title: Algorithm to Make a Set of Random Outcomes Approach a Specific Percentage
body: <p>Currently, I have a pool of basketball players where I have a projected total of points for each player. Additionally, I have a normal distribution function that gives me a random drawing from a normal distribution for each player. Currently, I have an algorithm that calculates n unique random lineups of 8 players based on some constraints. Between each lineup, the normal distribution function runs again to produce new predictions for each player. Then the best lineup is produced for that specific set of predictions. </p>
  
  <p>I would like to tweak this algorithm in the following way. I would like to have 4 tiers of maximum and minimum percentages where each player is assigned a tier. Within the number of lineups generated, I would like each specific player to occur with that frequency. So for example if I wanted to generate 10 lineups and player 1 is in tier 1 which requires the player to be between 50-60%, then the player would occur in 5-6 lineups ideally.</p>
  
  <p>I'm struggling with how to modify my current algorithm to include this stipulation. Any thoughts would be greatly appreciated! I just don't know how to force each player within a specific range of percentages.</p>