The concept is relatively simple, but unsure how to implement it. I want an output of a number between 0 and 1 where the inputs are the sum of the ranks of the teams and the point spread.
E.g. Suppose TeamA and TeamB were the #1 and #2 teams ranked in the country and the spread was 0. ∴ sum_rank = 3 and spread = 0. This would be the "perfect game" and should have a score of 1 or .999.
But the sum of the ranks should carry more weight:
Another e.g. #300 TeamA and #301 Team B were playing (sum_rank = 601), and the spread is 1. This would not be a great game because the teams are so bad, perhaps output of like .1.
Yet another e.g. #100 vs. #101 and spread of 0 (perhaps output of .50) is a better game than #1 vs. #100 and spread of 15 (perhaps output of .30).
If someone could get me started on a function, and I can play with the different numbers to weight it according to my likes. Might take some tweaking, but would appreciate the head-start! Thanks.
Let $N$ represent the number of teams in the league
and $R$ represent the sum of the Ranks
then $R_{min}=3$ and $R_{max}=N(N-1)$
let $S$ represent the point spread
so $S_{min}=0$ and you can decide what to put in for $S_{max}$
( since it's basketball you might start with $S_{max}=100$ )
Construct a rating function containing 3 arbitrary parameters as follows ...
$$ T(R,S) = aR+bS+c $$ Get 2 equations for the 3 unknowns by requiring that ...
$$ T(R_{max}, S_{max})=0 \text{ and } T(R_{min}, S_{min})=1 $$
Use these equations to eliminate 2 of the unknowns .
You will be left with one adjustable parameter which you can use to satisfy your requirement that Rank should carry more weight than spread.
Alternatively you could create a third equation $a=kb$ then you could solve the 3 equations for $a, b, ,c$ and adjust $k$ to satisfy your requirement that Rank should carry more weight than spread.
Expect to get negative values for $a$ and $b$ and a positive value for c.