It is a difficult question but only can be solved with mathematical tools.

In the 2 most important Australian competition (AFL and NRL) use a final stage that gives more advantage to those teams that ends better the regular season. The debate is that every spot you get better in regular season, more advantages you must have in the final stage. According to many people, it is better end 2nd than 1st, but to other not. The only way to solve that is using maths tool.

Then, my mathematical question is:

-Is This final stage draw mathematically flawed (comparing top two spots) or is mathematically fair (it is better finish 1st than 2nd in the regular season)?

This is the system (top 4 teams have a double chance, and 5th-8th go to knockout stage:

Day 1

A-1st vs 4th B-2nd vs 3rd C-5th vs 8th D-6th vs 7th

Losers C-D are eliminated

Day 2

E-Loser A vs Winner C F-Loser B vs Winner D

Losers are eliminated

Day 3

G.-Winner A vs Winner F H.-Winner B vs Winner E

Losers are eliminated

Day 4 (Final)

Winner G vs Winner H

Look that the point is that 1st has an easy opponent than 2nd in Day 1 (play against 4 instead 3) that is desirable; but if the favourites win their matches in Day 3 (semifinals) has a tougher opponent (3rd instead 4th). But on same time this match can be not produced if one the favourites lose in the first two days, even can play 1st against 2nd if one of them lose Day 1

I would like if somebody can solve this. I´m not Australian but there is a question than no math could solve until now

Salutations and Thanks in advance

  • 1
    $\begingroup$ This is difficult to answer since it is not mathematically possible to determine the outcome of a sports game. We could randomly assign a probability of, say, 70%, for the event that the best team wins against the 3rd best, and calculate probabilities from there. But that has nothing to do with reality. $\endgroup$ – ThomasR Feb 2 '17 at 20:58
  • $\begingroup$ But the point here it is determine if the system is flawed or not, in the meaning that teams that are playing should prefer end 2nd instead 1st or not. But I don´t find the way to calculate it. $\endgroup$ – elcesardeljuego Feb 3 '17 at 0:41
  • $\begingroup$ Good question, you are asking whether there is a strategic incentive not to place 1st in the regular season in order to have an easier time in the playoffs. I think to solve this question one would have to model the winning probabilities as functions of the regular rank. Then you can compute the probabilities of winning the cup when playing 1st or 2nd. $\endgroup$ – Nameless Feb 3 '17 at 2:14

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