A minor problem with the interest formula
is that the maximum value (a #1 vs #1 matchup) depends upon the size of the field N. Since we're using it to assign games to one of the buckets
Log10 [ ( N + 1 - R1) × ( N + 1 - R2 ) + 1 ] { 2 × max( R1, R2 ) - min( R1, R2 ) }
int < 0.5I'll normalize the value so that the maximum #1 vs #1 is 4.5. We do this by replacing the common (base 10) logarithm with the logarithm to base B
0.5 ≤ int < 1.5
1.5 ≤ int < 2.5
2.5 ≤ int < 3.5
3.5 ≤ int < 4.5
LogB [ ( N + 1 - R1) × ( N + 1 - R2 ) + 1 ] { 2 × max( R1, R2 ) - min( R1, R2 ) }
with
B = 4.5√( N2 + 1 ) = 9√{ ( N2 + 1)2 }
With 128 1A teams in 2014, B is about 8.64 and all of the interest values are about 7 per cent higher than those given
by the old formula. Graphs of the game-interest based upon opponents' ranks for #25, #50, #75, #100 and #125 look like this:
The revised list of "three star" interconference games is:
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Four-star matchups are extremely rare. There are only 18 rank combinations with interest values greater than or equal to 3.5: #1 vs #s 1, 2, 3, or 4; #2 vs #s 2, 3, 4, or 5; #3 vs #s 3, 4 or 5; #4 vs #s 4, 5 or 6; #5 vs #s 5 or 6; #6 vs #6 and #7 vs #7. The only one scheduled for 2014 is November 29, #2 Auburn at #5 Alabama.
© Copyright 2014, Paul Kislanko