A tough mathematical question in a sport competition

[elcesardeljuego]

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

 

[jvicens]

,

Thank you for bringing up this interesting topic for discussion. I agree that mathematical tools can be very useful in analyzing and solving complex problems like this one.

After reviewing the system you described, I can see that it is indeed a complex and potentially controversial one. In order to determine whether it is mathematically flawed or fair, we need to first define what we mean by "flawed" or "fair" in this context.

One way to approach this question is to look at the overall fairness of the system, rather than just comparing the advantages of the top two spots. This means considering factors such as the overall competitiveness of the teams, the likelihood of upsets, and the impact of the system on the integrity of the competition.

Another important factor to consider is the purpose of the final stage. Is it meant to reward the top teams for their performance in the regular season, or is it intended to create more excitement and unpredictability in the competition? This can have a significant impact on how we evaluate the fairness of the system.

To accurately answer your question, we would need to conduct a thorough analysis of the system using mathematical models and simulations. This would involve looking at different scenarios and outcomes, and determining the probability of each team winning the competition under the current system.

In conclusion, while I cannot provide a definitive answer to your question without further analysis, I believe that mathematical tools can certainly help in evaluating the fairness of the final stage system in the AFL and NRL competitions. I hope this response helps to further the discussion on this topic.