About These Ratings

I.    The BCS and College Football Championships

II.    Ratings Description

III.    Results from 1992 through 2013

IV.    Thanks and Acknowledgements

 


 

I.    The BCS and College Football Championships

There is no more controversial topic in sports than deciding who is #1 in college football.  NCAA Division I-A football is unique among college sports because before 1998, it had no playoff system to determine its national champion.  Sports writers and college football coaches have had their own polls for many years, but these have often disagreed.  The various post-season bowls, locked as they have been to specific conference tie-ins, frequently did not result in match-ups that produced a clear national champion.  There were (and are) a variety of mathematical rating systems that lacked consensus in their results. 

In 1998, Commissioner Roy Kramer of the SEC and the heads of the other major Division I-A conferences designed a system to select two teams that would be invited to play for the national championship, and the Bowl Championship Series was created.  In its sixteen years of existence, it produced fifteen undisputed national champions - a much better record than anything that preceded it.  The 2014 season will see a four-team playoff.

The BCS calculates for each contender a simple average of three terms: 1) the team's position in the Harris Interactive College Football Poll; 2) the team's position in the USA Today-AFCA Coaches' Poll; and 3) the team's average position in a set of six computer ratings.  The two top-rated teams at the end of the regular season play for the national championship.

 

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II.  Ratings Description

A lot has been written on how to rate football teams.   This is not surprising, because a good rating system has applications far beyond sports.  (A uesful bibliography is kept by David Wilson here.)   

Sports like college football with short seasons and many teams are much harder to rate than sports with many games and few teams, like baseball for example.  If teams in a league play a balanced schedule, then winning percentage is all you need to rank the teams.  College football schedules are far from balanced, though.  About 700 college football teams can be linked by schedules, but because each team plays only about eleven games, there is no direct way to compare each team with the vast majority of all the other teams.  Using winning percentage as the benchmark for comparison doesn't work.  (Was 2001 division III champion Mount Union at 14-0 as good as 2001 division I-A champion Miami FL, 13-0?  Each had a perfect winning percentage.) 

A significant but hard-to-measure factor in comparing teams is sportsmanship.  Running up the score is generally looked on as evidence of bad sportsmanship, behavior which should not be encouraged or rewarded.  With this in mind, the BCS has chosen computer systems that use only won/loss data (and not scoring margin) to compute ratings.  We have developed such a system that provides reasonable results.  We rate all varsity teams of four year colleges that can be connected by mutual opponents, taking note of game locations.  Games played against club teams, junior varsity teams, or junior or community college teams aren't counted.

The method we use is called a maximum likelihood estimate.  In it, each team i is assigned a rating value πi that is used in predicting the expected result between it and its opponent j, with the likelihood of i beating j given by:

 πi / (πi + πj)

The probability P of all the results happening as they actually did is simply the product of multiplying together all the individual probabilities derived from each game.  The rating values are chosen in such a way that the number P is as large as possible.  This is often called a Bradley-Terry model, and is described in papers listed at Wilson's site (see Bradley and Terry 1952, Ford 1957, Elo 1986, Keener 1993). 

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III.    Results from Past Years

Here are the pre- and post-bowl results from 1992 through 2013; the post-season position of the winners of the lower division playoffs are listed as well:

1992 Pre-bowl                   Final
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1 Miami FL             11-0-0   1 Alabama       13-0-0
2 Alabama              12-0-0   2 Miami FL      11-1-0
3 Florida St           10-1-0   3 Florida St    11-1-0
4 Texas A&M            12-0-0   4 Notre Dame    10-1-1
5 Notre Dame            9-1-1   5 Texas A&M     12-1-0

1992 Lower Division Champions
------------------------------------------------------
 82 Marshall           12-3-0   I-AA          Champion
116 Jacksonville St    12-1-1   II            Champion
169 Central St (OH)    12-1-0   NAIA          Champion
173 UW-La Crosse       12-0-1   III           Champion
186 Findlay            12-1-0   NAIA-II       Champion
 
 
1993 Pre-bowl*                  Final*
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1 West Virginia        11-0-0   1 Florida St    12-1-0
2 Nebraska             11-0-0   2 Auburn*       11-0-0
3 Florida St           11-1-0   3 Notre Dame    11-1-0
4 Auburn*              11-0-0   4 West Virginia 11-1-0
5 Notre Dame           10-1-0   5 Florida       11-2-0
* Auburn was ineligible for post-season play
 
1993 Lower Division Champions
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 76 Youngstown St      13-2-0   I-AA          Champion
 90 North Alabama      14-0-0   II            Champion
130 Mount Union        14-0-0   III           Champion
179 Pacific Lutheran   12-0-1   NAIA-II       Champion
310 East Central (OK)  10-3-0   NAIA          Champion
 
 
1994 Pre-bowl                   Final
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1 Nebraska             12-0-0   1 Nebraska      13-0-0
2 Penn State           11-0-0   2 Penn State    12-0-0
3 Colorado             10-1-0   3 Colorado      11-1-0
4 Florida St            9-1-1   4 Florida St    10-1-1
5 Florida              10-1-0   5 Alabama       12-1-0

 
1994 Lower Division Champions
------------------------------------------------------
 44 Youngstown St      14-0-1   I-AA          Champion
 87 North Alabama      13-1-0   II            Champion
144 Albion             13-0-0   III           Champion
234 Westminster (PA)   12-2-0   NAIA-II       Champion
240 NE Oklahoma St     11-2-0   NAIA          Champion
 
 
1995 Pre-bowl                   Final
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1 Nebraska             11-0-0   1 Nebraska      12-0-0
2 Florida              12-0-0   2 Florida       12-1-0
3 Northwestern         10-1-0   3 Tennessee     11-1-0
4 Ohio St              11-1-0   4 Colorado      10-2-0
5 Tennessee            10-1-0   5 Ohio St       11-2-0
 
1995 Lower Division Champions
------------------------------------------------------
 91 Montana            13-2-0   I-AA          Champion
105 North Alabama      14-0-0   II            Champion
116 UW-La Crosse       14-0-0   III           Champion
170 Central St (OH)    10-1-0   NAIA          Champion
312 Findlay            10-1-2   NAIA-II    Co-Champion
321 Central Washington 10-3-1   NAIA-II    Co-Champion
 
 
1996 Pre-bowl                   Final
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1 Florida St             11-0   1 Florida         12-1
2 Arizona St             11-0   2 Florida St      11-1
3 Florida                11-1   3 Ohio State      11-1
4 Ohio State             10-1   4 Arizona St      11-1 
5 Nebraska               10-2   5 Nebraska        11-2
 
1996 Lower Division Champions
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 66 Marshall             15-0   I-AA          Champion
148 Mount Union          14-0   III           Champion
150 Sioux Falls          14-0   NAIA-II       Champion
153 Northern Colorado    12-3   II            Champion
298 SW Oklahoma St        9-3   NAIA          Champion
 

1997 Pre-bowl                   Final
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1 Michigan               11-0   1 Nebraska        13-0
2 Nebraska               12-0   2 Michigan        12-0
3 Tennessee              11-1   3 Tennessee       11-2
4 Florida St             10-1   4 Florida St      11-1
5 Florida                 9-2   5 Florida         10-2
 
1997 Lower Division Champions
------------------------------------------------------
 92 Youngstown St        13-2   I-AA          Champion
135 Mount Union          14-0   III           Champion
138 Northern Colorado    13-2   II            Champion
159 Findlay              14-0   NAIA          Champion
 
 
1998 Pre-bowl                   Final
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1 Tennessee              12-0   1 Tennessee       13-0
2 Florida St             11-1   2 Florida St      11-2
3 UCLA                   10-1   3 Ohio State      11-1
4 Texas A&M              10-2   4 Wisconsin       11-1
5 Kansas St              11-1   5 Florida         10-2

1998 Lower Division Champions
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 91 Massachusetts        12-3   I-AA          Champion
115 NW Missouri St       15-0   II            Champion
123 Mount Union          14-0   III           Champion
200 Azusa Pacific        12-2   NAIA          Champion
 
 
1999 Pre-bowl                   Final                
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1 Florida St             11-0   1 Florida St      12-0
2 Virginia Tech          11-0   2 Nebraska        12-1
3 Nebraska               11-1   3 Virginia Tech   11-1 
4 Alabama                10-2   4 Michigan        10-2
5 Michigan St             9-2   5 Michigan St     10-2
 
1999 Lower Division Champions
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 91 Georgia Southern     13-2   I-AA          Champion
141 NW Missouri St       14-1   II            Champion
182 Pacific Lutheran     13-1   III           Champion
191 NW Oklahoma St       13-0   NAIA          Champion
 
 
2000 Pre-bowl                   Final                
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1 Oklahoma               12-0   1 Oklahoma        13-0 
2 Washington             10-1   2 Miami FL        11-1
3 Florida St             11-1   3 Washington      11-1
4 Miami FL               10-1   4 Oregon State    11-1
5 Oregon State           10-1   5 Florida St      11-2
 
2000 Lower Division Champions
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 64 Georgia Southern     13-2   I-AA          Champion
122 Delta State          14-1   II            Champion
129 Mount Union          14-0   III           Champion
171 Georgetown KY        14-0   NAIA          Champion
 
 
2001 Pre-bowl                   Final                
------------------------------------------------------
1 Miami FL               11-0   1 Miami FL        12-0
2 Nebraska               111   2 Tennessee       11-2
3 Oregon                 10-1   3 Oregon          11-1
4 Colorado               10-2   4 Florida         10-2
5 Tennessee              10-2   5 Nebraska        11-2
 
2001 Lower Division Champions
------------------------------------------------------
 74 Montana              15-1   I-AA          Champion
112 North Dakota         14-1   II            Champion
151 Mount Union          14-0   III           Champion
188 Georgetown KY        14-0   NAIA          Champion


2002 Pre-bowl                   Final                
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1 Ohio St                13-0   1 Ohio St         14-0
2 Miami FL               12-0   2 Miami FL        12-1
3 Georgia                12-1   3 Georgia         13-1
4 Southern Cal           10-2   4 Southern Cal    11-2
5 Oklahoma               11-2   5 Oklahoma        12-2
 
2002 Lower Division Champions
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 86 Western Kentucky     12-3   I-AA          Champion
110 Grand Valley St      14-0   II            Champion
158 Mount Union          14-0   III           Champion
225 Carroll MT           12-2   NAIA          Champion


2003 Pre-bowl                   Final                
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1 Oklahoma               12-1   1 LSU             13-1
2 LSU                    12-1   2 Southern Cal    12-1
3 Southern Cal           11-1   3 Miami OH        13-1
4 Miami OH               12-1   4 Georgia         11-3
5 Michigan               10-2   5 Oklahoma        12-2
 
2003 Lower Division Champions
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 69 Delaware             15-1   I-AA          Champion
100 Grand Valley St      14-1   II            Champion
150 St John's MN         14-0   III           Champion
177 Carroll MT           14-0   NAIA          Champion


2004 Pre-bowl                   Final                
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1 Oklahoma               12-0   1 Southern Cal    13-0
2 Southern Cal           12-0   2 Auburn          13-0
3 Auburn                 12-0   3 Oklahoma        12-1
4 Texas                  10-1   4 Texas           11-1
5 Utah                   11-0   5 Utah            12-0
 
2004 Lower Division Champions
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 62 James Madison        13-2   I-AA          Champion
106 Valdosta St          13-1   II            Champion
163 Linfield             13-0   III           Champion
247 Carroll MT           12-2   NAIA          Champion


2005 Pre-bowl                   Final                
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1 Texas                  12-0   1 Texas           13-0
2 Southern Cal           12-0   2 Southern Cal    12-1
3 Penn State             10-1   3 Penn State      11-1
4 Ohio State              9-2   4 Ohio State      10-2
5 Oregon                 10-1   5 Virginia Tech   11-2

2005 Lower Division Champions
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104 Appalachian St       12-3   I-AA          Champion
109 Grand Valley St      13-0   II            Champion
184 Mount Union          14-1   III           Champion
185 Carroll MT           14-0   NAIA          Champion


2006 Pre-bowl                   Final                
------------------------------------------------------
1 Ohio State             12-0   1 Florida         13-1
2 Michigan               11-1   2 Ohio St         12-1
3 Florida                12-1   3 Michigan        11-2
4 Southern Cal           10-2   4 Louisville      12-1
5 LSU                    10-2   5 LSU             11-2

2006 Lower Division Champions
------------------------------------------------------
 66 Appalachian St       14-1   I-AA          Champion
 91 Grand Valley St      15-0   II            Champion
126 Mount Union          15-0   III           Champion
185 Sioux Falls          14-0   NAIA          Champion


2007 Pre-bowl                   Final                
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1 Virginia Tech          11-2   1 LSU             12-2
2 Oklahoma               11-2   2 Kansas          12-1
3 LSU                    11-2   3 Georgia         11-2
4 Missouri               11-2   4 West Virginia   11-2
5 Ohio State             11-1   5 Missouri        12-2

2007 Lower Division Champions
------------------------------------------------------
 69 Appalachian St       13-2   I-AA          Champion
115 Valdosta St          13-1   II            Champion
184 UW-Whitewater        14-1   III           Champion
197 Carroll MT           15-0   NAIA          Champion


2008 Pre-bowl                   Final
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1 Oklahoma               12-1   1 Utah            13-0
2 Texas                  11-1   2 Florida         13-1
3 Texas Tech             11-1   3 Texas           12-1
4 Florida                12-1   4 Southern Cal    12-1
5 Utah                   12-0   5 Oklahoma        12-2

2008 Lower Division Champions
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112 Richmond             13-3   I-AA          Champion
140 Minnesota-Duluth     15-0   II            Champion
205 Mount Union          15-0   III           Champion
237 Sioux Falls          14-0   NAIA          Champion


2009 Pre-bowl                   Final
------------------------------------------------------
1 Alabama                13-0   1 Alabama         14-0
2 Cincinnati             12-0   2 Florida         13-1
3 Texas                  13-0   3 Boise St        14-0
4 Florida                12-1   4 Texas           13-1
5 TCU                    12-0   5 TCU             12-1

2009 Lower Division Champions
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 60 Villanova            14-1   I-AA          Champion
126 NW Missouri St       14-1   II            Champion
141 UW-Whitewater        15-0   III           Champion
153 Sioux Falls          15-0   NAIA          Champion


2010 Pre-bowl                   Final
------------------------------------------------------
1 Auburn                 13-0   1 Auburn          14-0
2 Oregon                 12-0   2 TCU             13-0
3 TCU                    12-0   3 Oregon          12-1
4 Arkansas               10-2   4 Stanford        12-1
5 Stanford               11-1   5 Ohio State      12-1

2010 Lower Division Champions
------------------------------------------------------
 81 Eastern Washington   13-2   I-AA          Champion
107 Minnesota-Duluth     15-0   II            Champion
147 UW-Whitewater        15-0   III           Champion
222 Carroll MT           14-0   NAIA          Champion


2011 Pre-bowl                   Final
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1 LSU                    13-0   1 Alabama         12-1
2 Alabama                11-1   2 LSU             13-1
3 Oklahoma St            11-1   3 Oklahoma St     11-1
4 Arkansas               10-2   4 Arkansas        11-2
5 Kansas St              10-2   5 Oregon          12-2

2011 Lower Division Champions
------------------------------------------------------
 72 North Dakota St      14-1   I-AA          Champion
181 Pittsburg St         13-1   II            Champion
200 UW-Whitewater        15-0   III           Champion
219 St Xavier            14-1   NAIA          Champion


2012 Pre-bowl                   Final
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1 Notre Dame             12-0   1 Alabama         13-1
2 Florida                11-1   2 Ohio State      12-0
3 Alabama                12-1   3 Notre Dame      12-1
4 Ohio State             12-0   4 Oregon          12-1
5 Stanford               11-2   5 South Carolina  11-2

2012 Lower Division Champions
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 75 North Dakota St      14-1   I-AA          Champion
218 Valdosta St          12-2   II            Champion
253 Mount Union          15-0   III           Champion
306 Marian IN            12-1   NAIA          Champion


2013 Pre-bowl                   Final
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1 Florida St             13-0   1 Florida St      14-0
2 Auburn                 12-1   2 Auburn          12-2
3 Alabama                11-1   3 Michigan St     13-1
4 Michigan St            12-1   4 South Carolina  11-2
5 Stanford               11-2   5 Missouri        12-2

2013 Lower Division Champions
------------------------------------------------------
 28 North Dakota St      15-0   I-AA          Champion
100 NW Missouri St       15-0   II            Champion
154 UW-Whitewater        15-0   III           Champion
184 Grand View           14-0   NAIA          Champion

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IV.    Thanks

I would not have been able to put this site together without help and encouragement from a lot of people!  I would particularly like to thank Ross Baker, Gib Bassett, Les Ford Jr., David Harville, Mark Hopkins, Jim Keener, Roy Kramer, Jeff Leake, Kenneth Massey, the late Herman Matthews, the late Dave Rothman, David Wilson, Rick Wilson, and especially Jeff Sagarin for many helpful suggestions.

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Peter R. Wolfe


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