It’s now mostly computerized, feeding in the necessary games based on league schedule rules — how many games against teams in their division, rest of conference & other conference. There are rules like series being 2-4 games and rest days at least every X days in baseball, number of consecutive days a team can plan in NBA (no more than two, etc.) Then additional rules are provided, like Red Sox have to be home on Patriots Day or league wants top 8 NBA teams playing on Christmas Day. For NBA and NHL there has to be some coordination for dates in shared arenas.
Prior to computerization, it was a manual process that took months. For 25 years, there was a husband/wife team who did the MLB scheduling — there is even an ESPN 30 for 30 about them! http://www.espn.com/30for30/film/_/page/the-schedule-makers
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