Team Roster

[orangeflow]

Problem: A team of basketball players is a mix of starters that play the whole game those that sit on the bench and sub in when the starters are hurt/fouled out or are absent. Occasionally the players (both starters and bench players) will need to leave the team permanently due to injuries, work schedules and family issues. However the starters leave the team at a much lower rate than those that sit on the bench. When a starter does leave the team a bench player will move into his spot and that the open bench slot must be filled through the coaches recruiting. Since this team is constantly shifting with players, try outs are held each week and only a percent of the players trying out actually make it. Please help me make a workable equation for how many players the coach needs to recruit (to try out) per week to keep his roster full.

So I'm kinda stuck on this problem. I apologize if this isn't a static problem as I haven't taken stats yet, but I *think* it is so I posted it here. Anyways the solution that I have so far looks something like this:

(( % of starters that leave * number of starters)+( % of bench players that leave * number of bench spots))/ % of tryout players that make it= number of player that need to try out each week to keep the roster full.

So if we had a team of 30 players (20 starters and 10 bench) and we guessed at what rate they left as well as half of the recruits making the cut we would have:

((10% * 20)+(30% *10))/50%=10

The only problem I have with this solution is that I feel I have not properly represented the graduation of those that go from the bench to the starter position. Does anyone know what I can do to fix this error?

 

[wjm11]

The only problem I have with this solution is that I feel I have not properly represented the graduation of those that go from the bench to the starter position. Does anyone know what I can do to fix this error?

My impression from your problem statement is that you have already accounted for all your player losses. New recruits just have to equal the total number of players lost, whether they leave from the bench or the starting positions. Players moving back and forth from the bench to playing don't matter.