I'm working on a football(american) management game for the PC. Every player has attributes like Speed, Acceleration, Catching, Football IQ etc. etc. and an overall rating from 50-99. The overall rating for quarterbacks is calculated the following way:

Attribute rating importance

Arm Strength 92 2x
Football IQ 90 5x
Ball Security 79 1x
Pass Accuracy 84 5x
Pocket Presence 89 2x
Throwing Mechanics 85 2x

The overall rating for this player would be

((92*2)+(90*5)+(79*1)+(84*5)+(89*2)+(85*2)) / 17 = 87,1

In other words:

((AS*2) + (FIQ*5) + (BS*1) + (PA*5) + (PP*2) + (TM*2)) / 17 = OverAllRating

Arm Strength = AS
Football IQ = FIQ
Ball Security = BS
Pass Accuracy = PA
Pocket Presence = PP
Throwing Mechanics TM

Now, I want to also give the player potential(peak) values for each attribute, which will be the maximum the player can reach. I would however want to save time and not have to give every player these peak values manually, and would instead like to know a formula that would calculate these peak values for the player by just knowing the peak overall rating.

In other words: If I wanted the player with an overall rating of 87,1 to have a peak rating of 96, how would I go about doing this.

((AS*2) + (FIQ*5) + (BS*1) + (PA*5) + (PP*2) + (TM*2)) / 17 = 96

Thanks for all your help!