If I have x number of wins and y number of losses, how do I calculate how many more wins I will need to achieve a certain win percentage.

Example:

• Wins: 17
• Losses: 4
• Target %: 83%

What is the formula which shows that I need 3 more wins to get to 83%

CodePudding user response：

The winning percentage is calculated like this:

17 / (17   4)

You want a certain number of wins on top of 17 to be equal to 83%:

(17   x) / (17   x   4) == 83 / 100

But you want x so first try to get it out of the denominator:

(17   x) == (83 / 100) * (17   x   4)
(17   x) == (83 / 100) * (17   4)   (83 / 100) * x
(17   x) - (83 / 100) * x == (83 / 100) * (17   4)

No you make sure only x is in the left-hand side:

x - (83 / 100) * x == (83 / 100) * (17   4) - 17
x * (1 - 83 / 100) == (83 / 100) * (17   4) - 17

Which results in:

x = ((83 / 100) * (17   4) - 17) / (1 - 83 / 100)