Thanks to both, that makes good and long answers to my question.
Well, both have seen that is not easy answer, even both know the procedures
Quote:
Originally Posted by nickthegeek
This is an interesting question and I guess that it could be answered with some assumptions. I'm not going to give the answer (due to laziness), but I'm just going to describe how I would approach the problem.
First, assign to each team an elo rating. For the question's sake, assume that elos of the first two teams are the same (we want to know which team the formula favours). The elos of the other teams are decreasing (elo[3]>elo[4] and so on).
Given the elos, you can estimate the probability of winning a match between two teams using the following formula (or equivalent others):
1/(1+10^((eloB-eloA)/400))
Since in total you have 9 matches, there are 2^9=512 possible outcomes. With the formula above, you can establish the likelihood of each outcome. (An outcome is a full path from matchday 1 to the winner of the final).
Finally, aggregate each outcome with respect to the winning team. This will give the probability of winning for each team. Then, see how the probability of team 1 compares to the probability of team 2.
The above is pretty easy to implement in a program. The answer will of course depend mainly on the elos of team 3 and 4. If they are the same, there is no advantage in being 1 or 2.
I'd start as the first attempt with these elo values:
2000
2000
1900
1800
1500
1500
1500
1500
I'd just assign the same elo to teams 5-8 and try a 100 difference between 3 and 4.
Yep, I thought just this, or even simplyfing, last giving some points to any team , to simplify the ELO system you exposed, that is more complicated
My problem is that Iīm good in maths, but not in computing; and this will be so tedious doing manually.
By the way, ELO simplified is a good, but 5-8 being the same, can simplify, but problem is that semis 2-5 and/or 1-6 are usual, and then 5-6 should be slightly different too (with only 1 upset these games happen)
Quote:
Originally Posted by TomCowley
There are obvious situations where it's significantly better to finish 2 (top 5 teams are equivalent and bottom 3 are drawing dead vs those teams) and obvious situations where it's clearly better to be #1 (top 7 teams are equivalent, 8 is 10% to win against those teams, 1 benefits from the lopsided game much more often than 2).
My gut instinct is that as long as seeding is correct, it's generally better to be #2. In the extreme case, where the top 3 teams are equal and the bottom 5 teams are drawing dead, you'd think that's awful for #2 because it has a tough opening match while #1 gets an effective bye, but it's not. #1 has to win a HFA against 2/3 and then a neutral field game, while #2 can win by winning a HFA game against 3 and then a neutral field game but also has the redraw after losing the first round, which is just better. I could have made a mistake scribbling it out, but I think the scenario of 1=2 > 3 > 4 >>> 5=6=7=8 is always better for #2.
In conclusion, this system is really, really, really stupid.
Yep, I have closely conclusions too, except in the case you told that 5 better are close, and 6 to 8 weaker, that I donīt understand why
And this format is used right now in the American Football League (that its final is like a Superbowl in Australia) and National Rugby League, not weaker leagues there
By the way, as a curiosity, the 8-team format that used before were also discussed in Australia, and complicated. I expose but this one, Iīm not interested in analyze it, only the 2 that I expose in 1st message
Matchday 1
Matches must play in this order, because if 1 and 2 wins, other 2 matches are dead matches, and teams, then, have not to know it
4 vs 5
3 vs 6
2 vs 7
1 vs 8
2 winners with best ranking advance to Matchday 3 (semi-finals, according to our nomenclature)
2 winners with worse ranking and 2 losers with best ranking go to Matchday 2
2 losers with worse ranking are eliminated
Matchday 2
(A)4th Winner vs 2nd Loser
(B)3rd Winner vs 1st Loser
Winners to semis, losers are eliminated
Matchday 3
1st Winner vs Winner A
2nd Winner vs Winner B
Winners to the final in Matchday 4 and losers are eliminated
*****
In this system 1 and 2 have always double chance (if win, go to home semi; if lose, you play matchday 2 away and semi away)
7 and 8 play knockout matches since beginning
And since 3 to 6 depend on their results and other results, to both, advance with a win straight to semis or not, or to have a double chance if loss; with better odds meanwhile higher in ranking
But have also flaws :
-If higher seed wins in Matchdya 1 in all 4 matches; 3 vs 6 and 4 vs 5 are dead games; and Matchday 2 would be , just crossing again these 4 teams but with different opponent
-If for example, higher seed wins in Matchday 1, and 1 lose against 8...
a) The winner between 4 vs 5 plays against 1 (but at least at home)
b) The loser between 4 vs 5 plays against 8 (but away)
-6 can lose his first match, and if 1 and 2 advances, he is alive yet, and in next round (in fact this sytem were abolished one year that 6 loses his 1st match, and reaches later the final)