Suggested formula for curving test results Take a test score represented by the fraction ${a\over b}$. This test score could be curved by removing a wrong answer to get ${a\over b-1}$ or adding a correct answer to get ${a+1\over b+1}$. Sometimes the former will cause a greater increase to the fraction, sometimes the latter will cause a greater increase, and sometimes they will be equal. For example ${99\over 100}$ would become either ${99\over 99}$ or ${100\over 101}$ (a is better) ${1\over 3}$ would become either ${1\over 2}$ or ${2\over 4}$, (same) ${0\over 3}$ would become either ${0\over 2}$ or ${1\over 4}$ (b is better) Is there a formula for at which points or intervals one way is better than the other? (Equal would be at $-a^2 + ab + a = 1$)

$${a\over b-1}\gt \frac{a+1}{b+1}$$

$$ab+a\gt ab+b-a-1\implies b\lt 2a+1$$

If $b$ is less than $2a+1$ the first is better. If it is equal, both options are equal. If it is more, then, the second option is better.