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A possible solution to an 18-game basketball schedule would be to go to three divisions at least for scheduling purposes, but you could still have one division for conference standings if you wish. Every member of the four-team division would play a home-and-home against the other members of that division (6 games), everyone else once (10 games), and a second game against one team from each of the other two divisions (2 games). Four of the members of each five team division would play a home-and-home in division (8 games), everyone else once (9 games), and the extra game from one of the teams in the small division (1 game). The last two members of the five-team divisions would play that extra game against each other instead. You could choose to reschedule each year based on the previous year's standings (the top team in the short four-team division would play the other two #1s, with the two #5's getting each other) or assign permanent rivals. Everyone in your division would be playing a similar schedule, you'd have a group of schools to be rivals year-after-year, and you'd still play everyone.
12 months ago on SEC Meetings Recap: Hoops Coaches Studying One 18-Game Plan (But Divisions Might Be Back In Play)