It's not really complex math...
Let's take a 100 pts fireball
If you had a 20% resistance to fire, it would block 20 fire damage, getting hit by 80 damage.
If you had a second layer of 20% fire resistance, it would block 20% of the remaining 80, resulting in a final 64 damage.
1-0.99^(resist) is just an abstraction of this line of thinking.
This guarantees that at any number of resistance you're at, adding 20 more will reduce the incoming damage around 20%... although that means that at 100 resist that 100 pt fireball would be doing 36 damage and boosting resist to 120 would just take those 36 to 30. You effectively got around 20% less damage taken out of that deal, and that's pretty much intuitive.
Diminishing resistance returns
Moderator: Moderator
Re: Diminishing resistance returns
As a single-question math problem, no, it's not that complicated. As a "figure it out in my head on the fly 4-15 times in quick succession while balancing against other things" question, however, that bandwidth slows the entire process down, in a way that addition, subtraction, and simple division do not - and the complexity of the numbers you get slow it down further. As a complete hypothetical, if I see 12% fire resist on a piece of armor and I'm in the yellow zone, I know that's worth 6%. It'll take me from 70% to 76% resist - basically cutting about a fifth off of any fire damage I take. I can take that in at a glance and hold these relatively simple numbers in my head relatively easily while I try to figure out whether that plus two points of armor is worth more or less than 10% more stun resist. As soon as you're throwing in exponents, I have to sit down with a sheet of paper - and if I decide that I'm going to swap in the boots that give fire resist it changes everything, and I have to bring out the sheet of paper again.
Of course, we could have the armor pieces display true percentages (ie, what the resist would be if that piece was worn by itself) and just have the multiplicative fractions thing - at which point figuring out whether 14% resist on one piece and 8% resist on another is more or less than 20% on a single piece and by how much is again an entertaining prospect that actually requires "have to think about it" levels of math. Math on the fly while figuring out which gear to wear is fine. Sit down and calculate math while figuring out which gear to wear is not - and that's aside from the fact that things like limits and derivatives and such are a calculus thing. I'd rather not put a barrier to entry in the game that simply forbids the vast majority of high school freshmen.
Yes, smooth curves are shiny. I get that - and there's a sort of ideological purity to a system that plays limit as x approaches infinity games. I get that too. User interface theory, though, says that the thing to do to make the game work is to keep those calculations simple for everyone that you want to have playing the game, rather than making it a math-based barrier to entry.
Of course, we could have the armor pieces display true percentages (ie, what the resist would be if that piece was worn by itself) and just have the multiplicative fractions thing - at which point figuring out whether 14% resist on one piece and 8% resist on another is more or less than 20% on a single piece and by how much is again an entertaining prospect that actually requires "have to think about it" levels of math. Math on the fly while figuring out which gear to wear is fine. Sit down and calculate math while figuring out which gear to wear is not - and that's aside from the fact that things like limits and derivatives and such are a calculus thing. I'd rather not put a barrier to entry in the game that simply forbids the vast majority of high school freshmen.
Yes, smooth curves are shiny. I get that - and there's a sort of ideological purity to a system that plays limit as x approaches infinity games. I get that too. User interface theory, though, says that the thing to do to make the game work is to keep those calculations simple for everyone that you want to have playing the game, rather than making it a math-based barrier to entry.