The Litkenhous Ratings were a mathematical system used to rank college football and basketball teams. Developed by Edward E. Litkenhous and his brother Francis H. Litkenhous, the system was used from 1934 to 1984.
The Litkenhous Ratings worked by calculating a team’s strength based on the scores of their games. The system took into account the margin of victory and the strength of the opponents. Essentially, it was a way to measure how dominant a team was throughout the season.
Key Components:
- Margin of Victory: The difference between the scores of the winning and losing teams.
- Opponent Strength: A measure of how strong the opponents were, often based on their own records and ratings.
Basic Formula:
The Litkenhous Ratings were calculated using a weighted average of the margin of victory and the strength of the opponents. The formula can be simplified as follows:
Step-by-Step Calculation:
- Calculate the Margin of Victory: For each game, subtract the losing team’s score from the winning team’s score.
- Determine Opponent Strength: Assign a strength value to each opponent based on their record and previous ratings.
- Multiply and Sum: Multiply the margin of victory by the opponent strength for each game and sum these values.
- Divide by Total Opponent Strength: Divide the sum from step 3 by the total strength value of all opponents.
10-Team League Example:
Teams:
- Team A
- Team B
- Team C
- Team D
- Team E
- Team F
- Team G
- Team H
- Team I
- Team J
Scores of their games:
- Team A: Beat Team B 35-10, Team C 42-14, Team D 28-7
- Team B: Beat Team E 21-14, Team F 28-21, Team G 35-21
- Team C: Beat Team H 24-17, Team I 31-28, Team J 27-20
- Team D: Beat Team A 14-10, Team B 21-17, Team E 28-24
- Team E: Beat Team F 20-14, Team G 27-21, Team H 17-14
- Team F: Beat Team I 24-21, Team J 31-27, Team A 21-20
- Team G: Beat Team B 14-10, Team C 21-17, Team D 27-24
- Team H: Beat Team E 31-28, Team F 24-20, Team G 21-17
- Team I: Beat Team J 28-21, Team A 24-20, Team B 31-28
- Team J: Beat Team C 27-24, Team D 20-17, Team E 24-21
Hypothetical Opponent Strength Values:
- High Strength: 1.5 (Teams A, B, C, D)
- Medium Strength: 1.0 (Teams E, F, G)
- Low Strength: 0.5 (Teams H, I, J)
Calculation and Double-Checking:
Team A:
- Scores: 25, 28, 21
- Opponent Strength: 1.5, 1.5, 1.5
- Total Score: (25×1.5) + (28×1.5) + (21×1.5) = 37.5 + 42 + 31.5 = 111
- Total Opponent Strength: 1.5 + 1.5 + 1.5 = 4.5
- Rating: 111 / 4.5 = 24.67
Team B:
- Scores: 7, 7, 14
- Opponent Strength: 1, 1, 1
- Total Score: (7×1) + (7×1) + (14×1) = 7 + 7 + 14 = 28
- Total Opponent Strength: 1 + 1 + 1 = 3
- Rating: 28 / 3 = 9.33
Team C:
- Scores: 7, 3, 7
- Opponent Strength: 1.5, 1, 0.5
- Total Score: (7×1.5) + (3×1) + (7×0.5) = 10.5 + 3 + 3.5 = 17
- Total Opponent Strength: 1.5 + 1 + 0.5 = 3
- Rating: 17 / 3 = 5.67
Team D:
- Scores: 4, 4, 4
- Opponent Strength: 1.5, 1.5, 1
- Total Score: (4×1.5) + (4×1.5) + (4×1) = 6 + 6 + 4 = 16
- Total Opponent Strength: 1.5 + 1.5 + 1 = 4
- Rating: 16 / 4 = 4
Team E:
- Scores: 6, 6, 3
- Opponent Strength: 1, 0.5, 0.5
- Total Score: (6×1) + (6×0.5) + (3×0.5) = 6 + 3 + 1.5 = 10.5
- Total Opponent Strength: 1 + 0.5 + 0.5 = 2
- Rating: 10.5 / 2 = 5.25
Team F:
- Scores: 3, 4, 1
- Opponent Strength: 1.5, 1.5, 1
- Total Score: (3×1.5) + (4×1.5) + (1×1) = 4.5 + 6 + 1 = 11.5
- Total Opponent Strength: 1.5 + 1.5 + 1 = 4
- Rating: 11.5 / 4 = 2.88
Team G:
- Scores: 4, 4, 4
- Opponent Strength: 1, 1.5, 1.5
- Total Score: (4×1) + (4×1.5) + (4×1.5) = 4 + 6 + 6 = 16
- Total Opponent Strength: 1 + 1.5 + 1.5 = 4
- Rating: 16 / 4 = 4
Team H:
- Scores: 3, 4, 4
- Opponent Strength: 1, 1.5, 0.5
- Total Score: (3×1) + (4×1.5) + (4×0.5) = 3 + 6 + 2 = 11
- Total Opponent Strength: 1 + 1.5 + 0.5 = 3
- Rating: 11 / 3 = 3.67
Team I:
- Scores: 7, 4, 3
- Opponent Strength: 0.5, 1, 1
- Total Score: (7×0.5) + (4×1) + (3×1) = 3.5 + 4 + 3 = 10.5
- Total Opponent Strength: 0.5 + 1 + 1 = 2.5
- Rating: 10.5 / 2.5 = 4.2
Team J:
- Scores: 7, 3, 3
- Opponent Strength: 1.5, 1, 0.5
- Total Score: (7×1.5) + (3×1) + (3×0.5) = 10.5 + 3 + 1.5 = 15
- Total Opponent Strength: 1.5 + 1 + 0.5 = 3
- Rating: 15 / 3 = 5
Summary Table:
| Team | Rating |
|---|---|
| Team A | 24.67 |
| Team B | 9.33 |
| Team C | 5.67 |
| Team D | 4 |
| Team E | 5.25 |
| Team F | 2.88 |
| Team G | 4 |
| Team H | 3.67 |
| Team I | 4.2 |
| Team J | 5 |
This integrated explanation and example should provide a clearer understanding of the Litkenhous Ratings.
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