Hi,
I am the top Joomla developer here on Freelancer.com site (https://www.freelancer.com/freelancers/skills/Joomla/)
I have read the full description of project, but regarding design, there is only one page (homepage) in pdf file with designs.
I will develop this system as a fully custom Joomla component. I will use the users, acl groups from Joomla core and develop in the custom component all required features: registration, subscription, payment, profiles (for coaches and players), navigation pages, search all this for frontend, and in backend will be all configuration required for admin only so admin will have a full control over website.
Regarding matching and scoring algorithms, this will not be an issue, I have understood partially the logic, of course, I think there is more.
Maybe my bid is not the lowest, but I am fully aware about the work amount required, so this is my bid. I have developed many custom Joomla components (from scratch) in past (some of them very big). I can show you examples if you require.
Please let me know if you are interested to work with me. For references please check my past projects, if you have time you can read all my reviews to convince about how I work:)
Regards,
Andrei