Missiles hit formula

[Alia]

I will use S as a "cumulative skill", it depends on actual player skill and his attributes,

normalized that S = 1 means average archery level.

Formula for S should be discussed later.

 

Bell functions:

Ermabwed's variant: B(x) = 1 - exp(-1/x^2). Behaves like 1/x^2 at infinity

My variant: B(x) = erf(1/x). Behaves like 1/x at infinity.

 

Ermabwed suggested to introduce another parameter for bows: average distance D (in my interpretation)

I'll use it this way: player with S = 1 will have probability 1/2 to hit at average distance.

 

Q > 1 - fixed constant (something like Q = 1.1)

Let r_0 be the root of erf(1/x) = 1/(2Q).

So basic probability (without consideration of target dexterity and lighting) is

P_0 = Q * erf(D * S / (r * r_0) )

bounded by 1 of course, where Q > 1 will make some radius with hit chance = 1.

 

Light and target dexterity I still think can be used as a factor modifier:

P = P_0 * (1 - erf(w / L) ).

This way we have probability = 0 in absolute darkness (L = 0).

 

P.S. Making pictures... please wait

I think discussion in game will be more active, and will help to clarify some points and ideas,

which are not obvious from formulas. Lets use channel 10001 for it

 

r - distance between bow and target. Bow average dist = 5.

P_0( r ) for S = 0.5, 0.75, 1.0, 1.25, 1.5

 

P_0(S) for r = D/2, D, 2D, 4D

 

P(w) for r = D, S = 1, L = 1, 0.75, 0.5, 0.25

 

P(L) for r = D, S = 1, w = 0.1, 0.25, 0.5, 0.75, 1.0

Edited January 11, 2008 by Alia

[Ermabwed]

Bell functions:

Ermabwed's variant: B(x) = 1 - exp(-1/x^2). Behaves like 1/x^2 at infinity

My variant: B(x) = erf(1/x). Behaves like 1/x at infinity.

 

I think discussion in game will be more active, and will help to clarify some points and ideas,

which are not obvious from formulas. Lets use channel 10001 for it

Yes, that function was off, it should be exp(-x^2), exp(-1/x^2) is for cutting off (see above).

edit: and I changed my approach to use a maximum range instead of an optimal range

Edited January 11, 2008 by Ermabwed

[Entropy]

Ok, let's talk in that channel. Although the forum is better for some stuff, such as posting graphs and things like that.