A question about mathematical fairness in competition

In USA is usual in a competition to be organized first in a regular season and afterwards in a single knockout stage. Sometimes, in order to give an advantage to top spots , these have a first round bye, as NFL does.

In Australia usually this advantage is given in a form of "Double chance", where top spots can´t be eliminated in their first postseason match. Next format is used in Australian Football Legue, National Rugby League (top two Australian leagues) and other minor leagues all around the world.

It is a 8 team system, where top 4 have double chance (in order to simplicity, homefield advantage is not announced here):

Matchday 1

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

Losers of C & D eliminated

Matchday 2

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

Losers are eliminated

Matchday 3

Winner A vs Winner F
Winner B vs Winner E

Matchday 4

Final: Winners of matchday 3 matches

This format gives an easier path to top 4. But here is the point. If best team wins, matchday 2 matches are 4 vs 5 and 3 vs 6 with 1,2 having a bye; but matchday 3 is 1 vs 3 and 2 vs 4, with 1 having a tough opponent in semifinals than 2 has (This is made in order to no repeat matchday 1 matches.)

My question is:

-Has mathematically 1 an easier path to win for 1 or for 2?

Because these are 3 main points:

a) 1 has an easier opponent than 2 in Matchday 1. It seems that finishes 1st is better than finishes 2. But it is a NOT ELIMINATION MATCH
b) If all results are hopeful, semi finals are 1 vs 3 and 2 vs 4 (2 has an easy opponent than 1). But meanwhile a) happens always, b) only happens if all results are hopeful, but now is AN ELIMINATION MATCH
c) If there are upsets in 2 first matchdays, then there are many combinations, with many of them playing 1 vs 2 in one semifinal.

What is your opinion? And if it is possible to mathematize this, in order to ensure if is better finishes 1st or 2nd .

It seems it was a difficult question .P

In my opinion, it depends on how much having a "bye week" is worth. Presumably, 2 is more likely than 1 to lose its first match, which means it would have a match in the second round instead of getting a bye.

Of course, sometimes having too much of a break can work against you. Back in the days when the AFL postseason had 5 teams with the #1 team getting a first-round bye and a draw in any match meant that the entire playoffs had to be put on hold for a full week to allow the tied teams to have a rematch, if, say, the #2-#3 match in the first round was a draw, then it would be three weeks between matches for the #1 team, and it could get "match stale". (Why, yes, I am thinking of 1990.)

Well. In order US people understand this system, that is usual in Australia (McIntyre Final Five) but it is not used outside this country.

5 best teams after regular season advance , but:

-Top 3 have double chance (they can lose one match if it is not the grand final and they are not eliminated)
-Top team has also a bye

Week 1

2 vs 3 (A)
4 vs 5 (B)
1 receives a bye

Loser of B is eliminated

Week 2

1 vs Winner A (C)
Loser A vs Winner B (D)

Loser of D is eliminated

Week 3

Loser C vs Winner D (E)
Winner C receives a bye

Loser E is eliminated

Week 4 (FINAL-No double chance)

FINAL: Winner C vs Winner E

In this system, much popular in Australia, a team can´t be champion if doesn´t win all teams that finish better in regular season


An interesting 12 team system that was studied by AFL, but finally rejected was:

1 vs 2 (A)
3 vs 12 (B)
4 vs 11 (C)
5 vs 10 (D)
6 vs 9 (E)
7 vs 8 (F)

Winner A advances to semi finals
Loser A and all other winners advance to quarter-finals
All other losers are eliminated

Quarter finals

Loser A vs Winner F
Wiiner B vs Winner E
Winner C vs Winner D
Winner A receives a bye

Semi finals

Winner QF1 vs Winner QF2
Winner A vs Winner QF3