Radical Alternatives: How SHOULD Size and Speed/Range Affect Chance to Hit?

[vicky_molokh]

Hmm. Talking to a shooting enthusiast resulted in some support of the quadratic hypothesis: he said that typically, someone with a 50% hit rate at 100m would have a 12½% rate at 200m against the same target under similar conditions. But in an RPG context, that seems to lead to hit chances quickly approaching 100% and 0% outside a relatively narrow range band, and I'm not sure how to feel about that.

As for Fitt's law, that seems to not be very applicable, since usually a turn length is defined before rolling (and is in GURPS and most systems a constant value).

[Gnomasz]

Originally Posted by vicky_molokh

As for Fitt's law, that seems to not be very applicable, since usually a turn length is defined before rolling (and is in GURPS and most systems a constant value).

Turn length, yes. But aiming time could be varied depending on roll. If you roll well, you shoot and hit. If you roll not-so well, but decent, you continue aiming. If you roll really poorly, you shoot and miss.

[johndallman]

Originally Posted by vicky_molokh

Hmm. Talking to a shooting enthusiast resulted in some support of the quadratic hypothesis: he said that typically, someone with a 50% hit rate at 100m would have a 12½% rate at 200m against the same target under similar conditions.

Yup, that's the inverse square law. Applying that to GURPS requires deciding how to convert that to a skill penalty.

The GURPS 3d6 mechanic's bell curve means that you pretty well have to start at the centre of the curve, and say that doubling range takes target number 10 (50% chance of a hit) down to target number 8 (25.6%). So far, so good, but not very granular.

The speed/range table has x10 distance as -6 to skill. By inverse square law, x10 distance should be 1% of the chance to hit, taking 50% down to 0.5%. That's the chance we have for a skill of 3, implying that x10 distance should be -7 to hit, so GURPS RAW is actually a bit friendlier than reality.

[Anthony]

Originally Posted by vicky_molokh

Hmm. Talking to a shooting enthusiast resulted in some support of the quadratic hypothesis: he said that typically, someone with a 50% hit rate at 100m would have a 12½% rate at 200m against the same target under similar conditions. But in an RPG context, that seems to lead to hit chances quickly approaching 100% and 0% outside a relatively narrow range band, and I'm not sure how to feel about that.

For people approaching their accuracy limits against unmoving targets, hit chance really does vary like that. The thing is, the reasons for missing at short ranges are not accuracy related; they're related to time to aim vs target motion, rushing the shot, and bad visibility.

[Eukie]

The ballistics-simulator-with-tabletop-roleplaying-applications Phoenix Command has a number of factors that determine the final to-hit chance of an attack, primarily:

• The actual angular dispersion of the shot, which is a function of skill, range, stance, aim time, darkness penalties, wind, etc.
• The mechanical accuracy of the firearm, which introduces a range-dependent minimum angular dispersion.
• The uncertainty in lead estimation location when the target is moving, which introduces a minimum angular dispersion that's dependent bullet flight-time and target speed.
• The uncertainty introduced by erratic target movement, which increases the minimum angular dispersion for lead estimation based on the proportion of time the target spends not moving in a straight line.
• Once the smaller of the above has been calculated to determine the actual minimum angular dispersion, the target size is added to that factor to determine the actual hit chance.

In GURPS-y terms, this is broadly min(Skill + modifiers - SM, MOA, X+Y)+SM, where X is the lead estimation error and Y is the erratic target error. Conveniently, the physical effects this models are such that X is calculated using the logarithm of target speed and projectile time of flight: in other words, the standard Speed modifiers can be used in a calculation with this level of detail.

Originally Posted by Anthony

For people approaching their accuracy limits against unmoving targets, hit chance really does vary like that. The thing is, the reasons for missing at short ranges are not accuracy related; they're related to time to aim vs target motion, rushing the shot, and bad visibility.

I found the suggested hit probabilities at various ranges for US Army soldiers in a Field Manual and used it to determine a (parametrized) shot dispersion at various ranges. The dispersion angle actually narrows with range, suggesting that they take more careful aim at longer ranges.

[Anthony]

Originally Posted by Eukie

I found the suggested hit probabilities at various ranges for US Army soldiers in a Field Manual and used it to determine a (parametrized) shot dispersion at various ranges. The dispersion angle actually narrows with range, suggesting that they take more careful aim at longer ranges.

A variant I was considering for ranged combat is adjusting turn length at long ranges and not adjusting skill.

[vicky_molokh]

Originally Posted by Anthony

A variant I was considering for ranged combat is adjusting turn length at long ranges and not adjusting skill.

I found a way to model that using a series applications of a logarithmic scale for almost everything, but that project's first steps went so far as to no longer be GURPS at all. But at least the issue of turn scale and RoF bonus interactions seems solved in my project.

[Humabout]

Vicky, you make the assumption that shots fired approximate a uniform distribution, which is not the case. They will be clustered more densely around the actual target and become less dense as you look further out. So the size of the target won't have a quadraric effect on hit chance.

Let's assume a normal distribution of distance from bullseye with a standard deviation of 1 unit. If the target is 1 unit radius, the shooter has about a 68% chance of hitting. If we double the target's radius, he now has a 95% chance of hit. Adding another 1 unit to radius increases his odds of hit to 99.8%. He'll never hit 100%.

Now that addresses target size. Distance effects I'm not sure of. It would definitely increase the standard deviation of the final spread, but at what rate, I don't know. The shooter's own ability to be on target plus the effects of atmospheric conditions would be factors, though.

[Anthony]

Originally Posted by Humabout

Vicky, you make the assumption that shots fired approximate a uniform distribution, which is not the case. They will be clustered more densely around the actual target and become less dense as you look further out. So the size of the target won't have a quadraric effect on hit chance.

It's generally going to be a chi-square distribution, but that comes very close to quadratic once hit probability is low.

[Agemegos]

Originally Posted by Anthony

It's generally going to be a chi-square distribution, but that comes very close to quadratic once hit probability is low.

It's a bivariate normal, so the chi-squared distribution simplifies to an exponential distribution. In the general case the pattern is ellipsoidal, but assuming that the vertical and horizontal dispersions are uncorrelated and have the same variance you get the result that the chance id a given hit falling more than a distance from the centre of the pattern falls off exponentially with the distance.