The proper place for Football is

Team B.

Because

All of the phrases in each staff a and staff b are compound phrases (in addition to soccer), however the entire phrases in staff A, when the 2 phrases that make up the compound phrase are reversed, they make up one other compound phrase.

Examples:

Butthead –> Headbutt/Birdsong–> songbird

And for set B:

Birdseed can’t develop into seedbird. Similarly, the others, like workload can’t be reversed as nicely.

So,

Football is in staff B as a result of there isn’t a such factor as a ‘ballfoot.’

Edit Dec. 2022:

Apparantly ‘seedbird’ is a phrase based on Merriam-Webster… Seedbird Definition Who would’ve thought? 🙂