This is just a toy model to learn how to use Pyro-PPL.
Uses games from 2002-2018 from Ryan Westerman's dataset on data.world.
Fits a classical elo model w/ mean field posteriors.
\logit(P(team a beats team b at home for team a)) = eta_a - eta_b + mu_home
eta_t ~ N(0, \sigma^2_T)
mu_home ~N(0, 1)
log(sigma^2_T) ~ N(0, 1)
And learns independent gaussian varitional posteriors (mean field) for all parameters.
The model does not address time in any way - all games are treated as coming from one 16 year season.
We learn a posterior mean and sigma for all team quality terms. You can see in the plot below that there is a line of teams with low uncertainty (D1 teams) and then a cluster of teams with lower quality and much higher uncertainty (the D2 and D3 teams that play a few games a year against D1 opponents).
Top 20 Teams (2002-2018)
| team_id | team_loc | team_scale | team_name |
|---|---|---|---|
| 3 | 4.117532 | 0.158716 | Kansas |
| 1142 | 3.925897 | 0.142423 | Duke |
| 811 | 3.673764 | 0.136719 | North Carolina |
| 926 | 3.521789 | 0.140202 | Kentucky |
| 270 | 3.417975 | 0.166304 | Gonzaga |
| 581 | 3.362034 | 0.134804 | Michigan State |
| 1173 | 3.329610 | 0.135522 | Louisville |
| 636 | 3.318774 | 0.126101 | Wisconsin |
| 228 | 3.252279 | 0.124778 | Villanova |
| 307 | 3.245923 | 0.130126 | Arizona |
| 937 | 3.231030 | 0.131917 | Syracuse |
| 791 | 3.173766 | 0.129211 | Florida |
| 733 | 3.109020 | 0.125651 | Ohio State |
| 424 | 3.074265 | 0.126176 | Texas |
| 657 | 3.058153 | 0.129009 | Pittsburgh |
| 705 | 3.036528 | 0.136308 | Notre Dame |
| 149 | 2.975302 | 0.124163 | Maryland |
| 827 | 2.896946 | 0.126974 | Xavier |
| 466 | 2.892369 | 0.115101 | Virginia |
| 607 | 2.860635 | 0.126801 | Oklahoma |
Top 10 most uncertain teams (just to show that they are non-D1)
| team_id | team _loc | team_scale | team _name |
|---|---|---|---|
| 68 | -0.447611 | 1.925912 | Middlebury |
| 1025 | -0.336367 | 1.896740 | Bemidji State |
| 49 | -0.526100 | 1.894665 | American International |
| 866 | -0.461130 | 1.861554 | Marietta |
| 1124 | -0.414623 | 1.859332 | Saint Joseph's (ME) |
| 847 | -0.448507 | 1.838682 | Lebanon Valley |
| 1039 | -0.252159 | 1.829058 | Morehouse |
| 1122 | -0.555787 | 1.823220 | Oklahoma Baptist |
| 1018 | -0.772689 | 1.801807 | Lawrence |
| 948 | -0.266656 | 1.800887 | Mountain State |