Around this time clubs in the lower half start talking about mathematical possibilities of making the 8.
Well, using a technique known as Monte-Carlo simulation, I've simulated the results of the remaining 64 games. Scores are derived by averaging a random number in the range of scores each team has scored this year vs their opponents range of scores conceded. This is done 2000 times to get the probabilities listed below.
ie Freo has averaged 90 points per game, top score 137, bottom score 61. Using this range (top and bottom values are set at 95 and 5th percentiles), draw a distribution (like a bell curve) and randomly pick a value from this distribution. Do the same for the Roos "scores against" and average them. Do the same for the Roos scores for and Freo scores against. that's 1 iteration for 1 game. Repeat for all 64 remaining games, repeat 2000 times. Computers are good at this sort of thing.
This does not take into account any home ground, form, injury or other influences.
The following is how the end of year ladder pans out, grouping the ladder spots by their finals effect
Freo have a 39% chance of hosting a final but still an 18% chance of missing the finals.
The Roos are about 50% chance of making the finals.
The Weagles and Carlton only have a 13% or 14% chance of making the finals.
The Dogs and Richmond only have a 1% chance of making the finals, as do Bris, Port and Melb of missing the finals.
Scores are also capped at 30 points for a low score too, no capping on the upper end, max scores simulated were about 200.
Again I stress that this only takes into account the range of scores each team has made and conceded so far this year (so that high scoring or low conceding teams are more likely to win) but doesn't apply any form of adjustments for home ground, recent form or anything else. Basically it is the opposite of the financial ads... past performance is the measure used to determine future performance!
I'll try to update it after each round.
Well, using a technique known as Monte-Carlo simulation, I've simulated the results of the remaining 64 games. Scores are derived by averaging a random number in the range of scores each team has scored this year vs their opponents range of scores conceded. This is done 2000 times to get the probabilities listed below.
ie Freo has averaged 90 points per game, top score 137, bottom score 61. Using this range (top and bottom values are set at 95 and 5th percentiles), draw a distribution (like a bell curve) and randomly pick a value from this distribution. Do the same for the Roos "scores against" and average them. Do the same for the Roos scores for and Freo scores against. that's 1 iteration for 1 game. Repeat for all 64 remaining games, repeat 2000 times. Computers are good at this sort of thing.
This does not take into account any home ground, form, injury or other influences.
The following is how the end of year ladder pans out, grouping the ladder spots by their finals effect
Freo have a 39% chance of hosting a final but still an 18% chance of missing the finals.
The Roos are about 50% chance of making the finals.
The Weagles and Carlton only have a 13% or 14% chance of making the finals.
The Dogs and Richmond only have a 1% chance of making the finals, as do Bris, Port and Melb of missing the finals.
Scores are also capped at 30 points for a low score too, no capping on the upper end, max scores simulated were about 200.
Code:
Team 1-2 3-4 5-6 7-8 >=9 16
St K 80% 16% 4% 1% 0% 0%
Bris 43% 40% 13% 3% 1% 0%
Port 39% 43% 14% 4% 1% 0%
Melb 30% 48% 18% 4% 1% 0%
Geel 2% 15% 40% 28% 15% 0%
Freo 3% 13% 36% 31% 18% 0%
Sydn 2% 11% 28% 31% 29% 0%
Essd 2% 10% 24% 33% 30% 0%
Kang 0% 4% 16% 32% 47% 0%
WCst 0% 1% 2% 10% 87% 0%
Carl 0% 0% 3% 10% 86% 1%
Adel 0% 0% 1% 7% 93% 1%
Coll 0% 0% 1% 5% 94% 1%
WBdg 0% 0% 0% 1% 99% 7%
Rich 0% 0% 0% 1% 99% 10%
Hawk 0% 0% 0% 0% 100% 79%I'll try to update it after each round.
