
Below are the updated estimates of teams' likelihood of making the Finals depending on the number of wins that they record.
(Recall that, because we're working with a sample of simulated final ladders, our estimates have sampling error, so we show them as 95% confidence intervals here with the mean estimate shown as a point. In some cases, our sample is so large that the interval essentially collapses to a point, at least to the resolution shown here.)
Only Geelong and Melbourne are assessed as having any chance at all of finishing in the Top 8 with just 12 wins, and neither would be better than about 1 in 3 chances of doing so should they finish 12 and 10.
Even 13 wins remains no guarantee for most teams, however, and each of Sydney, North Melbourne and Essendon have estimated chances of only about even-money should they finish the season on 13 and 9. Fourteen wins, however, guarantees all teams a spot in the Finals.
Looking next at the analysis for Top 4 finishes, we find that Melbourne is now the only team with a roughly even-money chance of finishing in the Top 4 with only 14 wins. All other teams have estimated chances of 30% or lower - lowest of all for GWS and Sydney.
Fifteen wins, however, virtually assures all teams of a Top 4 finish.
The uncertainties associated with exactly 13 and 14 wins are again reflected in the chart below, manifested in the broad range of feasible ladder outcomes for some teams when they record exactly those number of wins.
A similar analysis, aggregating across teams, gives us an idea of the overall spread of likely ladder finishes for a generic teams with a specified number of wins. We see that 13 wins is still most associated with 8th spot, but also with 7th and 9th (and, to a lesser extent, 6th), and that 14 wins is most associated with 5th, but also with 4th and 6th.
As we noted earlier, percentage seems very likely to play a role in separating 8th from 9th, and somewhat likely in separating 4th from 5th this season.
Next, we explore the inter-team dependencies in the composition of the final 8 by estimating the probability that a particular teams makes the 8 conditioned on some other team making or missing the 8.
These are shown in the charts below, as usual, as arrows with the base of an arrow marking the estimated probability that a team makes the 8 conditioned on a nominated team missing the 8, and the arrow head marking the estimated probability that a team makes the 8 conditioned on a nominated team making the 8.
(Note that these images can be clicked on to access larger versions.)
This chart got considerably simpler this week as a number of teams' estimated finals hopes moved above 95% or below 5%. That left just six teams to consider and, among them, only Geelong, Melbourne, Port Adelaide, and Sydney show significant levels of dependence on the fates of other teams.
We can do the same analysis for positions in the Top 4, which we do below.
This chart too has been considerably simplified and we the highest levels of dependence for Collingwood, GWS, and Hawthorn.
GAME IMPORTANCE
Below are the updated estimates of game importance for all remaining games in the fixture, and calculated on the basis of the game's expected impact on all 18 teams' finals chances.
Two of the top three games involve Port Adelaide.
In the next and final table we have the estimated importance of each remaining game to the composition of the Top 4.
Here we find that Sydney are involved in two of the top three most important games, and Collingwood in two of the top four.
