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01082020, 09:12 AM  #1 
GURPS FAQ Keeper
Join Date: Mar 2006
Location: Kyïv, Ukraine

Radical Alternatives: How SHOULD Size and Speed/Range Affect Chance to Hit?
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' fourfold. 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! Last edited by vicky_molokh; 01082020 at 09:35 AM. 
01082020, 11:35 AM  #2  
Join Date: Feb 2005
Location: Berkeley, CA

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


01082020, 12:49 PM  #3  
Join Date: Dec 2013

Re: Radical Alternatives: How SHOULD Size and Speed/Range Affect Chance to Hit?
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.
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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%) 

01082020, 05:09 PM  #4 
Join Date: Feb 2005
Location: Berkeley, CA

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

01102020, 02:43 AM  #5 
GURPS FAQ Keeper
Join Date: Mar 2006
Location: Kyïv, Ukraine

Re: Radical Alternatives: How SHOULD Size and Speed/Range Affect Chance to Hit?
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). 
01102020, 03:58 AM  #6 
Join Date: Aug 2009
Location: Poland

Re: Radical Alternatives: How SHOULD Size and Speed/Range Affect Chance to Hit?
Turn length, yes. But aiming time could be varied depending on roll. If you roll well, you shoot and hit. If you roll notso well, but decent, you continue aiming. If you roll really poorly, you shoot and miss.
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01102020, 04:02 AM  #7  
Night Watchman
Join Date: Oct 2010
Location: Cambridge, UK

Re: Radical Alternatives: How SHOULD Size and Speed/Range Affect Chance to Hit?
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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.
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01102020, 09:34 AM  #8  
Join Date: Feb 2005
Location: Berkeley, CA

Re: Radical Alternatives: How SHOULD Size and Speed/Range Affect Chance to Hit?
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01102020, 10:16 AM  #9  
Join Date: Dec 2013

Re: Radical Alternatives: How SHOULD Size and Speed/Range Affect Chance to Hit?
The ballisticssimulatorwithtabletoproleplayingapplications Phoenix Command has a number of factors that determine the final tohit chance of an attack, primarily:
In GURPSy 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. Quote:


01102020, 10:33 AM  #10  
Join Date: Feb 2005
Location: Berkeley, CA

Re: Radical Alternatives: How SHOULD Size and Speed/Range Affect Chance to Hit?
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Tags 
range, ranged combat, reality check, size, ssrt 
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