Mathematical modeling paper NBA schedule planning

To measure the pros and cons of a race, in addition to the upper limit of the interval between every two games, the difference e of the total interval between teams in the whole race is also an important indicator. E=Emax-Emin can be set, and the greater the e, the greater the difference in the overall rest interval between teams. See Table 2 and Table 3, which are the schedules with n=8 and n = 9 satisfying d=[(n-3)/2] respectively. The schedule with n = 8 is e =19-17 = 2; N=9 E=28-2 1=7 timetable. There is a small difference in the schedule with n=8, which means that the rest time of each team is relatively even, so this schedule is fair in terms of indicators, and the schedule with n=9 is quite different, so this schedule is still unfair.

In addition, in addition to the number of times between every two games, the rest time before each team's game, that is, the order of the first round, still has a certain impact on the performance of the game (for example, playing in the back of the first round can reduce the fatigue of the journey, you can observe the situation of each team first, and so on). For example, in Table 2, Team 4 and Team 5 played the last game in the first round, and in Table 3, Team 9 played the last game in the first round. In practice, this factor cannot be solved, and the order of the first round is often decided by drawing lots.

As for the advantages and disadvantages of the curriculum, in addition to fairness, there is also the issue of efficiency, that is, how to arrange the curriculum reasonably and compactly to make the curriculum shorter.

6. Model evaluation

6. 1 The results of this model successfully give the formula for calculating the upper limit of the interval between every two games of each team in a single round-robin match in the same venue, which has certain theoretical and practical significance.

6.2 Up to now, the arrangement of single round robin in the same venue has actually adopted the "Round Robin Rules" (see the above figure, where n is an even arrangement). Through our research, it is found that this rule is simple, but it is fair for even-numbered scheduling because it conforms to d=[(n-3)/2]. For odd numbered plans, d

East 15 Team, West 15 Team: A team will play four games (two home games and two away games) with teams from different regions (one home game and one away game). So each team will play 82 games in the regular season. By the way, write out the algorithm: the total number of games in a district is15×14× (4+2)-30 =1230 (field). The total number of teams in a district is 15, and the number of games of each team in a season is 1230.

After the regular season, the top eight in each division entered the playoffs. First place versus eighth place, second place versus seventh place, third place versus sixth place, fourth place versus fifth place. The playoffs are knockout rounds, and each round is the best of seven games.

Finally, the first place in the division was decided. The first place in the two divisions competed for the championship.