In a series of posts, we developed a new method for ranking college football teams. The method evolved a little over time, but it currently has three basic steps. First, all applicable teams are listed in a table in the same order down the rows and across the columns from left to right. Second, one entry is made in the table for each game; that entry can simply be a 1 to indicate a victory by the row team over the column team, it can be coded to reflect the margin of victory and location of the game from the victor’s perspective (home, away, or neutral), and it can also give more weight to games later in the season. Third, the model uses hill climbing to iteratively swap teams in the rows and columns to minimize the sum of the values below the diagonal weighted by the distance below the diagonal; in effect, the model is trying to find the ranking with the smallest degree of upsets by lower ranked teams over higher ranked teams.
Thus far, we have applied our method only to ranking college football teams. Of course, it can be applied to rank teams in any sport or activity. The model is most useful when there is a relatively large number of games, including a significant number of nonconference games, but not enough games so the standings alone can be used to rank teams.
We use the method here to rank women’s college volleyball teams. However, at least initially, we do not include all 348 Division 1 teams, which would require a great deal of both coding time and computational time. Instead, we include only the 99 teams from the top seven conferences: the Big Ten, the Southeastern Conference, the Big 12, the Atlantic Coast Conference, the Big East, the Mid-American Conference, and Conference USA.
Similar to our method for college football, we coded the games so a 3-0 set win is worth twice as much as a 3-2 set win and a road win is worth 10 percent more than a neutral court win, with a home win being worth 10 percent less than a neutral court win. We did not adjust for when the games were played in the season. So, our ranking is meant to capture the teams’ overall performance during the season, not their current performance. Following is our ranking of the 99 teams from those seven conferences.
|
Rank |
Team |
Conference |
|
1 |
Nebraska |
Big Ten |
|
2 |
Pittsburgh |
ACC |
|
3 |
Brigham Young |
Big 12 |
|
4 |
Florida |
SEC |
|
5 |
Southern Methodist |
ACC |
|
6 |
Kentucky |
SEC |
|
7 |
Louisville |
ACC |
|
8 |
Wisconsin |
Big Ten |
|
9 |
Texas |
SEC |
|
10 |
Tennessee |
SEC |
|
11 |
Arizona St. |
Big 12 |
|
12 |
Oregon |
Big Ten |
|
13 |
Penn St. |
Big Ten |
|
14 |
Texas A&M |
SEC |
|
15 |
Purdue |
Big Ten |
|
16 |
Minnesota |
Big Ten |
|
17 |
Washington |
Big Ten |
|
18 |
Indiana |
Big Ten |
|
19 |
Texas Christian |
Big 12 |
|
20 |
Kansas |
Big 12 |
|
21 |
Baylor |
Big 12 |
|
22 |
Colorado |
Big 12 |
|
23 |
Utah |
Big 12 |
|
24 |
Michigan St. |
Big Ten |
|
25 |
California Los Angeles |
Big Ten |
|
26 |
Illinois |
Big Ten |
|
27 |
Michigan |
Big Ten |
|
28 |
Southern California |
Big Ten |
|
29 |
Stanford |
ACC |
|
30 |
Vanderbilt |
SEC |
|
31 |
North Carolina |
ACC |
|
32 |
Marquette |
Big East |
|
33 |
Creighton |
Big East |
|
34 |
Miami |
ACC |
|
35 |
Missouri |
SEC |
|
36 |
Mississippi St. |
SEC |
|
37 |
Georgia |
SEC |
|
38 |
Georgia Tech |
ACC |
|
39 |
Oklahoma |
SEC |
|
40 |
California |
ACC |
|
41 |
Houston |
Big 12 |
|
42 |
Iowa St. |
Big 12 |
|
43 |
Kansas St. |
Big 12 |
|
44 |
Cincinnati |
Big 12 |
|
45 |
Louisiana St. |
SEC |
|
46 |
Auburn |
SEC |
|
47 |
South Carolina |
SEC |
|
48 |
Mississippi |
SEC |
|
49 |
Central Florida |
Big 12 |
|
50 |
West Virginia |
Big 12 |
|
51 |
Maryland |
Big Ten |
|
52 |
Arkansas |
SEC |
|
53 |
Rutgers |
Big Ten |
|
54 |
Iowa |
Big Ten |
|
55 |
Alabama |
SEC |
|
56 |
Ohio St. |
Big Ten |
|
57 |
Northwestern |
Big Ten |
|
58 |
Duke |
ACC |
|
59 |
DePaul |
Big East |
|
60 |
North Carolina St. |
ACC |
|
61 |
Florida St. |
ACC |
|
62 |
Wake Forest |
ACC |
|
63 |
Western Kentucky |
CUSA |
|
64 |
Missouri St. |
CUSA |
|
65 |
Bowling Green |
MAC |
|
66 |
Toledo |
MAC |
|
67 |
Miami Ohio |
MAC |
|
68 |
Ball St. |
MAC |
|
69 |
Xavier |
Big East |
|
70 |
St. John’s |
Big East |
|
71 |
Providence |
Big East |
|
72 |
Butler |
Big East |
|
73 |
Villanova |
Big East |
|
74 |
Georgetown |
Big East |
|
75 |
Connecticut |
Big East |
|
76 |
Seton Hall |
Big East |
|
77 |
Middle Tennessee State |
CUSA |
|
78 |
Florida International |
CUSA |
|
79 |
Kennesaw St. |
CUSA |
|
80 |
Sam Houston St. |
CUSA |
|
81 |
Liberty |
CUSA |
|
82 |
New Mexico St. |
CUSA |
|
83 |
Notre Dame |
ACC |
|
84 |
Boston College |
ACC |
|
85 |
Virginia Tech |
ACC |
|
86 |
Virginia |
ACC |
|
87 |
Clemson |
ACC |
|
88 |
Delaware |
CUSA |
|
89 |
Ohio |
MAC |
|
90 |
Western Michigan |
MAC |
|
91 |
Buffalo |
MAC |
|
92 |
Syracuse |
ACC |
|
93 |
Akron |
MAC |
|
94 |
Kent St. |
CUSA |
|
95 |
Eastern Michigan |
MAC |
|
96 |
Arizona |
Big 12 |
|
97 |
Texas Tech |
Big 12 |
|
98 |
Central Michigan |
MAC |
|
99 |
Jacksonville St. |
CUSA |
So, we actually needed to include only five conferences to rank the top teams. The highest ranked team from the MAC or Conference USA is Western Kentucky at number 63. We note that Western Kentucky is effectively ranked number 30 in the current AVCA rankings, as it received the fifth most voting points out of teams not ranked in the top 25. However, it is easy to understand why our model ranks it much lower. Western Kentucky does not have any wins against teams ranked above it in our model; its best win is against Pepperdine, which is not included in our model. Western Kentucky lost to all three teams ranked above it in our model, including Oklahoma, which is currently in 11th place in the SEC and is ranked number 39 in our model.
Among the Division 1 teams not included in our model, the team that would rank highest is probably Colorado State, which is effectively ranked number 29 in the current AVCA rankings. Colorado State might rank similarly to Colorado in our model, as the teams split a home-and-home series against each other.
The table below compares the top 25 teams in our rankings with the 25 teams in the current AVCA rankings. Both rankings include teams only from four conferences. However, our model is more impressed with teams from the Big Ten (with 10 teams versus 8 in AVCA’s ranking) and less impressed with teams from the ACC (with only 3 teams versus 5 in AVCA’s ranking).
|
Rank |
My Model |
AP |
|
1 |
Nebraska |
Nebraska |
|
2 |
Pittsburgh |
Pittsburgh |
|
3 |
Brigham Young |
Louisville |
|
4 |
Florida |
Florida |
|
5 |
Southern Methodist |
Southern Methodist |
|
6 |
Kentucky |
Kentucky |
|
7 |
Louisville |
Wisconsin |
|
8 |
Wisconsin |
Brigham Young |
|
9 |
Texas |
Arizona St. |
|
10 |
Tennessee |
Tennessee |
|
11 |
Arizona St. |
Penn St. |
|
12 |
Oregon |
Oregon |
|
13 |
Penn St. |
Texas |
|
14 |
Texas A&M |
Purdue |
|
15 |
Purdue |
Kansas |
|
16 |
Minnesota |
Texas Christian |
|
17 |
Washington |
Texas A&M |
|
18 |
Indiana |
Washington |
|
19 |
Texas Christian |
Minnesota |
|
20 |
Kansas |
North Carolina |
|
21 |
Baylor |
Indiana |
|
22 |
Colorado |
Vanderbilt |
|
23 |
Utah |
Stanford |
|
24 |
Michigan St. |
Baylor |
|
25 |
California Los Angeles |
Colorado |
We note that including the other 249 Division 1 teams in our model would likely have little effect on our top 25 teams. Our top 25 teams have only two losses to teams not included in our model: Arizona St.’s loss to California Davis and Utah’s loss to Long Beach St. So, those two teams might be ranked slightly lower if all Division 1 teams were included.