Realignment in the NFL

John E. Mitchell

An integer programming approach was used to find the alignment that minimizes the sum of intradivisional distances. The locations of the cities and the distances between any two of them can be found here.


 
Table 1: Optimal alignment for the unrestricted problem. Value: 27957km. See map.
Division Teams
1 Atlanta Carolina Cincinnati Tennessee
2 Baltimore Buffalo Pittsburgh Washington
3 New England New York Giants New York Jets Philadelphia
4 Chicago Cleveland Detroit Indianapolis
5 Dallas Denver Arizona Houston
6 Jacksonville Miami New Orleans Tampa Bay
7 Kansas City Green Bay Minnesota St Louis
8 Oakland San Diego San Francisco Seattle


 
Table 2: Realignment chosen by the NFL. Value: 50480km. See maps of the NFC and AFC.
NFC  
South Atlanta Carolina New Orleans Tampa Bay
North Chicago Detroit Green Bay Minnesota
West Arizona St Louis San Francisco Seattle
East Dallas NY Giants Philadelphia Washington
AFC  
East New England Buffalo Miami NY Jets
North Baltimore Cincinnati Cleveland Pittsburgh
West Denver Kansas City Oakland San Diego
South Houston Indianapolis Jacksonville Tennessee

The alignment chosen by the NFL has a sum of intradivisional distances of 50480km, which is 80% greater than the alignment given in Table 1. In the alignment given in Table 1, no team is more than one time zone from any other team in its division. If the teams in the NFC are selected as in Table 2, then San Francisco must be at least two time zones away from at least one other team in its division.

The choice made by the NFL minimizes the sum of intradivisional distances, given the composition of the AFC and NFC and subject to three additional restrictions:

A map of the solution in Table 1 is available.

If the AFC and NFC are optimized with no additional restrictions, the optimal value is 41152km, as in Table 3.

 
Table 3: Optimal realignment for the NFL's choice of AFC and NFC. Value: 41152km See maps of the NFC and AFC.
NFC  
South Atlanta Carolina New Orleans Tampa Bay
North Chicago Green Bay Minnesota St Louis
West Arizona Dallas San Francisco Seattle
East Detroit NY Giants Philadelphia Washington
AFC  
East Baltimore New England Buffalo NY Jets
North Cincinnati Cleveland Indianapolis Pittsburgh
West Denver Kansas City Oakland San Diego
South Houston Jacksonville Miami Tennessee

 
Table 4: Optimal realignment for the NFL's choice of NFC, with Dallas and Washington in the same division. Increase over the NFC distance in Table 3: 4208km. This differs from the NFL's choice in the alignment of Minnesota and St. Louis, and is 791km smaller than their choice for the NFC.
NFC  
South Atlanta Carolina New Orleans Tampa Bay
North Chicago Detroit Green Bay St Louis
West Arizona Minnesota San Francisco Seattle
East Dallas NY Giants Philadelphia Washington

If the Houston Texans had been placed in the NFC then the optimal value, with the additional conditions, is 48499km. but the AFC alignment is quite different -- see Table 5.

 
Table 5: Optimal NFC alignment if Houston placed in NFC, with the following restrictions: (1) Dallas and Washington in the same division as each other, (2) Chicago, Detroit, Green Bay and Minnesota in the same division, (3) Buffalo, Miami, the New York Jets, and New England in the same division. Optimal value: 48499km
Division Teams
South Atlanta Carolina New Orleans Tampa Bay
North Chicago Detroit Green Bay Minnesota
West Arizona St Louis San Francisco Houston
East Dallas NY Giants Philadelphia Washington
AFC 1 New England Buffalo Miami New York Jets
AFC 2 Baltimore Cleveland Jacksonville Pittsburgh
AFC 3 Denver Oakland San Diego Seattle
AFC 4 Cincinnati Indianapolis Kansas City Tennessee

A team other than Seattle could have been moved from the AFC to the NFC. Given the three additional conditions imposed by the NFL, the best choice is to move are the Kansas City Chiefs. The optimal solution exchanges these two teams in Table 2, giving a value of 48296km. This is 4.3% less than the chosen solution.

If all three restrictions are imposed without assigning each team to a particular conference, the optimal solution has value 37126km, with the alignment given in Table 6.

 
Table 6: Optimal alignment without preselecting conferences but with three restrictions: (1) Dallas and Washington in the same division as each other, (2) Chicago, Detroit, Green Bay and Minnesota in the same division, (3) Buffalo, Miami, the New York Jets, and New England in the same division. Optimal value: 37126km.
Division Teams
1 Atlanta Carolina Jacksonville Tampa Bay
2 Chicago Detroit Green Bay Minnesota
3 Arizona St Louis Denver Kansas City
4 Dallas New Orleans Washington Houston
5 New England Buffalo Miami New York Jets
6 Baltimore New York Giants Philadelphia Pittsburgh
7 Cincinnati Cleveland Indianapolis Tennessee
8 Oakland San Diego San Francisco Seattle