I don't know if this is known, but I haven't seen it posted:
The damage reduction from your defense is = 1- 0.986233^defense = 1- 0.5^(0.02*defense)
Multiply by 100 to express it as a percentage.
This is a very good fit so I doubt it is just a close approximation.
One good thing about doing it this way is that perks always have roughly the same effect (with errors from rounding). For example, if you have 0 melee defense and it gets bumped to 50, damage will be reduced by 50%. If it is already 50%, 50 more will give defense 100, which cuts damage by 75%, reducing the remaining damage by half.
Great job! I've checked this out, and it fits every point within half a percent. Also, it would be really nice to check whether those numbers are actual reductions, or the ones given by the formula are used for damage calculation, while truncated numbers are shown in UI. The "simplest" way would be hitting some high hp unit with some 100-power unit, with damage shown to decimals it would be possible to calculate the next digit of reductions. Actually, I've just thought of a more realistic method, gonna try it.