# Find H $\langle H \rangle=P+\frac{1}{AD} \sum_{i=0}^{D} ( \sum_{j=0}^{A} ((j-i)Step(j-i)))$

Hi all, I was reading a post about how certain stats work in a game. Most expressions where simple, but then there was this one and I am completely stumped on how to do it. After some research I now know how to do the entire expression, Except for the " ( (j-i)STEP(j-i) ))" part! From what i've gathered I believe they are using either the Step (staircase) function or the Heaviside Step function. However even after knowing this I am still unable to get a number close to theirs.
I'm very much so a math "noob." So I understand that possibly this is very simple, this is not even a correct expression or somthing else.
If anyone can help me on this that would be much appreciated! ! !

How it was written in the post:

<H> = P + (1/AD) * SUM(i=0 to D)(SUM(j=0 to A)( (j-i)STEP(j-i) ))

In one example they define A=30 P=5 D=80 with an answer of "~10"
In another they define A=20 P=6 D=75 with an answer of 8.4

My main goal is to get the same outputs he got with the same variable definitions, so I hope thats possible.

• M F H

well, parts of this is reproducable but that after giving that formula the OP writes "However, the results are much messy, highly dependent on if A > D or not...not able to solve...". (Side note, the name of the variables [and functions P and H=avg.dam.!] is extremely awkward, and the same letters stand for different things in that formula compared to the other one (for P)...) So I fear that if I accept to answer the question you won't be satisfied.

• Nirenberg

Could you please clarify the definition of the step function: Step (x)?

• Nirenberg

Do you mean the Heaviside step function?

• M F H

I think I have found the explanation which I think might be correct, and I'm now able to reproduce the figures -- not exactly but up to a difference of less than 1 unit. Unfortunately, if you consider my answer only partially correct, then it might even cost me money to answer, therefore I'm a bit reluctant to accept to answer the question ...

Answers can be viewed only if
1. The questioner was satisfied and accepted the answer, or
2. The answer was disputed, but the judge evaluated it as 100% correct.
• Ian Todd

Your an absolute genius, thank you so much!

• M F H

Thanks a lot!

• M F H

Oops! actually I had changed the name of the function H() to avg_dam(), but then changed back to H() in the definition, but not in the subsequent lines. Instead of " avg_dam(...) " it should be " H(...) " (or you can define " avg_dam = H " in the PARI interpreter).

• Ian Todd

That had me hung up for a bit, while inputting it on the PARI interpreter site, but I figured it out.