Monday, November 30, 2015

Using the Schulze Voting System on the CBB AP Poll

Observation: The AP poll for college basketball is a system where each of N voters lists ("votes for") their top 25 teams, so we can use any number of voting systems to get an overall ranking.

The official AP Poll just so happens to run a truncated Borda count, where a pollster ranking a team nth earns 26 - n points for that team. Here is the most recent AP Poll under this voting system, where the number on the right hand side of each row is the number of points that team earned:

1. Kentucky, 1619
2. Maryland, 1512
3. Michigan State, 1510
4. Kansas, 1342
5. Iowa State, 1338
6. Oklahoma, 1269
7. Duke, 1253
8. Villanova, 1218
9. North Carolina, 1155
10. Virginia, 965
11. Purdue, 904
12. Xavier, 801
13. Gonzaga, 788
14. Syracuse, 696
15. Oregon, 628
16. Vanderbilt, 587
17. Cincinnati, 551
18. Texas A&M, 522
19. Arizona, 504
20. West Virginia, 363
21. Miami (FL), 289
22. SMU, 256
23. Providence, 247
24. Louisville, 173
25. Baylor, 162
26. Connecticut, 153
27. Utah, 72
28. Butler, 62
29. George Washington, 45
30. Indiana, 26
31. UNI, 25
32. Notre Dame, 22
33. California, 19
34. Pittsburgh, 11
35. Dayton, 8
36. South Carolina, 5
36. San Diego State, 5
38. Georgetown, 4
39. UTEP, 3
40. Northwestern, 2
40. LSU, 2
40. Iowa, 2
40. Arkansas-Little Rock, 2
44. Colorado State, 1

Just for fun, I decided to run the poll under the Schulze voting system:
1. Kentucky
2. Maryland
3. Michigan State
4. Iowa State
5. Kansas
6. Oklahoma
7. Duke
8. Villanova
9. North Carolina
10. Virginia
11. Purdue
12. Xavier
13. Syracuse
14. Gonzaga
15. Vanderbilt
16. Oregon
17. Cincinnati
18. Arizona
19. Texas A&M
20. West Virginia
21. Miami (FL)
22. SMU
23. Providence
24. Baylor
25. Connecticut
26. Louisville
27. Butler
28. Utah
28. George Washington
30. UNI
31. California
32. Notre Dame
33. Indiana
34. Dayton
35. Pittsburgh
35. South Carolina
37. Northwestern
38. Georgetown
39. Iowa
40. Colorado State
40. UTEP
40. LSU
40. Arkansas-Little Rock
40. San Diego State

It's very similar to the Borda count, as expected. In the top 10, the only change is that Kansas and Iowa State switch spots. For the rest of the top 25, a few pairs of teams switch places, and Loiusville falls from #24 to #26. (Of course, there's a lot less precision in the lower places, where very few votes are being cast.)

I might run the AP Poll on a few other rating systems in the future if I have time.

* All data taken from the AP Poll web page.