I don´t know if it is the appropiate forum, but if not mod can move it where it should be this post

In US or Europe usually the final stages are knockout stages, where top seeds have advantage like weaker opponents, home field or even sometimes , first round byes

In Australia, in the final stages usually use a format that allow some competitors lose one match (or even serie) and not be eliminated (but, of course, with disadvantages), during part of the final stage (it is called "Double Chance"

Then , my question, it is , in order to be a fair system, that higher seeds have more advantage to win the tournament

Then, I expose the format (this format is used in the 2 main important leagues in Australia: AFL and NRL).

8 teams advance to the final stage, and the top 4 have double chance (therefore, they can´t be eliminated if lose their first match)

Matchday 1

(A) 1 vs 4
(B) 2 vs 3
(C) 5 vs 8
(D) 6 vs 7

Winners of A,B advance to home semi-finals* (I use standard nomenclature, due to Aussie call semi-finals Matchday 2, and preliminary finals when only 4 teams are remaining). Losers of C, D are eliminated. Other teams play Matchday 2

Matchday 2

(E) Loser A vs Winner C
(F) Loser B vs Winner D

Losers are eliminated, Winners advance to Semi-finals away

Matchay 3 (Semi-Finals)

Winner A vs Winner F
Winner B vs Winner E

Losers are eliminated, and winners play the final in neutral site in Matchday 4

Then, my question:

-If you look carefully, 1 plays his 1st match against 4th team ; meanwhile 2 plays against a stronger team (3rd). This is fair

But if higher seeds win their matches, semifinals are 1 vs 3 and 2 vs 4; that favours 4

Then it is not clear if is better to end 1st in regular season (that it shows that format is fair) or 2nd (that it will be unfair)

-Also, if 1 or 2 (but not both) lose its 1st match, will play between them the semifinals (therefore 1 is better, because starts final stage against weaker opponents)

In summary:

a) 1 starts against a weaker opponent that 2 (that is good)
b) There are a lot of combinations, that some favours 1 and some favours 2
c) If higher seeds always win: 2 has a weaker opponent in semis (that it would be a flaw)
d) 1 then had a weaker opponent, but in a non-elimination match, adn 2 would have a weaker opponent in a elimination match

Then, my question, and I would like an answer according to MATHS, or a big computer simulation, is...

-Is it better to end 1 with this system (then the format is right and fair) or is it better to end 2 (then is it a flawed system) ?

*****


BONUS TRACK

The format I wrote here is very used , as I exposed, in Australia. It was once , very short time, for 6 teams, and it could have the same problem (maybe was flawed, maybe not). I expose the system and same, if somebody can solve it:

Matchday 1

(A) 1 vs 2
(B) 3 vs 6
(C) 4 vs 5

Losers B,C are eliminated

Matchday 2

(D) Winner A vs Winner B or C with higher Seed (if 3 won, always here)
(E) Loser A vs Winner B or C with lower Seed (if 6 won, always here)

Winner D advance to the final; Loser E is eliminated

Matchday 3

Loser D vs Winner E

The winner of this match plays the final against Winner D in neutral site

Then, here, same as before.

-Is it better to end 1-2 (same situation) that has a strong opponent, but they can´t be eliminated in his 1st match? Or is it better 3, that if he wins 6 (weakest opponent) that if he wins, he is in the same situation that winner between 1-2?
-But on same time 3 can be eliminated in his 1st match, and 1-2 not

It means, that if 1 beats 2 in his 1st match; and 3 beats 6 (much weaker). 1 and 3 would be in same situation

But if 1 loses (or 2 loses) his 1st match, have double chance , meanwhile 3 has no double chance if loses his 1st match

I know it is long, but I´m interested in the answer, if somebody can answer (it is more difficult that it seems)

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.

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.

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

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 I´m 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)

Yep, I have closely conclusions too, except in the case you told that 5 better are close, and 6 to 8 weaker, that I don´t 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, I´m 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)

If 1 wins its first round, it will always have to beat 2 more competent teams to win, and same for 2, so that's a wash. If 1 loses its first round, it has to beat a competent team (the 5) to get to the final 4, while if 2 loses its first round, it gets an effective bye (the 6 or 7) into the final 4, which is advantage 2 (both then have to win 2 more matches against competent teams).

Oh, thanks. I was thinking only in Matchday 3 (where 1 vs 6 or 2 vs 5 are highly possible) and I didn´t see this scenario

And yes, you are right, it is another example that shows that 1 can be worse than 2

I found the time to win my laziness and write a bunch of very inelegant lines of code to implement what I described in the previous post. Here is the code in the R programming language:

The above functions build all the possible paths and establish for each path its likelihood given the elos of the teams involved. Just an example of usage:

Next, I run a simulation in which elos are random in the 1000-2000 range and elos of the first two teams are the same. Here is the code:

The results show that Team2 has, on average, 3.9% of probability of winning more than Team1. This is huge. Furthermore, in just about ~90 cases out of the 10000 simulation Team1 had a better chance of Team2.

I didn't take into account home court advantage and there is no reason that the actual elos are uniformly distributed. Nonetheless, it seems pretty clear that being Team2 is much better than Team1.

Wow! Really thanks This is the time that most I grate to an answer in a forum (even in this forum I´m a new guy, I´m not in other).

This is a big flaw then, that is best to end as Seed 2 instead Seed 1, and it is not a small league

This is the last year final, it is a big day in Australia



Also, the Rugby League there, that it is important also, uses it. How is it possible that the league don´t spend a few bucks to check it before implement it? I´m really surprised

And really good job, Nick, really !!

PS: The home field was not important, because 1 and 2 play same games at home (Matchday 1 - Home ; and then, if win -Marchday 3 at home, and if lose Matchday 2 at gome ; Matchday 4, that is the final, it is in neutral site)

PPS: Is it possible to compare too the 6-team (in one side, 1 or 2, that they are in same situation; and in the other , team number 3). I guess, in this one the tournament is not flawed except when it is a huge gap between top team and number 6, but it would be interesting too.

Note that in this case, if best team always the semi final is 2 vs 3 and 1 waiting in the final (that is good), but previous round 1 vs 3 and 2 vs 4 (that is not good, because the ideal way would be 1 vs 2 in DOuble chance match; and 3 vs 4 in the elimination match)

Today has been in Australia the final game of the AFL season, that uses this format, and probably is the most important day about sport issues there...

...and Seed 2 has been crowned champions. Coincidence or not, it has been like this

The semis were 1 vs 3 and 2 vs 5, with 2 and 3 winning these matches.

And 2 have won after a large comeback

I linked something related to it

https://researchbank.swinburne.edu.a...version%29.pdf

I wonder; why not just reseed match days 2 and 3 instead of having them bracketed? That is the highest seed playing in match day 2 plays the lowest remaining seed and the same happens in the semifinals. That would seem to eliminate any advantage to finishing 2nd instead of 1st, would it not?

I agree with you

I think the reason is because they don´t want to repeat games in Matchday 3, therefore winner and loser of top 4 in Matchday 1 goes to different halves of the bracket in the knockout stage