Permutations and combinations with SRRT scheduling

[jlasdf]

17 Aug 2021 - 

I recently stumbled into this forum, as I recently had a project that explored the permutations and combination possibilities of a Single Round Robin Tournament.  

The project was to create an educational video that showed the underlying mathematical complexity in SRRT scheduling.  What are all the permutations with respect to match-ups and how many possible seasons can be created?

https://youtu.be/vxK2zKhTfv4

I found that Python scripting was easier to iterate through the possibilities - you can see the supporting code here: 

https://github.com/jlasdf/math

Professional schedule makers must consider subjective, dynamic factors.  The National Football League here in the United States receives $USD 16.5B per annum, so it invests heavily in creating a fungible product made for television and stadium schedules.  The NFL put together a very entertaining video.  While it did not go far into the math per se, it did add colour commentary to the subjective factors when scheduling seasons.  

https://www.youtube.com/watch?v=bS1xGetyrh0

[Ian Wakeling]

Hi Justin,

Thanks for posting the links.  I had a look at your video and have some suggestions of things you might want to follow up on.  Mathematicians have studied the number of different round-robin schedules, and for 8 teams there are only 6 fundamentally different schedules that exist, all the others can be formed by permuting the team numbers or changing the order of the rounds.  As more teams are added the number of so called 'non-isomorphic' schedules rises extremely rapidly, and is about 527 million for 12 teams - there are some details of recent results here at the OEIS website.  You can find schedules for the 6 fundamentally different 8 team schedules here.

[jlasdf]

Hello,

Belated thanks for your reply.  I had no idea what branch of mathematics I was dealing with, nor did I know the academic or formal disciplines that the papers and OEIS refer to.    

Thanks also for your feedback on watching the video.  As you might have interpreted from the video, I don't necessarily have any formal training on this subject.  I also don't really know 100% if my video is even 100% correct in its thinking.  For the 8 team league with 7 rounds in the season, I do not 100% know if the valid weekly rounds are complete.  I also do not know if the way I "calculated" possible seasons is 100% valid either.  It was mathematics / analysis via intuition, not necessarily mastery.  Still always learning!!! 

Thanks again!! Justin