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

[vicky_molokh]

Greetings, all!

I'm doing some musings about the Size and Speed/Range Table. Currently, the SSRT scales as a logarithm of linear distance, and each point of penalty affects the chance to hit in accordance to the 3d6 probability table. But if one were to make a radical rewrite of the relationship between range and chance to hit, what should it be? Note that I'm talking about the chance/probability more directly, not necessarily constraining it to the current 3d6 curve.

Asking because as far as I understand, for a given cone of likely directions a projectile can go, every doubling of distance quadruples the the area of the beaten zone, thus reducing 'bullet density' four-fold.

Similarly, currently speed is being added to distance directly, but is there perhaps a more elegant way to make target (and perhaps shooter) speed affect hit ratios?

Note: normally I criticise radical rewrites that result in other bits of the system breaking down hard, but this is more of a hypothetical question with the hopes of seeing how things would look if designed without worry about legacy support and with an eye towards verisimilitude and general universality.

Thanks in advance!

[Anthony]

Originally Posted by vicky_molokh

But if one were to make a radical rewrite of the relationship between range and chance to hit, what should it be?

Realistically, it's likely that aiming at an unmoving target follows some variant on Fitt's law, and aiming at a moving target is equivalent to the steering law. What these boil down to is that the time to aim in the right general direction is proportional to the logarithm of (distance gun has to move to aim at target)/(size of target), and whether you can successfully keep your gun pointed at the target is dependent on the ratio of the target's positional uncertainty to the target's speed.

This has the somewhat surprising effect that hit probability is not correlated to range -- for a target that pops into view for a brief period it's dependent on the size of the area you're watching vs the size of the object, for a target moving evasively it just depends on speed vs area, and in both cases the actual effect is on how long it takes to line up the shot, not the actual accuracy you can achieve. Range comes back into play in a couple ways:

• Mechanical Accuracy: there's a limit (determined by skill and stabilization) to how accurately you can aim a gun, and also a limit to how accurate the gun itself can be. Once you drop below that limit, hit probability will drop off quite fast.
• Bullet Drop: you have to aim above the target at long ranges. The amount by which you miss is equal to 0.5 * (range error) * (range) * (gravity) / (bullet speed^2).
• Leading the target: you have to aim ahead of the target at long ranges. The amount by which you miss is equal to (range error) * (target lateral velocity) / (bullet speed).
• Predicting the target: an erratically moving target might just move out of the way; this is uncorrectable error best implemented as an active defense.

[Eukie]

Very little data has been published on actual aim time/accuracy tradeoffs in ranged weapon use, though what I found seemed to suggest that the standard deviation in accuracy was proportional to time spent aiming to the ^-x power, where x is a number 1 < x < 2, such as 1.22 - which does map to some empirical power law results for Fitts's Law.

Originally Posted by Anthony

Range comes back into play in a couple ways:

• Bullet Drop: you have to aim above the target at long ranges. The amount by which you miss is equal to 0.5 * (range error) * (range) * (gravity) / (bullet speed^2).
• Leading the target: you have to aim ahead of the target at long ranges. The amount by which you miss is equal to (range error) * (target lateral velocity) / (bullet speed).

This is broadly true of ballistic weapons in a vacuum, but the environment where players are most likely to use ranged weapons is in an atmosphere. Here the interactions of the projectile with the atmosphere becomes quite significant.

Additionally, when leading, the error in target lateral velocity estimation is also significant. (British studies on tanks in WWII suggested something like an average estimation error of 30%)

[Anthony]

Note that Fitt's law was originally designed for analysis of the difficulty of using a control panel, and is also applicable to computer UI design, but while that probably implies that it's also applicable to hitscan weapons in FPS games, deciding it also applies to an actual physical gun is at best an unproven hypothesis.

[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.