What Is a Resume Ranking?
The Quality Resume model is designed to evaluate what a team has accomplished during a season. It is not primarily designed to predict which team would be favored in a hypothetical game.
The central question of the model is:
To answer that question, every game is evaluated using two forms of context: the quality of the opponent and the way the team performed in the game. A victory over a strong opponent generally contributes more to a resume than a comparable victory over a weak opponent, while the margin of the result provides additional information about the quality of the performance.
Because the strength of an opponent depends on that opponent's own results, the model treats the season as a connected system rather than a collection of independent games.
1. Establishing Initial Ratings
The process begins by assigning every team an initial rating. These ratings provide a starting estimate of team quality before the model begins its iterative evaluation process.
The initial ratings are based on the results and connections created by the schedule. Teams are not evaluated in isolation. Every game creates a relationship between two teams, and those relationships connect the entire college football schedule into a larger network.
For example, if Team A defeats Team B, and Team B later defeats Team C, the results involving all three teams help establish their relative positions in the initial rating system.
These initial values are not the final rankings. Their purpose is to provide the model with a reasonable starting point for estimating opponent strength.
2. Calculating Opponent Strength
Once each team has a rating, that rating is used to estimate the strength of every opponent it has faced.
The raw team ratings cannot be used directly because they exist on a different numerical scale than the margin component of the model. Opponent ratings are therefore transformed onto a comparable scale between 0 and 1.
The function f represents the model's normalization process. The goal of normalization is not simply to make the best team equal to 1 and the worst team equal to 0. Instead, it attempts to preserve meaningful differences throughout the distribution of team ratings.
This is important because a simple linear transformation can create undesirable results. If one team is significantly stronger than every other team, using the minimum and maximum ratings alone can compress many strong teams into a narrow range.
The normalization function is therefore designed to maintain separation between teams while keeping the resulting values on a scale that can be compared directly with margin performance.
Strong Opponent
A highly rated team receives an opponent strength value closer to 1. A strong performance against that team therefore contributes more to the resume.
Weak Opponent
A lower-rated team receives a smaller opponent strength value. Beating that team still counts, but the quality of the accomplishment is evaluated differently.
3. Transforming Margin of Victory
Wins and losses alone do not describe the complete result of a game. The model therefore converts the point margin into a margin performance value between 0 and 1.
A value near 1 represents a dominant victory, while a value near 0 represents a substantial loss. Results near the middle of the scale represent close games.
The function g is nonlinear. The purpose of using a nonlinear transformation is to prevent every additional point from having exactly the same value.
For example, the difference between winning by 1 point and winning by 10 points can provide meaningful additional information. However, the difference between winning by 50 points and winning by 60 points should not necessarily have the same impact.
The margin transformation therefore allows the value of larger margins to gradually level off rather than increasing indefinitely.
Close Win
A narrow victory receives a positive margin value above the midpoint of the scale.
Dominant Win
A large victory receives a higher value, although the additional benefit gradually decreases as the margin becomes extremely large.
Close Loss
A narrow loss receives a value below the midpoint but is treated differently from a substantial defeat.
4. Calculating Game Performance
Every game is assigned a single performance score by combining opponent strength with the margin value.
Where:
Pᵢ
The performance score for game i.
Oᵢ
The normalized strength of the opponent.
Mᵢ
The margin value for the result.
wₒ and wₘ
The weights assigned to opponent strength and margin.
The weights satisfy the relationship:
This ensures that the performance score remains a balanced combination of the two components.
For example, suppose a team defeats an opponent with a strength value of 0.80 and earns a margin value of 0.70. If the two components are weighted equally:
This score represents the quality of that individual result relative to the rest of the teams and games being evaluated.
5. Updating Team Ratings
After every game has been assigned a performance score, those performances are used to update the rating of each team.
Conceptually, a team's new rating is based on the collection of performances it has produced throughout the season.
A team that consistently performs well against strong opponents will tend to produce a higher rating than a team whose strongest performances came primarily against weaker competition.
Importantly, the model evaluates both positive and negative results. A close loss to a highly rated opponent can produce a stronger performance score than a poor result against a weak opponent.
This is one of the primary reasons the model is designed as a resume evaluation system rather than a simple win-loss ranking.
6. The Iterative Process
The model contains an important circular relationship.
To evaluate a game, the model needs to know how strong the opponent is. However, an opponent's strength depends on the results and performances from its own schedule.
This means opponent strength and team ratings must be solved together through repeated calculations.
Start with initial team ratings
Normalize the ratings into opponent strengths
Calculate the performance of every game
Update every team's rating
Repeat the calculation using the new ratings
Each iteration uses the results of the previous iteration as a new estimate of team strength.
7. Convergence
The iterative process continues until the team ratings stabilize.
After each iteration, the model measures how much the ratings changed from the previous calculation.
The model examines the largest change among all teams. When that change falls below a predetermined convergence threshold, the rankings are considered stable and the iteration stops.
For example, the calculation may progress as follows:
Iteration 2 → Change: 0.027
Iteration 3 → Change: 0.005
Iteration 4 → Change: 0.002
Iteration 5 → Change: 0.001
As the ratings converge, the effect of the schedule becomes incorporated throughout the entire network of teams.
Why the Iteration Matters
Consider a team that defeats an opponent early in the season. At the time of that game, it may be unclear how valuable that victory should be.
If that opponent later defeats several strong teams, the quality of the original victory should increase. Conversely, if the opponent performs poorly throughout the remainder of the season, the value of the victory may decrease.
The iterative process allows these relationships to develop naturally. A game is not evaluated only by the information available on the day it was played. Its value is influenced by the complete network of results included in the ranking.
The Purpose of the Model
College football schedules are unequal. Teams play different opponents, compete in different conferences, and face varying levels of competition.
A simple win-loss record does not capture those differences. Two teams with identical records may have achieved those records against dramatically different schedules.
The Quality Resume model attempts to account for that context by asking two questions about every result:
The final ranking represents the model's attempt to combine those answers across an entire season into a single measure of resume quality.
Resume Ranking vs. Predictive Ranking
A predictive ranking attempts to estimate future performance.
A resume ranking evaluates past accomplishments.
The Quality Resume model is designed around the second question. A highly ranked team is not necessarily being identified as the most talented team in the country. Instead, the ranking reflects the quality of the results that team has produced against the competition it has faced.
The Complete Calculation
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Opponent Strength Normalization
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Margin Transformation
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Individual Game Performance
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Updated Team Ratings
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Repeat Until Convergence
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Final Resume Rankings