I am working on a project, which tries to form a cricket team within a given budget with a high winning chance. So the main goal is to enhance the winnability of a cricket team by forming the best possible team. For this, I have identified the best set of attributes that impose high impact towards the winnability using machine learning feature selection techniques. Say for example the set of attributes found are $A = \{A_1, A_2, A_3, A_4, A_5, A_6\}$.
I also implemented a bid value prediction system for each player using nonlinear regression (based on each player's performance matrix and their past auction bid values).
Now I somehow have to map these with the winning percentage of any formed team. I thought of modeling this problem as a constraint optimization problem. Where the function $f(x)$, which is the winning percentage of a team expressed in terms of a weighted sum of player performances including bid price details, has to be maximized. The attributes set found earlier (set $A$) will be calculated for each individual player and player performances will be represented as a product of a weight vector and this performance vector. The constraint would be the maximum budget allocated to select the entire team.
I am really confused how to really solve this problem and how to form an equation for $f(x)$ in terms of a weighted sum of each player's performances and bid value.
I believe that finding this core relationship would solve this problem. Any bits of help or ideas or comments will be highly appreciated. Thanks in advance.