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Applying the Hungarian Algorithm to NFL Scheduling

Applying the Hungarian Algorithm to NFL Scheduling. The Question. What method can be used to ensure a fair schedule for the NFL’s 16-game, 32-team schedule? A “fair” schedule: Weighted schedule (by strength) Ensure good competition All teams have fair shot at the playoffs. The Rules.

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Applying the Hungarian Algorithm to NFL Scheduling

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  1. Applying the Hungarian Algorithm to NFL Scheduling

  2. The Question • What method can be used to ensure a fair schedule for the NFL’s 16-game, 32-team schedule? • A “fair” schedule: • Weighted schedule (by strength) • Ensure good competition • All teams have fair shot at the playoffs

  3. The Rules • Each team plays 16 games • Each team must play every team in its division twice (4 teams per division, 3 opponents x 2 games = 6 games) • Each team plays all teams from one other division in their conference (4 games) • Each team plays all teams from one division in the other conference (4 games) • The two remaining games are played against two of the remaining eight teams in their conference that they have not played.

  4. Calculating Strength • Strength will be determined by a team’s performance the previous year, quantified by the team’s number of wins. Example: • Patriots in 2003 were 14-2 = strength of 14 • Texans in 2003 were 5-11 = strength of 5 • Patriots vs. Texans = difference of 9 Poor Matchup!

  5. The Procedure • The purpose of the Hungarian Algorithm is to optimize solutions to assignment problems where a one-to-one relationship is required. • This is done with matrix operations that find an independent set of zeros. • An independent set of zeros exists when no two of them are in the same row or column

  6. Worker/Job • Each worker can do each job in x hours. We want to know how to assign each worker to a different job in order to minimize the time required to complete all jobs. Job 1 Job2 Job3Worker 1 2 5 7Worker 2 4 2 1Worker 3 2 6 5

  7. Drawbacks and Problems • Without NFL rules (grouping by division), the Hungarian Algorithm would be a very tedious process • Coding the algorithm is difficult, brute force method was used

  8. References • Applications of Discrete Mathematics, Rosen & Michaels, McGraw Hill, 1991 • Scheduling a Bridge Club, Elenbogen & Maxim, Mathematics Magazine, Vol. 65, No. 1, 1992 • www.footballguys.com/shick_parity.htm • www.espn.com • www.nfl.com

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