HATCH
MATHEMATICAL COLLEGE FOOTBALL RANKINGS
RANKING
PROCEDURES
1.0
Rankings
1.1
Definitions
1.1.1
Initial Ranking (IR): The final results from the previous season's poll. In the
event that new teams join Division 1-FBS, new teams will be assigned a
preseason ranking of a position immediately lower than the lowest ranked team
from the previous season.
1.1.1.1
The Initial Ranking is used only in the first iteration of each season's
results. For subsequent iterations, the final ranking of the previous iteration
will be used as the Initial Ranking. As a result, the Initial Ranking's effect
will be filtered out as each successive iteration is conducted.
1.1.2
Stable Rankings: achieved when one set of final rankings is used as the Initial
Rankings for a further iteration which produces the same set of final rankings
that are identical to the Initial Rankings.
1.1.3
Rank (RK): the rank of a given team is its position in the order of teams'
Rating scores, sorted descending. (E.g., a team that has the highest Rating
score’s Rank is 1.)
1.1.4
Points (PT): the Points total for a given team is the result of the following
formula:
130 - RK = PT
(E.g., a team that has a Rank
of 1 has a Points total of 129.) Points should not be confused with Rating
score or Rank.
1.2
Calculating Performance Ratings
1.2.1
Part One.
For a game in which A defeats
B by a margin of M,
Where M < 11,
IPRA = PTB x 1.05
IPRB = RKA x -1.05
Where 10 < M < 20,
IPRA = PTB x 1.10
IPRB = RKA x -1.10
Where M > 20,
IPRA = PTB x 1.12
IPRB = RKA x -1.10
Where a tie,
IPRA = (.5 x (PTB
x 1.05)) + (.5 x (RKB x -1.05))
IPRB = (.5 x (PTA
x 1.05)) + (.5 x (RKA x -1.05))
1.2.2
Part Two.
Where A is at home:
PRA = IPRA x 1.00
PRB = IPRB x 0.95
Where the Away Team wins:
PRA = IPRA x 1.05
PRB = IPRB x 1.05
Where the game is at a neutral
site or is a bowl game:
PRA = IPRA
PRB = IPRB
1.3
Calculating Ratings
RATING = (PRGame 1 + PRGame
2 + PR... + PRFinal Game + (130-IR)) Ö (Games Played)
1.3.1
Rating scores will be rounded to one thousandth of a point. Decimal values
beyond this value will not be considered.
1.3.2
Only teams considered part of Division 1-A/FBS, or the equivalent for the year
in question will be ranked. All teams outside of those ranked will be
represented by the Division 1-AA Placeholder. The Division 1-AA Placeholder
will always be ranked below all rated teams in the preseason rankings.
1.3.3 In
the event that the results of a given season would create an irresolvable
infinite loop for two or more different teams, teams will be rated based on the
average of the results produced. (e.g., when team A is ranked 3rd
and team B is ranked 4th in the initial ratings it produces a final
rating having team B in 3rd and team A in 4th. Further
iterations keep all other ranked teams in identical positions except for A and
B that alternatively switch positions without any possibility of a conclusion.
The dilemma is resolved by averaging team AÕs final rating when it begins in 3rd
and 4th position and doing the same for team B. Whichever teamÕs
average rating is higher will be ranked 3rd and the other 4th.)
1.3.4 For the first week of a season, the system will be iterated a maximum of five times. Thereafter, the system will be iterated until it becomes Stable as defined in 1.1.2, and subject to the procedures in 1.3.3. Teams that have not played a game will retain their Preseason Ratings until they have played their first game.
2.0
Determination of the National Champion
Teams will be
ranked according to their IR. Scores from each game will be assigned Ratings as
discussed in 2.3. The final rankings of each team based on their overall Rating
will then become the IR for a next iteration. This process will continue until
all rankings have become a Stable System, and any teams that are caught in an
irresolvable infinite loop have their ratings determined by 1.3.3 as described
above. The team with the highest Rating will be declared the national champion.