How much do you have to subtract from the value of a coin if it has a small scratch, or other small defect? Here is such a coin, which I paid $25 for Saturday.
It depends on the coin how rare it how bad the damage is every coin varies !! This 1852 three cent is a rather common coin. This coin would most likely bring in around 10 dollars on the bay !!
I really don't think on your piece that the scratch matters much at all . It may bother some more than me but for the grade of your coin I'd have paid about the same with or without . Now if it was a higher grade piece the scratch would really cut into the price , and if sent to a tpg might bring a detail grade instead of a regular grade .
As a general rule of thumb, a problem coin can be worth anywhere from 20% to 80% of what a problem free example is worth. The more severe the problem the more the value is reduced. Your coin looks to have two problems to me, 1 the scratch and 2 it looks to have been harshly cleaned. So that would put it at the lower end of the scale.