Relative SOS

© Copyright 2009, Paul Kislanko

In my previous post I wrote

The formula for the "interest factor" is (120-better_rank) × (120-worse_rank) ÷ (2×worse_rank − better_rank) and since for each team that includes its own rank and how much better or worse its opponents' ranks are we can use that to define a relative "SOS" measurement.

We have to be a little bit careful describing the "average interest factor" as an SOS - that is really only the case for teams that have the "better_rank." Since North Texas finished 120th last year, the value for all its games is zero. That's consistent for the Mean Green's opponents' SOS (and its amazing that averaging in that zero doesn't hurt more than it does for them) but to say NT's SOS is zero wouldn't make any sense.

It only takes some tweaks to the formula to define a true "relative" SOS. For each game team t plays we calculate:

N + 1 − opponent's_rank ( | team's_rank − opponent's_rank | + opponent's_rank )

where N is the number of ranked teams (120 for FBS.) We use N+1 instead of N in the numerator to assign FCS opponents a zero value (instead of -1 as in the interest calculation.) With this change, we have basically a "one-sided" version of the interest factor. When the team's rank is worse than the opponent's, the denominator is just the team's rank. When it is better than the opponent's, the denominator is 2×opponent's_rank − the team's rank.

Here's the top 40 non-conference schedules by relative SOS:

ix Avg 08 Rank Team Conf 1 5.946 13 Oregon P10 10-Boise St 78-Purdue 4-Utah   2 2.802 18 Virginia Tech ACC 7-Alabama 93-Marshall 22-Nebraska 49-East Carolina 3 2.695 12 Ohio State B10 49-Navy 3-Southern California 108-Toledo 111-New Mexico St 4 2.486 19 Florida St ACC 121-Jacksonville St 28-BYU 44-South Florida 1-Florida 5 2.063 39 Rice CUSA 9-Texas Tech 20-Oklahoma St 44-Vanderbilt 49-Navy 6 2.025 3 Southern California P10 84-San Jose St 12-Ohio State 53-Notre Dame   7 1.995 28 BYU MW 4-Oklahoma 114-Tulane 19-Florida St 100-Utah St 8 1.921 20 Oklahoma St B12 12-Georgia 52-Houston 39-Rice 121-Grambling 9 1.678 10 Boise St WAC 13-Oregon 116-Miami-Ohio 77-Bowling Green 121-UC Davis 37-Tulsa 10 1.611 37 Tulsa CUSA 84-New Mexico 4-Oklahoma 121-Sam Houston 10-Boise St 11 1.610 12 Georgia SEC 20-Oklahoma St 66-Arizona St 121-Tennessee Tech 26-Georgia Tech 12 1.494 16 Oregon St P10 121-Portland St 81-UNLV 20-Cincinnati   13 1.454 49 East Carolina CUSA 121-Appalachian St 29-West Virginia 31-North Carolina 18-Virginia Tech 14 1.421 26 Georgia Tech ACC 121-Jacksonville St 85-Mississippi St 44-Vanderbilt 12-Georgia 15 1.376 4 Utah MW 100-Utah St 84-San Jose St 13-Oregon 80-Louisville 16 1.343 22 Nebraska B12 80-Florida Atlantic 89-Arkansas St 18-Virginia Tech 91-UL Lafayette 17 1.219 20 Cincinnati BigE 121-SE Missouri St 16-Oregon St 72-Fresno St 116-Miami-Ohio 70-Illinois 18 1.214 39 Maryland ACC 20-California 121-James Madison 99-Middle Tenn St 38-Rutgers 19 1.184 40 Clemson ACC 99-Middle Tenn St 9-TCU 121-Coastal Car 42-South Carolina 20 1.150 42 Miami-Florida ACC 4-Oklahoma 121-Florida A&M 99-UCF 44-South Florida 21 1.100 52 Houston CUSA 121-Northwestern St 20-Oklahoma St 9-Texas Tech 85-Mississippi St 22 1.051 35 Arizona P10 71-Central Michigan 121-Northern Arizona 27-Iowa   23 1.040 62 Nevada WAC 53-Notre Dame 59-Colorado St 18-Missouri 81-UNLV 24 1.026 44 Vanderbilt SEC 121-Western Carolina 39-Rice 107-Army 26-Georgia Tech 25 1.011 59 Stanford P10 30-Wake Forest 84-San Jose St 53-Notre Dame   26 0.994 4 Oklahoma B12 28-BYU 121-Idaho St 37-Tulsa 42-Miami-Florida 27 0.958 71 Central Michigan MAC 35-Arizona 27-Michigan St 121-Alcorn St 29-Boston College 28 0.947 77 Bowling Green MAC 63-Troy 18-Missouri 93-Marshall 10-Boise St 29 0.921 7 Alabama SEC 18-Virginia Tech 97-Florida Intl 120-North Texas 121-Chattanooga 30 0.894 70 Illinois B10 18-Missouri 121-Illinois St 20-Cincinnati 72-Fresno St 31 0.884 84 San Jose St WAC 3-Southern California 4-Utah 59-Stanford 121-Cal Poly 32 0.873 63 Troy SBC 77-Bowling Green 1-Florida 102-UAB 60-Arkansas 33 0.851 66 Auburn SEC 69-Louisiana Tech 29-West Virginia 36-Ball State 121-Furman 34 0.851 52 North Carolina St ACC 42-South Carolina 121-Murray St 121-Gardner Webb 23-Pittsburgh 35 0.847 42 South Carolina SEC 52-North Carolina St 80-Florida Atlantic 121-S Carolina St 40-Clemson 36 0.844 97 Florida Intl SBC 7-Alabama 38-Rutgers 108-Toledo 1-Florida 37 0.836 1 Florida SEC 121-Charleston So 63-Troy 97-Florida Intl 19-Florida St 38 0.826 44 South Florida BigE 121-Wofford 118-Western Kentucky 121-Charleston So 19-Florida St 42-Miami-Florida 39 0.789 85 UTEP CUSA 66-Buffalo 32-Kansas 111-New Mexico St 3-Texas 40 0.780 116 Miami-Ohio MAC 54-Kentucky 10-Boise St 20-Cincinnati 38-Northwestern

Here's the Relative SOS for full schedules.