Game math problem

The Game Room
1

I’m trying to figure out the rate of magic point (MP) savings for spells and how it is affected by an ability. The ability in question activates on 25% of spells cast, and when it activates, the saves an amount of MP based on the following formula:

(n/16) * (spell MP cost), rounded down
n= integers 8-15. All occurences of n has an equal chance of appearing

The faq for the ability then says that “…thus, each activation of the ability saves 28.125% of MP cost on average.”

I admit it, I’m bad at math. I skated through pre-calc in high school and took more than one try in college calculus. Plus, its been like a decade since I took any math class. I can’t seem to figure out how they got from “all occurences of n has an equal chance of appearing” to “28.125%”. Can anyone help? :smack:

2

With an equal chance of all numbers 8-15 coming up, that means on average you’ll have a value of 11.5 for n.

16 - 11.5 = 4.5.

So on average you’ll save 4.5 which is 28.125% of 16.

3

Why do you minus 11.5 from 16? Why isn’t it 11.5/16 average savings?

4

11.5/16 is average cost. Full cost - average cost = average savings.

5

Thanks!

I really need a refresher math course…

6

It’s been answered, but I thought I’d present it another way. Assume you cast a spell that costs 100 mana and this kicks in.

n/16 * MP
average n = 11.5
11.5/16 *100
.71875 * 100
71.875

That’s how much MP the spell costs. Well, 71 since it rounds down, but we’re talking math here, not reality. You save:

100 - 71.875 = 28.125, or 28.125%.

Of course, it only occurs every 1 in 4 spells, which means you’re really only saving about 7% overall.

7

This is the important part to remember. The ability saves a little more than 7% of your mana, overall.