Another Measurement of Schedule Difficulty

© Copyright 2011, Paul Kislanko

For each team's rank, the maximum "interest value" occurs when their opponent has the same rank as them, so the set of all maxima is given by

( N + 1 - R)2 R

It strikes me that if the "interest factor" of all a team's games gives something of a relative SOS then we could define an absolute SOS just by averaging this function for all opponents' ranks.

Aside: When we have rating values to work with, there are much better approaches. Here we have only ranks as input and averaging ranks is not very illuminating.

Now, while I kinda like this, there's a bit of a problem. Giving a value of zero to games against unranked teams distorts the averages for non-conference SOS. One way to address that would be to include bye weeks in the average (and that thought is not indefensible, but there's no way - or too many ways - to assign bye weeks to "noncference" or "conference" schedule strength.)

So, instead of averaging them in, we'll just pretend that games against unranked teams are the same as bye weeks. As the season is played out, I'll average in the games that ranked teams lose to unranked teams.

Based upon 48 computer ratings as of today (3 Sep) - meaning I use the 25^th-best ranking - here're the lists:

Non-Conference ix Total Avg Rank Team Conf 1 5077.4 2538.70 73 Toledo MAC 2 8077.5 2019.38 38 Tulsa CUSA 3 4950.9 1650.32 9 LSU SEC 4 8194.5 1638.90 26 Nevada WAC 5 4710.5 1570.16 100 Kent State MAC 6 4665.2 1555.06 41 Penn State B10 7 3818.3 1272.75 13 Florida State ACC 8 4874.2 1218.55 111 North Texas SBC 9 3481.4 1160.47 33 Georgia SEC 10 3348.9 1116.31 101 UL Monroe SBC 11 2927.6 975.88 70 SMU CUSA 12 2709.3 903.11 82 Duke ACC 13 3549.7 887.42 109 Ball State MAC 14 1740.9 870.45 3 Oregon P12 15 4325.1 865.02 72 Fresno State WAC 16 771.0 770.99 30 Arizona State P12 17 1481.0 740.51 112 Western Kentucky SBC 18 1232.8 616.41 35 Arizona P12 19 3004.8 600.95 108 San Jose State WAC 20 1765.4 588.46 33 Miami-Florida ACC 21 1686.5 562.17 68 Colorado P12 22 1668.6 556.19 119 Akron MAC 23 1069.6 534.82 41 Oregon State P12 24 1560.0 520.00 40 Clemson ACC 25 1447.8 482.61 112 UL Lafayette SBC ix Total Avg Rank Team Conf 26 1716.5 429.13 111 Florida Atlantic SBC 27 1688.2 422.04 79 East Carolina CUSA 28 419.9 419.94 28 Utah P12 29 1567.6 391.89 28 West Virginia BigE 30 1465.7 366.42 114 New Mexico MW 31 723.5 361.74 44 Washington P12 32 1079.8 359.95 4 Oklahoma B12 33 1037.9 345.97 17 Texas A&M B12 34 1032.1 344.04 100 Arkansas State SBC 35 656.7 328.34 95 Central Michigan MAC 36 1271.0 317.76 93 Marshall CUSA 37 1248.5 312.12 79 Troy SBC 38 920.6 306.87 50 Northern Illinois MAC 39 905.2 301.75 24 Florida SEC 40 1171.6 292.89 98 Utah State WAC 41 842.6 280.88 40 Maryland ACC 42 835.3 278.43 90 Idaho WAC 43 1066.7 266.67 32 Pittsburgh BigE 44 519.2 259.60 85 Wake Forest ACC 45 518.1 259.03 27 Michigan State B10 46 674.5 224.82 50 Boston College ACC 47 659.0 219.66 12 Arkansas SEC 48 860.8 215.19 95 UAB CUSA 49 643.0 214.32 97 Wyoming MW 50 611.5 203.85 36 Air Force MW ix Total Avg Rank Team Conf 51 587.6 195.87 23 Southern California P12 52 751.4 187.86 50 South Florida BigE 53 725.2 181.29 75 Miami-Ohio MAC 54 530.2 176.72 5 Stanford P12 55 347.5 173.77 45 Texas Tech B12 56 520.5 173.51 80 Purdue B10 57 339.1 169.54 71 Iowa State B12 58 334.4 167.18 78 Temple MAC 59 828.0 165.60 4 Boise State MW 60 654.8 163.70 48 Michigan B10 61 314.8 157.42 109 Bowling Green MAC 62 304.2 152.12 17 Missouri B12 63 451.0 150.32 61 Syracuse BigE 64 449.6 149.87 106 UNLV MW 65 596.6 149.16 82 Louisiana Tech WAC 66 445.9 148.64 82 Minnesota B10 67 444.9 148.29 116 Buffalo MAC 68 267.1 133.56 117 Eastern Michigan MAC 69 393.3 131.11 10 Oklahoma State B12 70 256.9 128.46 13 Wisconsin B10 71 247.8 123.88 61 Georgia Tech ACC 72 239.1 119.54 58 Kansas State B12 73 337.3 112.44 79 Western Michigan MAC 74 410.1 102.52 62 Cincinnati BigE 75 302.8 100.92 44 Illinois B10 ix Total Avg Rank Team Conf 76 289.5 96.51 48 UCF CUSA 77 286.7 95.57 32 Iowa B10 78 273.6 91.20 19 South Carolina SEC 79 269.1 89.70 84 Rutgers BigE 80 159.8 79.92 92 Kansas B12 81 234.2 78.07 63 Louisville BigE 82 307.6 76.89 8 Ohio State B10 83 229.7 76.56 45 Texas B12 84 224.3 74.77 67 Mississippi SEC 85 443.0 73.83 117 New Mexico State WAC 86 213.5 71.18 6 TCU MW 87 282.0 70.49 96 Rice CUSA 88 352.4 70.48 53 Hawaii WAC 89 124.4 62.20 85 Washington State P12 90 174.0 58.01 17 Nebraska B10 91 170.3 56.77 12 Auburn SEC 92 169.1 56.37 64 UCLA P12 93 161.4 53.80 3 Alabama SEC 94 186.0 46.49 101 Middle Tenn State SBC 95 183.0 45.75 84 Florida Intl SBC 96 179.1 44.76 107 Tulane CUSA 97 132.4 44.15 58 Southern Miss CUSA 98 173.9 43.46 46 San Diego State MW 99 121.6 40.52 63 Northwestern B10 100 121.0 40.35 92 Vanderbilt SEC ix Total Avg Rank Team Conf 101 104.1 34.70 98 UTEP CUSA 102 33.3 33.35 50 California P12 103 63.3 31.63 30 North Carolina State ACC 104 92.0 30.67 41 North Carolina ACC 105 91.5 30.49 76 Virginia ACC 106 60.5 30.26 63 Kentucky SEC 107 70.2 23.41 69 Houston CUSA 108 60.3 20.11 49 Tennessee SEC 109 66.9 16.72 52 Connecticut BigE 110 53.7 13.42 103 Colorado State MW 111 25.7 12.83 22 Mississippi State SEC 112 35.2 11.72 13 Virginia Tech ACC 113 28.9 9.62 88 Indiana B10 114 24.9 8.29 89 Ohio MAC 115 6.5 6.51 55 Baylor B12 116 8.4 4.19 117 Memphis CUSA

Overall ix Total Avg Rank Team Conf 1 12692.5 1153.86 9 LSU SEC 2 9027.2 902.72 23 Mississippi State SEC 3 9911.1 901.01 35 Arizona P12 4 9507.2 864.29 41 Oregon State P12 5 9303.1 845.73 44 Washington P12 6 9062.2 823.84 68 Mississippi SEC 7 8988.3 817.12 24 Florida SEC 8 8914.8 810.44 12 Arkansas SEC 9 10497.0 807.46 67 Colorado P12 10 8828.7 802.61 11 Auburn SEC 11 8727.0 793.37 50 California P12 12 8535.0 775.91 85 Washington State P12 13 8505.4 773.22 56 Baylor B12 14 8312.4 755.67 49 Tennessee SEC 15 9016.3 751.36 25 Southern California P12 16 8263.8 751.26 41 Penn State B10 17 8357.4 696.45 26 Nevada WAC 18 8290.8 690.90 38 Tulsa CUSA 19 7436.9 676.08 114 New Mexico MW 20 6703.3 670.33 32 Arizona State P12 21 6608.7 660.87 97 Wyoming MW 22 7126.3 647.84 95 Vanderbilt SEC 23 6423.4 642.34 106 UNLV MW 24 6342.3 634.23 35 Air Force MW 25 6675.6 606.88 71 Iowa State B12 ix Total Avg Rank Team Conf 26 6591.0 599.18 45 Texas Tech B12 27 6530.4 593.67 58 Kansas State B12 28 6522.5 592.95 92 Kansas B12 29 6773.2 564.43 17 Texas A&M B12 30 6146.2 558.75 33 Georgia SEC 31 6024.9 547.72 103 Colorado State MW 32 6023.2 547.57 46 San Diego State MW 33 6011.3 546.48 17 Missouri B12 34 6469.0 539.08 45 Texas B12 35 5262.4 526.24 72 Toledo MAC 36 5710.0 519.09 3 Oregon P12 37 6216.3 518.02 5 Stanford P12 38 5078.4 461.67 82 Duke ACC 39 5532.8 461.07 10 Oklahoma State B12 40 4912.9 446.62 111 North Texas SBC 41 4883.2 443.93 100 Kent State MAC 42 4799.4 436.31 13 Florida State ACC 43 4609.1 419.01 3 Alabama SEC 44 4799.6 399.97 72 Fresno State WAC 45 4231.2 384.66 40 Clemson ACC 46 4078.7 370.80 34 Miami-Florida ACC 47 4444.7 370.39 21 Notre Dame ND 48 4055.0 368.63 6 TCU MW 49 4053.4 368.49 27 Michigan State B10 50 4350.6 362.55 65 UCLA P12 ix Total Avg Rank Team Conf 51 4029.4 335.78 4 Oklahoma B12 52 3655.4 332.31 80 Purdue B10 53 3578.6 325.33 19 South Carolina SEC 54 3577.9 325.27 17 Nebraska B10 55 3200.4 320.04 63 Kentucky SEC 56 3156.0 315.60 13 Wisconsin B10 57 3152.6 315.26 86 Wake Forest ACC 58 3460.8 314.62 88 Indiana B10 59 3748.9 312.41 109 Ball State MAC 60 3401.5 309.23 100 UL Monroe SBC 61 3652.5 304.37 48 Michigan B10 62 3345.0 304.09 71 SMU CUSA 63 3294.6 299.51 51 Boston College ACC 64 3515.0 292.92 108 San Jose State WAC 65 3136.8 285.16 44 Illinois B10 66 3099.1 281.74 39 BYU Ind 67 3379.2 281.60 4 Boise State MW 68 2825.4 256.86 85 Minnesota B10 69 2784.0 253.09 77 Virginia ACC 70 2563.2 233.02 40 Maryland ACC 71 2171.5 217.15 61 Georgia Tech ACC 72 2595.5 216.29 8 Ohio State B10 73 2183.4 198.49 28 West Virginia BigE 74 1746.1 174.61 26 Utah P12 75 1631.2 163.12 30 North Carolina State ACC ix Total Avg Rank Team Conf 76 1786.1 162.38 98 Utah State WAC 77 1934.2 161.19 79 East Carolina CUSA 78 1767.8 160.71 41 North Carolina ACC 79 1759.4 159.95 119 Akron MAC 80 1755.7 159.61 63 Northwestern B10 81 1748.2 158.93 32 Pittsburgh BigE 82 1881.9 156.82 111 Florida Atlantic SBC 83 1541.6 154.16 112 Western Kentucky SBC 84 1619.8 147.25 32 Iowa B10 85 1704.8 142.07 93 Marshall CUSA 86 1530.0 139.09 50 South Florida BigE 87 1504.2 136.75 113 UL Lafayette SBC 88 1331.5 133.15 88 Idaho WAC 89 1416.5 128.78 52 Navy Ind 90 1269.8 126.98 61 Syracuse BigE 91 1182.9 118.29 85 Rutgers BigE 92 1286.5 116.96 65 Cincinnati BigE 93 1106.6 110.66 63 Louisville BigE 94 1285.4 107.12 78 Troy SBC 95 1267.2 105.60 96 UAB CUSA 96 1084.7 98.61 100 Arkansas State SBC 97 1058.0 96.18 82 Louisiana Tech WAC 98 990.8 90.07 50 Northern Illinois MAC 99 830.6 83.06 95 Central Michigan MAC 100 898.0 81.64 52 Connecticut BigE ix Total Avg Rank Team Conf 101 950.1 73.08 117 New Mexico State WAC 102 790.9 71.90 13 Virginia Tech ACC 103 810.8 67.57 75 Miami-Ohio MAC 104 773.4 64.45 52 Hawaii WAC 105 657.1 59.74 86 Army Ind 106 614.2 55.83 48 UCF CUSA 107 611.9 55.63 116 Buffalo MAC 108 539.4 53.94 109 Bowling Green MAC 109 568.6 51.69 97 UTEP CUSA 110 619.0 51.58 99 Rice CUSA 111 509.6 46.33 79 Western Michigan MAC 112 436.7 43.67 117 Eastern Michigan MAC 113 414.7 41.47 78 Temple MAC 114 478.9 39.90 106 Tulane CUSA 115 334.4 30.40 69 Houston CUSA 116 329.7 29.97 58 Southern Miss CUSA 117 267.3 26.73 117 Memphis CUSA 118 221.7 20.15 83 Florida Intl SBC 119 239.0 19.91 101 Middle Tenn State SBC 120 90.1 8.20 89 Ohio MAC