Minimally Adjusted Reduced Score (MARS) Ranking Method
Explanation:
The Minimally Adjusted Reduced Score Ranking Method, or MARS Rank, or MARS, is an accurate and impartial ranking system primarily used for college football (NCAA FBS teams) though it may be applied to any sport. The purpose of MARS is to provide a non-biased ranking method that acknowledges close games while ignoring runaway scoring. The ranking system is non-biased, beginning with all teams having equal rank. Teams then exchange “rank points” based on the actual results of the games played. Rank points can only be exchanged among teams based on game results and are not created or destroyed within a season.
What is the Minimal Adjustment?
MARS is not “winner-take-all”. The minimal adjustment, then, amounts to assuming the game starts with the score tied at 1-1 rather than 0-0.
What is the Minimally Adjusted Reduced Score?
The lowest possible final score in a football game is 2-0. I adjust that to 3-1 per above. Therefore, out of the four points possible, the winning team has three, or 75%. This is also applicable to other sports. In most sports the unit of score is one point. So in the same way the adjustment would be 1-1 and the lowest final score becomes 2-1, with the winning team having 67%.
How do these concepts work together in MARS?
In a close game, say 21-20, the winner has 51% of the available points, so my system would use the actual final score. Where there is a large margin of victory, say 35-7, the actual score indicates the winning team has 83% of the points so my system would adjust that result down to the Minimally Adjusted Reduced Score, or 75%.
Algorithm:
· Begin with all teams having one rank point and, therefore, equal rank.
· Games are worth the average of the rank points of the two teams in the game, so each team gives half its rank points towards the game value.
· The score of the game determines the apportionment of the available rank points (the game value) with a max of (3/4) to the winner.
· Add the corresponding apportioned value back to the rank points of each team.
· At any given time, the team with the highest rank point value is considered to be in “first place”, the team with the next highest value is second and so on.
· Continue through the season.
· Only games amongst teams in the same league are considered (for the MARS rankings of NCAA FBS football teams, only games amongst two FBS opponents are considered.)
Conclusion:
MARS is a system where margin of victory is capped to ignore runaway scoring, while still allowing a close game to count as such. The cap is not arbitrary, but based on the lowest possible naturally occurring shutout score. The adjustment is the minimum value added to that score to avoid winner take all scenarios. Only “runaway scores” will even be subject to the “adjusted cap” as the intent is to disturb the actual and natural outcome of the game as little as possible.
Copyright 2009 Nicholas F. Trombetta