Graph Theory Ranking: Post-Season

Submitted by joeyb on

This is my first time using Windows Live Writer to post something, so if something looks weird, that’s why. I’m making some changes to my database to allow me to rank past and future seasons, other sports, etc. I wanted to get these ranking out there before I make these changes and before most of the bowls get underway.

There are a few tweaks that I made to the algorithm. The major thing is that I took out FCS teams. Imagine you have Team A that plays 12 FBS teams and Team B that plays 11 FBS teams and 1 FCS team. In graph theory, playing that FCS team gives Team B shorter pathways to the 120ish teams in the FCS. I felt this was an unfair advantage for teams playing weaker schedules.

I also experimented with how to factor in Win-Loss (long story short, nothing changed with this, so you can skip to the next paragraph if you would like). Think about MSU, Wisconsin, and Iowa. MSU beat Wisconsin by 10, which gave them a path of .5 (1 / 2 scores). Iowa beat MSU by 31, which gave them a path of .25 (1 / 4 scores). When multiplied by the Win-Loss factor at the end, Wisconsin would receive a lower path score for Iowa’s win over MSU because they had the better record. I didn’t like the idea that Wisconsin could get more credit for Iowa’s win over MSU than Iowa would. I messed around with applying the winning team’s overall record to each game, then the same with the losing team’s record. I tried lots of different things, but none of them looked right. I didn’t like the idea of doing something just because it looked right, though. I decided that the additional path length that Wisconsin accrues by having to beat Iowa (they only beat Iowa by a point, so the path to Iowa is 1 and the path to MSU is 1.25) was enough of a penalty on Wisconsin.

The last main change since I last posted is that I am now factoring in homefield advantage. I have calculated homefield advantage to be worth 3.77 points in FBS games this year. In the Big Ten games it was roughly 6 or 7 points. When I did the power ranking for the Big Ten, I experimented using the two values and decided that 3.77 was the better number to use. One, it’s closer to the value that is usually associated with homefield advantage, and two, it would change from conference to conference. Mostly, though, it would change the path lengths between teams when going from the NCAA ranking to the conference power rankings, which is something that I didn’t want.

Without further ado, here are your top 25 and conference power rankings to start out the post-season. Keep in mind that because the conference power rankings only take into account the games that are played within the conference, teams might not be in the same order in the conference and in the top 25.

  FBS Top 25  
1 Oregon 1.677444
2 Stanford 1.963008
3 TCU 2.011924
4 Auburn 2.066706
5 Oklahoma 2.252090
6 Boise State 2.321805
7 Wisconsin 2.461991
8 Ohio State 2.473381
9 Missouri 2.555164
10 Virginia Tech 2.564181
11 Nevada 2.565927
12 Oklahoma State 2.609843
13 Nebraska 2.610955
14 Michigan State 2.687252
15 Arkansas 2.776214
16 Utah 2.942520
17 Navy 3.108798
18 LSU 3.119942
19 Alabama 3.128550
20 South Carolina 3.163205
21 Texas A&M 3.174412
22 Florida State 3.509243
23 Hawaii 3.525703
24 USC 3.628385
25 West Virginia 3.764604
30 Mississippi State 4.113444
40 Michigan 4.652036

 

ACC
Virginia Tech
Florida State
Miami (YTM)
North Carolina State
Maryland
Clemson
North Carolina
Georgia Tech
Boston College
Virginia
Duke
Wake Forest

 

Big 12
Oklahoma
Oklahoma State
Nebraska
Missouri
Texas A&M
Baylor
Iowa State
Texas
Kansas State
Texas Tech
Colorado
Kansas

 

Big East
West Virginia
Pittsburgh
Connecticut
Syracuse
Louisville
South Florida
Cincinnati
Rutgers

 

Big Ten
Wisconsin
Michigan State
Ohio State
Iowa
Illinois
Penn State
Northwestern
Michigan
Minnesota
Purdue
Indiana

 

Conference USA
UCF
Tulsa
Southern Miss
Southern Methodist
East Carolina
Houston
Marshall
Rice
UTEP
UAB
Tulane
Memphis

 

MAC
Northern Illinois
Toledo
Miami (NTM)
Ohio
Western Michigan
Temple
Kent State
Ball State
Central Michigan
Eastern Michigan
Bowling Green
Buffalo
Akron

 

MWC
TCU
Utah
Air Force
Brigham Young
San Diego State
UNLV
Colorado State
Wyoming
New Mexico

 

PAC 10
Oregon
Stanford
USC
Washington
Oregon State
Arizona State
Arizona
California
UCLA
Washington State

 

SEC
Auburn
Arkansas
LSU
Alabama
South Carolina
Florida
Mississippi State
Georgia
Tennessee
Kentucky
Mississippi
Vanderbilt

 

Sun Belt
Troy Trojans of Troy (We’re from Troy!)
Florida International
Middle Tennessee
Arkansas State
Louisiana-Monroe
North Texas
Florida Atlantic
Louisiana-Lafayette
Western Kentucky

 

WAC
Boise State
Hawaii
Nevada
Fresno State
Louisiana Tech
Idaho
Utah State
New Mexico State
San Jose State

I have an idea for game predictions, so I’ll probably post another poll along with bowl game predictions and comparisons to actual results. Sometime in January I’ll post polls for Basketball and Hockey.

Comments

justingoblue

December 25th, 2010 at 4:18 PM ^

I love these rankings you do. It really is a unique way to look at college ball and you deserve a lot of credit for coming through with this over and over again.

Two things real quick:

I think there's a typo in your SEC standing, should be South Carolina instead of South Florida, but no big deal.

Where does Mississippi State rank overall? They're two behind South Carolina in the SEC, so...mid-30's ish?

joeyb

December 26th, 2010 at 9:39 PM ^

Boise beat Hawaii. Hawaii beat Nevada. Nevada beat Boise. It's a circular reference and all of them were 7-1. This method tries to figure out who performed better overall. Beating a team head-to-head gives you a big advantage, but doesn't immediately mean that you are the better team.

Consider this: If Boise's kicker hadn't missed that FG, this would be the order they would be ranked by their records.

joeyb

December 28th, 2010 at 12:50 AM ^

I'm looking at the paths and it just looks like they played a diverse schedule, pulverized a majority of their schedule, and had a 10-2 record.

They beat Iowa State, which gets them a path to the Big 12. They beat Pitt, which gets them a path to the Big East. They beat BYU, who beat Washington, which gets them a path to the Pac 10.

To get to Michigan:

68-27 @Iowa State (.167)

27-10 vs. N. Illinois (.500)

34-23 @Minnesota (.500)

27-24 vs. Iowa (1.000)

38-28 @Michigan (.500)

That gives them a path of 2.667, which is what the database has. I can tinker around with weighting, but I promised myself that everything I do is because it makes sense and not because it looks how I think it should.