One banzuke for every oyakata. Every manager on the site, across all leagues, ranked like real sumo. It's the same rank shown on your Oyakata page.
Each basho becomes one 15-bout record. Your finish in each league is scored by where you placed: first counts as 15–0, last as 0–15, the middle about 8–7. If you play in several leagues, those finishes are averaged into one record, so more leagues doesn't mean faster promotion.
8 or more wins moves you up; 7 or fewer moves you down. The better the record, the bigger the move, up to 4 ranks a basho. Winning a league adds 2.
The top ranks are earned like the real ones. A debut lands no higher than Maegashira 7. Komusubi takes a winning record from the top of Maegashira. Ōzeki takes 33 wins over three straight bashos at Sekiwake or Komusubi. Yokozuna takes two title-grade bashos in a row as Ōzeki (a league title or 13+ wins). An Ōzeki with a losing record is kadoban and drops after a second one.
Ranks change when a season closes. Once a league's Riji-chō closes the basho, its results count. Within a rank, the stronger latest basho is listed first.