Hit probability formula

This is not homework, and I got my math degree in 1975, I just can't remember this information.

I have gathered data (see http://s264.photobucket.com/user/counter139/media/Storm1.png.html for plot) of the hit probability of a character in a video game with an abstract hit statistic of x. X cannot be 0, but f(x)->0 as x->0 and f(x)->1 as x->infinity. f(1) happens to be .11 on the red curve and .88 on the blue curve. I have tried variations of 1/(1-e^x) with no luck, what might the formula for these curves be.

Thank you for any help

Counter123 said:

This is not homework, and I got my math degree in 1975, I just can't remember this information.

I have gathered data (see http://s264.photobucket.com/user/counter139/media/Storm1.png.html for plot) of the hit probability of a character in a video game with an abstract hit statistic of x. X cannot be 0, but f(x)->0 as x->0 and f(x)->1 as x->infinity. f(1) happens to be .11 on the red curve and .88 on the blue curve. I have tried variations of 1/(1-e^x) with no luck, what might the formula for these curves be.

Click to expand...

Are you asking about trying to do a regression of some sort? If so, you might want to try a spreadsheet program.

I have this data in a spreadsheet, and have posted the curve resulting from the collected data. I am trying to identify the nature of the mathematical formula used to create these curves. I am able to get x values from particular situations, and the resultant Y value (rounded to nearest percent).

That is, there is a formula f(x) that produces this data. I can apply certain x values to f(x) and record the rounded result. I need to identify the function f(x). There are two functions plotted Fred(x) and Fblue(x).

Thank you.

Have I asked in the wrong place? I asked the question of a math tutor, and she said it was a statistics question, to ask someone else.

Or have I expressed the problem poorly?

You're asking us for "the" formula, when all we have is a picture of a graph of a curve which, presumably, passes through some set of (unstated) points. As such, there is nothing we can do. (In addition, we offer tutoring, not computer-programming subcontracting. We'd help you learn how to do this yourself; we wouldn't do it for you.)

If you have a set of data points, and perhaps also a set of conditions (related maybe to whatever game you're talking about), then "a" model could be found by running those data points through the "regression" feature of a spreadsheet program. But "the" model will be whatever is coded into the game.

Counter123 said:

I am trying to identify the nature of the mathematical formula used to create these curves.

Click to expand...

We'll need the explicit algorithms, before we can help you do that.

I have tried variations of 1/(1-e^x) with no luck

Click to expand...

If you'd like to explore, try googling keywords examples+"continuous functions"+"two horizontal asymptotes". You'll find examples like y=x/(x^2+1)^(1/2) and y=arctan(x).

ETA: To Quaid, I have tried, including exactly the search terms you showed. Problem is the left end is f(x)->0 as x->+0, values of x<0 don't make sense. It might not be an asymptote.

stapel said:

You're asking us for "the" formula, when all we have is a picture of a graph of a curve which, presumably, passes through some set of (unstated) points. As such, there is nothing we can do. (In addition, we offer tutoring, not computer-programming subcontracting. We'd help you learn how to do this yourself; we wouldn't do it for you.)

If you have a set of data points, and perhaps also a set of conditions (related maybe to whatever game you're talking about), then "a" model could be found by running those data points through the "regression" feature of a spreadsheet program. But "the" model will be whatever is coded into the game.

Click to expand...

I am a player in this game, not trying to create the program. A hero in the game is attacking a villain in the game, and the hero has an unscaled accuracy of H, while the villain has a unscaled evasion of V [H and V are positive integers], so the formula for hit probability Hp(H,V) is what I have been trying to establish. When I, as the hero, am deciding whether to make the attack, the game tells me the probability (to the nearest 1%) of hitting, and of a critical hit. I have tried enough cases to verify that the results are dependent on H/V (IE Hp(5,10)=HP(10,20). The data in the graph comes from the following data points (I didn't think anyone would want the raw data, or want a detailed explanation). I do not expect anyone to work out the exact formula, I would just like a pointer as to roughly the nature of the formula. I have read about sigmoids, but I don't think that is quite the right thing.

H/V Hit_Prob Crit_Prob
NOTE: The last value, far to the right of the others, has not been plotted.

Counter123 said:

I am a player in this game, not trying to create the program.

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But you're asking us to somehow backwards-engineer what that program contains. We can't do that.

You included a data set. Now plug that data set into your spreadsheet program (such as Excel), and do regressions on it until you find a model with which you're happy.

stapel said:

But you're asking us to somehow backwards-engineer what that program contains. We can't do that.

You included a data set. Now plug that data set into your spreadsheet program (such as Excel), and do regressions on it until you find a model with which you're happy.

Click to expand...

Thank you. I have the data in Excel, and if by doing regressions you mean trying different formulas until I find one that matches the data, I have tried many. Most of what I have tried are sigmoid functions, but I have come to the conclusion that having the left end of the curve end at f(0)=0 (rather than lim(x->-inf=constant) means it isn't a sigmoid. All I am asking is what kind of a function produces a curve of the nature shown.

Nature of curve: x is a positive rational number. f(x)->0 as x->0 , f(x)->1 as f->+inf. Curve is roughly sigmoid as shown.


For example, If I had said f(x)->constant1 as x->-inf and f(x)->constant2 as x->inf, you could have said "that is a sigmoid curve", I could take it from there by Googling "sigmoid". I am coming under the impression that curves of the nature in my data are not useful enough to be generally used, and have no specific name.

[h=1]Cumulative distribution function[/h]
Take derivative, then calculate mean and variance.

Counter123 said:

...if by doing regressions you mean trying different formulas until I find one that matches the data....

Click to expand...

No. By "doing regressions", I mean doing regressions.