Hardin-Bernhardt Ranks

Hardin-Bernhardt Ranks is a new way of ranking Quiz Bowl and History Bowl teams using a modified version of the Glicko-2 Elo formula that takes into account strength of field and margin of victory.

The Formulas

Adjusted Score Formula

This formula, based on the similar FiveThirtyEight formula for NFL teams, attempts to calculate an adjustment to the rating calculation given by the glicko-2 formula on the basis of margin of victory and relative pregame rating.

\[MovMod = (0.5+{{ln(1+{S_A\over S_A+S_B})}\over 5})({2.2\over0.001(R_A-R_B)+2.2})\]

Expected Score Formula

This formula uses the Elo ratings (R) of a given lower-rated Team A and higher-rated Team B to calculate what percentage of the total points Team A would be expected to score in a game against Team B. This formula will always result in a value for the expected score of A (S_E(A)) between 0 and 1.

\[S_E(A) = {1\over e^{(R_B-R_A)/400}+1}\] S_E(A) = expected score of A
R_B = current rating of B
R_A = current rating of A

New Rating Formula

Following a game between Team A and Team B, this formula calculates the new Elo rating of Team A. The new rating formula takes the percentage of the game’s points scored by Team A, multiplies it by T to adjust for conversion issues, and compares it to the expected score for A (S_E(A)). That result is then multiplied by the variables q and K to adjust for strength of field, and games played respectively.

\[R_n(A) = {R_o(A)+K[({qS_A\over S_A+S_B})-S_E(A)]}\] R_n = new rating
R_o = old rating
q = strength of field value
S = score
S_E(A) = expected score of A
K = game weight value

The Variables

q-Value

The q-value is used to represent strength of field at a tournament and intended to help improve elo as a measure of skill unaffected by the field a team is up against, and thus more useful and accurate as a comparison between teams from different regions. It is calculated as a ratio of average total points scored per game at a given tournament : average total points scored per game on a given set, and is calculated independently for the Varsity and JV fields.

K-Value

The K-value is a multiplier to adjust for the different formats of tournaments which lead some teams to play more or fewer games, as well as to account for the uncertainty inherent in early games before rankings are more finalized. It is set equal to 800 over the number of games played by the team (not counting byes or crossover matches), multiplied by the square root of the current number game.

Varsity C-Set Rankings (2021)

Junior Varsity C-Set Rankings

*Note: Due to allegations of cheating, certain teams have been excluded from these rankings pending further investigation.

Tournaments