# 2018 : Simulating the Final Ladder After Round 19

/Updated final home and away ladder simulations appear below.

(For details on the methodology, see this post from earlier.)

Four teams gained one half of an Expected Win or more this week:

**Carlton**(+0.7)**North Melbourne**(+0.6)**Hawthorn**(+0.5)**Essendon**(+0.5)

Five more saw their Expected Win count drop by half a game or more:

**West Coast**(-0.6)**Gold Coast**(-0.6)**Sydney**(-0.5)**Fremantle**(-0.5)**Western Bulldogs**(-0.5)

In terms of likelihood of making the Finals, the week's big gainers were:

**Hawthorn**(+12% points, making it +26% points over the past two weeks)**North Melbourne**(+7% points)**Melbourne**(+7% points)**Port Adelaide**(+7% points)

The week's big losers were:

**Sydney**(-28% points, making it a whopping -53% points over the past two weeks)**Adelaide**(-13% points)

Just eight 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:

**Melbourne**+9% points**Port Adelaide**+9% points**Hawthorn**+7% points**Collingwood**-13% points**West Coast**-11% points**Sydney**-11% points (making it -41% points over the past two weeks)

Three teams now (one more than last week) have estimated better than even-money chances for a place in the Top 4. Five other teams have between 19% and 45% chances.

The weekend's results made percentage an even more likely tie-breaker for a number of key ladder positions.

There's now an estimated 53% chance (up 4% 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 12% chance that 6th and 9th will all be equal on wins, and about a 46% chance that the teams in 4th and 5th will finish equal on wins.

### 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".)

Five teams became less certain about their final ladder positions this weekend, most significantly West Coast, Collingwood and North Melbourne, though all of those teams remain relatively certain about their most-likely finishes.

Sydney this week moved from being the team whose final position is least certain to a position of far greater clarity, leaving Port Adelaide as the team with most uncertainty. They have an estimated 10% or greater chance of finishing in any of the positions 2nd through 8th.

Overall though, certainty was again on the rise, with the average Gini coefficient rising by 1.6%.

The largest increases in certainty came for Adelaide and Sydney, with Richmond now the team most certain about their final ladder finish. They're now estimated to be 92% chances for 1st spot. Carlton, who are about 84% chances for 18th, are the team next-most certain about their final ladder finish.

No ladder position saw a significantly large increase in the uncertainty associated with it this week, though there were small increases for 2nd, 18th, 8th, 6th and 17th.

Most uncertain of all now is 8th place, for which nine teams have estimated chances of about 6% or higher of eventually filling. Next-most uncertain is 7th spot where eight teams have estimated chances of about 6% or higher. More broadly, positions 3rd through 10th are now 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 just under a 2% 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.)*

This week's results were such that we now need to look more closely at the team-by-team prospects even for as many as 13 wins, which we do below.

Geelong and Melbourne remain the teams most likely to make the Finals should they finish on only 12 wins, but the estimated conditional probability of them doing so has fallen again and is now only about 25 to 30%. No other team has a better than about 10% chance of playing Finals after recording just 12 wins.

The estimates for 13 wins now vary markedly by team, with Melbourne, Geelong and Hawthorn near-certainties with 13 wins, and Sydney and Essendon only about even-money chances with the same final win count. The remaining teams have estimates roughly in the 65 to 75% range.

Looking next at the analysis for Top 4 finishes, we find that Melbourne is the only team with a better than even-money chance of finishing in the Top 4 with only 14 wins. A large number of teams have less than 25% chances of finishing Top 4 with only 14 wins.

Fifteen wins, however, virtually assures teams of a Top 4 finish.

Looking at the relationship between every possible ladder finish for a team and the number of wins that team records we continue to see quite wide ranges of relatively plausible finishes for a number of teams given a specified number of wins - say Geelong, for example, with 13 or 14 wins. We can also see how 13 wins for Sydney and Essendon is no guarantee of a spot in the Finals.

A similar analysis, aggregating across teams, gives us an idea of the overall spread of likely ladder finishes for teams with a specified number of wins. We see that 13 wins is now much more often associated with 8th spot than is 12 wins, and that 14 wins is more often associated with 4th spot than is 13 or 15 wins.

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.)

The magnitude of the arrow lengths in the chart denotes the extent to which one team's chances are linked to another's, and the number of relatively long arrows reflects the general level of dependence. We see this week that Essendon, Hawthorn, North Melbourne and Sydney are the teams with the highest levels of dependency on other teams' fates. Between them, they fill 7th, 9th, 10th and 11th positions on the competition ladder.

We can do the same analysis for positions in the Top 4, which we do below.

Here we find the highest levels of dependence across a range of teams for Collingwood, Geelong, GWS, Melbourne, and Port Adelaide. Between them, they fill 3rd, 4th, 5th, 6th and 8th positions on the competition ladder.

### GAME IMPORTANCE

Below are the updated estimates of game importance, now shown for all remaining games in the fixture, and calculated on the basis of the game's expected impact on all 18 teams' finals chances.

The top four games all involve Sydney, while Hawthorn is involved in three of the top six.

There are three of the Round 20 games in the top seven: Sydney v Collingwood, Hawthorn v Essendon, and Brisbane Lions v North Melbourne.

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 Collingwood are involved in two of the top three most important games, though the most important of all is the Round 23 Melbourne v GWS clash.

From this week's games, only the Sydney v Collingwood, and Adelaide v Port Adelaide games appear in the top ten.