Right, sorry if the title makes no sense, I severely lack math terms, but will try to explain best I can!
I have a passion for soccer rating systems, so I'm trying to assign ratings to teams based on the number of goals they have scored / conceded in relation to the league average.
So, there's a fixed number of points to be assigned to the teams, half of the points are assigned based on the teams' ability to score goals. The other half is assigned based on the teams' ability to not concede goals.
First half is easy to assign: $$TeamRating1 = \frac{TotalTeamGoalsScored}{AvrGoalsScored}*\frac{HalfPts}{Teams}$$ But I can't figure out a formula to assign the other half of the points. Obviously if a team concedes less goals than average they should have more points and vice versa.
But doing this is the opposite of what I need: $$TeamRating2 = \frac{TotalTeamGoalsConceded}{AvrGoalsConceded}*\frac{HalfPts}{Teams}$$
Damn, let me know if it doesn't make sense or you need more info :-)
Thanks!
EDIT I have three teams; A, B and C They play each other, like so: AvB 3-0 AvC 1-1 BvC 1-4
$$A1 = \frac{4}{10}*50=20,0 $$ $$B1 = \frac{1}{10}*50=5,0 $$ $$C1 = \frac{5}{10}*50=25,0 $$
$$A2 = ?$$
Why not try $$TeamRating2 = \left(1 - \frac{AvrTeamGoalsConceded}{AvrGoalsConceded}\right)*HalfPts$$