How is a sports league fixture list actually made?
By solving a constraint satisfaction problem — one with so many competing requirements that it is generated by software, and the days when a person did it with pen and paper are long gone in professional sport.
The constraints that must be satisfied simultaneously:
Every team plays every other, home and away, in a double round robin for most leagues.
Home and away balance, avoiding long runs of either. Three consecutive home or away fixtures is generally treated as unacceptable, and the algorithm penalises it heavily.
Paired clubs. Teams sharing a city, a stadium or policing resources cannot both be at home on the same day, which is a hard constraint imposed by police forces rather than by the league.
Broadcast requirements. Attractive fixtures must be distributed across the season and across slots, since television rights pay for the league and the contract specifies what the broadcaster receives.
European and cup competitions, requiring domestic fixtures to be moved around midweek commitments for some clubs and not others.
International windows, when players are unavailable.
Public holidays and traditional dates, which fans expect.
Travel distance, particularly in geographically large leagues, where consecutive long trips are grouped deliberately.
Stadium availability, for grounds shared with other sports or used for concerts.
Local events — marathons, festivals, elections using the stadium — supplied by clubs in advance.
Why it is genuinely hard. These constraints conflict, and the number of possible arrangements is astronomically large. The problem is of a class where no method guarantees an optimal answer in reasonable time, so software searches for a good solution rather than the best one, and human schedulers then adjust.
The sequence in practice: clubs submit unavailable dates; a provisional list is generated; it is checked with police and broadcasters; and it is published months ahead — then changed repeatedly as cup draws, European progress and broadcast selections land.
Fairness concerns are real and measurable, including the strength of opposition faced around key periods and the imbalance created when fixtures are rearranged unevenly.