This is the first time I post in Mathematics as I'm normally in programing. But for this question, I think I can get better help here.
I'm trying to create a gamification system where different teams are competing against each other to score points by doing certain tasks.
The problem I have is that the teams aren't equal balanced. They have a different amount of players and workload. So I need to figure out a formula to balance the score or create a "handicap" to let the smaller teams have same chance.
| Team | Players | Total Cases |
|---|---|---|
| A | 2 | 500 |
| B | 4 | 4000 |
| C | 6 | 5000 |
| D | 4 | 3000 |
| E | 6 | 7000 |
Cases is what they score points on so it changed every day. Easiest calculation would be 1 case = 1 point
But for Team A who is a small team of only 2 people and a very low amount of cases every month. The people in that team have no chance competing against the people in team E as they have way more cases per person.
What I would like to end up with is this.
| Player | Cases | multiplier | Points |
|---|---|---|---|
| Player 1 | nn | xx | bb points |
| Player 2 | nn | xx | bb points |
| Player 3 | nn | xx | bb points |
| Player 4 | nn | xx | bb points |
...and so on.
Players compete against each other disregarding which team they are in and thanks to the multiplier their score will be fairly equal.
Question is; How do I calculate the multiplier for each team?
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