Why Sydney Won't Finish Fourth

As the ladder now stands, Sydney trail the Dogs by 4 competition points but they have a significantly inferior percentage. The Dogs have scored 2,067 points and conceded 1,656, giving them a percentage of 124.8, while Sydney have scored 1,911 points and conceded 1,795, giving them a percentage of 106.5, some 18.3 percentage points lower.

If Sydney were to win next week against the Lions, and the Dogs were to roll over and play dead against the Dons, then fourth place would be awarded to the team with the better percentage. Barring something apocalyptic, that'll be the Dogs.

Here's why. A few blogs back I noted that you could calculate the change in a team's percentage resulting from the outcome of a single game by using the following expression:

(1) Change in Percentage = (%S - %C)/(1 + %C) * Old Percentage

where %S = the points scored by the team in the current game as a percentage of the points it had already scored in the season,

and %C = the points conceded by the team in the current game as a percentage of the points it had already conceded in the season.

Now at this stage of the season, a big win or loss for a team will be one where the difference between %S and %C is in the 6-8% range, bearing in mind that a single game now represents about 1/20th or 5% of the season, so a 'typical' %S or %C would be about 5%. Scoring twice as many points as 'expected' then would give a %S of 10%, and conceding half as many as 'expected' would give a %C of 2.5%, a difference of 7.5%.

Okay, so consider a big loss for the Dogs, say 30-150. That gives a (%S - %C) of around -7.5%, which (1) tells us means the Dogs' percentage will change by about -7.5%/1.1 x 1.25, which is 8.5 percentage points. That drops the Dogs' percentage to about 116.

Next consider a big win for the Swans, again say 150-30. For them, that's a (%S - %C) of 6%, which gives them a percentage boost of 6%/1.02 x 1.06, which is about 6 percentage points. That lifts their percentage to about 112.5, still 3.5 percentage points short of the Dogs'.

To completely close the gap, Sydney needs its percentage change plus the Dogs' to exceed 18.3 percentage points, the percentage chasm it currently faces. Using this fact and the expression in (1) above for both teams, you can derive the fact that, to lift its percentage above the Dogs', Sydney needs the following to be true:

Sydney's (%S - %C) > 18.3% - 1.15 times the Dogs' (%S - %C)

Now my worst case 30-150 loss for the Dogs gives them a (%S - %C) of -7.6%. That means Sydney needs its (%S - %C) to be about 9.5%. So even if Sydney were to concede no points at all to the Lions - making %C equal to 0 - they'd need to score about 180 points to achieve this.

More generally still, Sydney need the sum of their victory margin and the Dogs' margin of defeat to be around 300 points if they're to grab fourth.

Sydney won't finish fourth.