True Hit Discussion (lots of math)

[Kil0]

So I wanted to know a reliable and fast way to calculate true hit on your own, for it has boggled me for a long time.

Here is one basic formula that is....almost correct:

y=(x+(x^2)*20)/1000 if x <= 50

y=100-((100-x+((100-x)^2)*20)/1000) if x > 50

Notice how this formula shifts to the right when graphing when compared to real true hit: http://serenesforest.net/general/true-hit/

Another problem is that it is two formulas. I wanted one that is one single formula. Notice also how it gets lower when they meet at 50 briefly

So, noticing the graph shape, I realized it looked like a trig function, to which I came up with a close solution, but not as close as the previous two formulas

y=50sin((π/100)x-(π/2))+50

The advantage of this one is that it is one formula instead of 2, but sacrifices accuracy instead

Now, like the link before, I could painfully point out every possible average that could create my possible hit chance, but I am looking for an easy algebraic formula for true hit

Here is all the true hit formulas graphed if anyone wants to contribute a better formula: https://www.desmos.com/calculator/9l5tapjiue

Edited March 20, 2017 by arctic.fox0708

[Slumber]

Meh, I've seen more math.

[Kil0]

13 hours ago, Slumber said:

Meh, I've seen more math.

This is simplified as much as I could. I just challenge anyone to try to find a better single formula than mine.

[Dragrath]

So If I understand this you are bothered by the piece-wise nature of true hit and want a single generating function that works for all integer values between 0 and 100?

The problem I see here is that as it is a piece-wise function mathematically there is no single generating function. 

Now by Fourier series expansion you can recreate any distribution using a series of trig functions but that will not get around the piece-wise nature as a whole...

Quite simply a piece-wise function is only defined over the interval where it is bounded so there is no single generating function... You really can only blame IS for using a piece wise function...

[Kil0]

3 hours ago, Dragrath said:

So If I understand this you are bothered by the piece-wise nature of true hit and want a single generating function that works for all integer values between 0 and 100?

The problem I see here is that as it is a piece-wise function mathematically there is no single generating function. 

Now by Fourier series expansion you can recreate any distribution using a series of trig functions but that will not get around the piece-wise nature as a whole...

Quite simply a piece-wise function is only defined over the interval where it is bounded so there is no single generating function... You really can only blame IS for using a piece wise function...

Yeah that's fair, but I was looking for something that would be accurate to the nearest percent. It seems close enough to a normal function to be able to find something close.

I attempted it with a sine wave function, and I want to see if anyone has any ideas that can do it better.

Edited March 20, 2017 by arctic.fox0708