Graph Theory Ranking: Post-Season
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.
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?
December 25th, 2010 at 4:33 PM ^
Thanks for pointing that out. I can't just copy and past it, so I have to manually type each one. I just corrected it. I also added Miss. St. above. They are ranked 30.
December 25th, 2010 at 4:38 PM ^
Nice. Maybe we're a little less of an underdog than people seem to think.
I love this whole idea for team rankings. Why was nobody official ever able to put this together when the BCS started?
/rhetorical question
December 26th, 2010 at 12:36 PM ^
Hawaii over Nevada kinda makes no sense...especially after they just got torn apart. And Nevada beat Boise...
December 26th, 2010 at 6:05 PM ^
after the bowl season. Beside, no computer ranking are perfect. Hawaii beat Nevada in the regular season.
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.
December 27th, 2010 at 10:05 PM ^
I'd be concerned that your calculations gave Utah such a high ranking.
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.
December 30th, 2010 at 2:55 AM ^
I looked into this and nothing that I did could really did much with their position. I did however make some good changes which coincidentally move Auburn up. I'll talk about it more when I write up my next post after the bowl games.
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