Math for the Sports Minded - Maximizing Recruit Talent w/Available Cash
This is prolly gonna be a long post. Hope to be able to make it clear enough to follow. I also hope this is in the right section of the forums. If you have any further questions after I make an attempt at explaining, please ask me to clarify.
I play an online college football game/simulation. In this game, you compete with other online coaches during recruiting season to land the best recruits you can with the money you have. The farther a recruit is from you, the more they cost. If another coach and yourself both pursue the same recruit, it basically becomes a bidding war, with distance becoming a factor due to cost being related to distance. Each recruit has numerous numerical ratings such as Endurance, Stamina, Speed, Hands, Blocking, etc.
I have built myself a spreadsheet that uses basic fuzzy logic to determine the best recruit for the best cost. In a nutshell, I create a fuzzy rating between 0 and 1 for talent, and a fuzzy rating between 0 and 1 for estimated cost to recruit that individual. Then, I logically AND those two numbers, giving me in essence, a bang for the buck type fuzzy number between 0 and 1. The spreadsheet also calculates a hard estimated dollar figure to recruit, like say, 5230 dollars.
Okay, this is the part where I describe the math problem I need figured out. How would I go about maximizing my bang for the buck rating and it's associated dollar figure, with my available cash? Let me give you a for instance:
I have 35,000 dollars available.
I know I need to recruit 2 Offensive Linemen (OL), 2 Defensive Linemen (DL), 1 Linebacker (LB), and 2 Defensive Backs (DB)
I have a ranked list of the best players for the buck at each position. Some players offer better talent for the dollar than others.
I have an estimated cost to recruit each player.
How do I go about (mathematically) determining the best way to spend my money? I could take the best available at each position, but may still end up spending over my limit. Do you see what I'm after?
I hope that was clear. I'd just like to say in advance, thanks for taking the time to try to help. Even if you can't help directly, I would greatly appreciate any steering you might provide to get me to the right destination! big_smile