Methodology

RAMS is a Retrodictive rating system rather than a Predictive one. Odds, Probabilities, and Point Spreads are reflections of past games, and are not necessarily designed to predict upcoming games. Early in the season, RAMS must sometimes traverse a string of several dozen games (e.g., A plays B, B plays C, C plays D, etc.) in order to establish a basis of comparison. When a single basis of comparison exists, differences in Point Ratings correspond exactly to actual winning margins and a few atypical results in a string can affect the entire ranking. Consequently, early ratings should be taken with a large grain of salt. Ratings after two games often look particularly bizarre, but by the fourth game, the dust typically settles, and the RAMS rankings more accurately reflect the teams’ true strength.

RAMS generates two sets of ratings – Point Rating and Winning Propensity. Point Rating is based on a team’s Average Scoring Margin and Schedule, while Winning Propensity is determined mainly by a team’s Record and Schedule, with an adjustment for Average Scoring Margin.

In most instances, Winning Propensity serves as the basis for the RAMS rankings. Early in the season however, if every contest has been won by the team with the higher Point Ranking, RAMS uses Point Rating as the basis for its rankings. (The Winning Propensity model assumes a chance for an upset. If no upsets have occurred, Winning Propensity cannot be calculated.)

Winning Propensity (WP)

RAMS presumes that each team has a Winning Propensity that represents the Odds of a team defeating an opponent. A team with a WP of 300 would be considered a 3:1 favorite over a team with a WP of 100. A WP of 100 is considered average.

If you know the WP values of a team and its opponent, you can calculate the team’s Probability of Winning (POW). The probability of a team with a WP of 300 defeating a team with a WP of 100 would be .75

   

If you know a team’s Probability of Winning against each opponent, and add the Probabilities together, you get the Estimated number of Wins for that team.

RAMS requires that every team’s Winning Propensity is consistent with its record. In other words, the Estimated Wins for each team must be within one-half game of the team’s Actual Wins. Any variations between estimated and actual wins are a result of scoring margin adjustments.

Point Rating (PR)

RAMS presumes that each team has a Point Rating that reflects Point Spread relative to other teams. A team’s Point Rating equals the average Point Rating of its opponents plus or minus its Average Scoring Margin. A team with a PR of 3 would be considered a 6-point favorite over a team with a PR of negative 3. Zero is considered an average PR.

Correlation Factor (CF)

Correlation Factor represents the correlation between Point Rating and Winning Propensity, based on the combined data from all league games over the course of the season. RAMS presumes that a one-point difference in PR corresponds to a certain percent difference in WP. Adding 1 to that percent gives you the Correlation Factor. A CF of 1.20 indicates that a one-point difference in PR equates to a 20% difference in WP.

If you know the Correlation Factor and a team’s Point Rating, you can calculate the team’s Estimated Winning Propensity (EWP). If CF = 1.20, a team with a PR of 1 would have an EWP of 120, and a team with a PR of 2 would have a PR of 144. A team with a PR of 0 has an EWP of 100 regardless of the Correlation Factor.

   

If you know the EWP for two teams, you can calculate the Probability of Upset (POU). For this discussion, an “upset” is a game in which the winning team has a PR lower than or equal to the team it defeated. The “favorite” is the team with the higher PR and the “underdog” is the team with the lower PR.

   

RAMS calculates the Correlation Factor so that the sum of the POUs for every league game over the course of the season equals the total number of Upsets.

Definitions

Cluster – a group of teams that

• are all connected either directly or indirectly thru games played, and
• have not played any other teams outside the group.

Peer – a hypothetical opponent with a Winning Propensity that corresponds to a team’s Point Rating.

League Game – a game in which both teams are Members of the organization being rated.

Non-League Game – a game between a Member and a Non-Member. Non-League games are included in statistics and calculations unless noted otherwise.

The Process

1. Find the Point Ratings that satisfy the following conditions. This is done through simple algebra, but since a large number of teams are usually involved, the process is best accomplished by building a matrix.
   • The Point Rating for each team must equal its opponents’ average PR plus or minus the team’s average scoring margin.
   • If all teams are connected, the average PR for all Member teams must equal zero.
   • If multiple Clusters exist, the average PR for each Cluster must equal the average PR for those teams at the end of the previous season. (Teams without a previous PR are not included in the average.)
2. If every game this season has been won by the team with the higher PR, the Point Ratings determine the RAMS rankings, and WE ARE DONE. If Upsets have occurred, continue with the next steps.
3. Determine the Correlation Factor (based on League games only)
   • Assign an initial value to the Correlation Factor (use previous CF if available).
   • Compute each team’s EWP based on the CF and the team’s PR.
   • Compute the Probability of Upset (POU) for every game, based on EWPs.
   • Compare the sum of POUs to the total number of Upsets.
   • Increase CF if sum of POUs exceeds number of Upsets; reduce CF if number of Upsets exceeds sum of POUs.
   • Repeat previous four steps until the sum of POUs equals the total number of Upsets.
4. Calculate an Estimated Winning Propensity for each team

      

5. Credit each team with an artificial tie (½ win and ½ loss) against a hypothetical opponent called a Peer. Each team’s Peer is assigned a Winning Propensity equal to that team’s Estimated Winning Propensity calculated in the previous step. The artificial tie serves two purposes. One, it adjusts a team’s Winning Propensity up or down based on its Point Rating. And two, it eliminates perfect records, which the Winning Propensity model cannot handle.
6. Determine the Winning Propensity for each team.
   • Initially set each team’s Winning Propensity to 100 as a starting point.
   • Using WP values, compute the Probability of Winning (POW) for each game (including ties vs. Peers).
   • For each team, compare the sum of its POWs to its number of Wins (including ½ win vs. Peer).
   • Reduce a team’s WP if the sum of its POWs exceeds its number of Wins; increase a team’s WP if its number of Wins exceeds the sum of its POWs.
   • Repeat previous three steps until the sum of each team’s POWs equals its total number of Wins.
7. Use the Winning Propensity values to determine the RAMS rankings – WE ARE DONE.