# Math Help - Math for the Sports Minded - Maximizing Recruit Talent w/Available Cash

1. ## 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

2. Wouldn't the best way to determine this be to rate each player by bang per buck?

$\frac{bang}{buck} = \frac{rating}{cost}$

Higher values are better

3. Yep.... They are already rated bang for buck, in a sort of roundabout way. Talent has been rated 0-1 and cost 0-1 and then both totals logically "AND"'ed. So I have a bang for buck for each player. What I need is a formula to determine the best set of players to maximize bang for buck without going over a set cash limit. And, in a way, reciprocally (if that is a word) see when I have extra money to either spend, or bank for the next recruiting season.