T:COTEC - Accuracy, How to calculate a Value

[RobMuadib]

Hello people

Yes I am still working on my game. (Currently titled Teramyr: Chronicles of the Eternal Cycle)  Currently I am tweaking details of combat and one that's got me in a pickle is how to figure weapon Accuracies for Firearms. The Accuracy would be a score somewhere around 10 to 20 or more that would be gained by aiming the weapon, which would be applied against a Range/SPeed and size penalty. I find myself wanting a formula, Since I figure most of the other characteristics of a firearm based on formulas using muzzle energy, muzzle velocity, bullet weight, sight radius, weight, etc for Penetration, damage, snap shot penalty, recoil, Aim Time steps.

I have read through Understanding Firearms Ballistics, so I have a better grasp on the subject. I have also downloaded some ballistics programs that will let me calculate some drop charts but I haven't seen anything that will give me a solid formula to use. I know that using something based on the Ballistic coeffecient might work. But I was wondering if anyone else knew a good method to come up with this.

I have GUNS, GUNS, GUNS by BTRC/Greg Porter, and it mentions the equations you can use to calculate accuracy at range, but it doesn't provide them. What it does provide is it's RC system, which provides a listing of to hit modifiers at various ranges for various categories of firearms. Currently I am considering swiping it's +0 ranges and setting them as my base accuracies for Pistols/Rifles, and simply fudging the values for various weapons, but I would be much more happy with an actual formula to figure it out for me. If Greg reads this maybe he can point out something to use for this.

For those wondering, all of this detail will be encoded into the basic ranged attack "power" allowing for detailed twiddling of power effects and characteristics for people using the system. (a ranged attack will be constructed that can have these characteristics such as having aim time steps, snap shot penalty, accuracy, recoil, etc. With options to have none of these a higher cost for the power). This is part of the design architecture, which I envision as a grittier, more realistic design system than HERO.

Best

[Mike Holmes]

I think you need a more generalized rule, basically a situational bonus. That is, Aiming = sit bonus for the condition of aiming. See what I'm getting at? Otherwise, if the detail is kept as aiming specifically, you're getting into details that are favoring combat. What would be better, is a rule that works as well for Steady Hand Technique = sit bonus for condition of using said technique with a paintbrush.

See what I'm getting at? Generalize the principles, and the specifics all become easier.

In terms of setting levels, it's effects first. So the levels are whatever's paid for, right? So leave it to the opinion of the players.

Mike

[Roger]

With all respect, as far as I can tell, Rob has already drastically simplified and generalized this problem.

One number for a piece of equipment.  You aim it, that's the bonus you get.  Regardless of whether the target is 1 foot away or 1 mile away, or it's dead calm versus hurricane force winds, or even if the shooter is an Olympic marksman compared to someone who has never even seen a rifle before.

One number for the M-16.  If you aim it, that's the bonus you get.

All that being said, I don't think there's a set of equations that is going to give Rob what he wants.  What I'd do is set the accuracy bonus for a top quality Olympic target rifle at 20.  I'd set the bonus for a piece of crud rusted out Saturday Night Special at 10.  And then work towards the middle.

Speaking to someone who shoots competitively or runs a gun range or something of that sort might be helpful.  People love to talk about their hobbies.



Cheers,
Roger

[Mike Holmes]

With respect, I've been working on this with Rob for literally years now. First, this is just one rule, I'm betting he has more regarding guns, so he's not simplified anything, AFAICT. Second, my solution would simplify the rules system while allowing the system to address all of the things that you're mentioning that his system may or may not currently. So the problem is?

Mike

[eef]

If you're really going for turbo-sim, be advised that aiming a gun actually has very little to do with using it in combat.

IIRC, trained police officers hit assailants 3-10 feet away only 30% of the time. It's trivial to hit a target like that in a gallery, but hiting someone while they are trying to hit you is pretty tough.  For a cinematic example, see 'Unforgiven'.

Most gun combat today is automatic fire. Toss a boatload of bullets in the general direction and if nothing hits they have to hide and not shoot you.

Unless your game is Skeet: the Shooting, I suspect that what you mention in your post will be pretty tertiary to gun combat.

[Mike Holmes]

Well, rules for aiming are important in combat to the extent that you want to look at this level of detail, and one might, at some point, actually managed an aimed shot in combat. Actually the Navy SEAL "One shot, one kill" training is based on making people aim.

The real question, which you're right about, however, is whether or not he has a rule that handles whether or not the character gets to aim. Or is it complete player control of character morale at all times?

Mike

[RobMuadib]

Well, rules for aiming are important in combat to the extent that you want to look at this level of detail, and one might, at some point, actually managed an aimed shot in combat. Actually the Navy SEAL "One shot, one kill" training is based on making people aim.

The real question, which you're right about, however, is whether or not he has a rule that handles whether or not the character gets to aim. Or is it complete player control of character morale at all times?

Mike

Hey, I think explaining how the rules work so far would be illustrative. So people will understand what I am driving at.

First, combat uses an action point system, where action points are referred to as action counts. During each 2 second action phase, persona gets so many AC's worth of action. for average character would be 5, 7 for combat capable character. It is based on speed and combat sense. It costs 1 AC to move 1 meter in a running stance. Aiming is on an action count basis, with 1 AC representing a snap shot. Other actions are given a cost in action counts.

THe idea is to give weapons an aim time profile. So an M-16 would look like. (Using the fudged Accuracy values)

M16
Aim Time (AC)            ACC
1                    -5 (Snap shot penalty, length/mass based)
2                    +0
3                    +1
4                    +2
5                    +3
6                    +5
7                    +7
8                    +10
9                    +13
10                    +15
11                    +17
(Aim Time steps based on weapons sight radius (SQRT(sight radius in cm)x1.5, rounded down.)

A Glock 17 Would Look like
AT (AC)     ACC
1   -1 (Snap shot penalty based on SQRT (Length/cm*mass kg)/4
2   +1
3   +2
4   +3
5   +5
6   +7
(Aim Time steps based on weapons sight radius (SQRT(sight radius in cm)x1.5, rounded down.)

Now, ranged weapon attacks pit an acting score equal to the character's skill score plus Coordination aptitude (1/2x Coordination (Attributes on 1-20 scale with 10 avg) against an Opposing Score. The Opposing score is equal to 10+ Range/Speed Modifier + SIZE Modifier + Visibility Modifier
-Stance/Position Modifiers - Aim Time ACC.

Range/Speed and SIZE Modifiers are based on CORE Table
R/S        SIZE           Value
0   0   2.0 m
+1   -1   2.5 m
+2   -2   3.0 m
+3   -3   4.0 m
+4   -4   5.0 m
+5   -5   6.0 m
+6   -6   8.0 m
+7   -7   10.0 m
+8   -8   12.5 m
+9   -9   15.0 m
+10   -10   20.0 m
+11   -11   25.0 m
+12   -12   30.0 m
+13   -13   40.0 m
+14   -14   50.0 m
+15   -15   60.0 m
+16   -16   80.0 m
+17   -17   100.0 m
+18   -18   125.0 m
+19   -19   150.0 m
+20   -20   200.0 m


This is what weapon accuracy goes against to reduce.

A major miscellaneous modifier is whether or not the character assumed a firing stance before firing. (which costs 2 AC to take.) If so he makes his attack as normal. If not he suffers the -3 Hip Firing penalty.

Being in a standing Firing Stance is +0, Being in Kneeling Firing Stance is +1, Being in a prone firing stance is +2 Being Braced adds +1 to this.

A moving character is automatically assumed to be firing from the hip.

So for a character with a skill score of 7 and a coordinatin of 12, good for an aptitude of 6, his acting score would be 13. If he aimed his glock for 2 AC's at a target moving 3 meters per second, 3 meters away his Opposing Score would be 10+5(6.0 Range/Speed modifier)+0(human size of 1.5-2.0 meters)+0 for visibility- -3 for hip firing (he is ducking back into cover)-1 for Aim Time ACC, which yields a 17 OS (10+5+0+3-1). So he would pit his Acting Score of 13 against an Opposing score of 17. Which would give him about a 21% chance of hitting.

He could get an easy shot if he didn't move and aimed for longer, But would be making himself an easier target. (Keen readers will recognize this system as being a rip off of both Phoenix Command and GURPS).

Currently the Accuracy values are hand picked numbers based on the Range Classes from 3G3.

I also need to figure how to do recoil in the system as well. I calculated some Recoil scores that looked good to me, they were based on formula of SQRT (recoil energy in Joules)/4 (a formula I find myself using alot). They come out to a Recoil of 1 for 9mm, .38 special, and 2 for .45/.357M/.44M/10mm. M16 comes out Recoil 1, 7.62N weapons come out around Recoil 2.

So the recoil penalty would be added to subsequent shots, with aim time again starting for the weapon as usual. Any thoughts on how to implement this? I have figures I determined just not sure how to apply them.

Currently aiming requires that the character actually expose himself to fire, and requires the discipline to stay exposed and assume a firing stance to fire at target. I don't have a coolness under fire rule at present. Persona are assumed to be brave and disciplined as they need to be. Still players will likely use shoot and duck tactics, if only to keep their character's from being easy targets, as a character in a firing stance would be.

best

[Passer by]

Yes I am still working on my game. (Currently titled Teramyr: Chronicles of the Eternal Cycle)  Currently I am tweaking details of combat and one that's got me in a pickle is how to figure weapon Accuracies for Firearms. The Accuracy would be a score somewhere around 10 to 20 or more that would be gained by aiming the weapon, which would be applied against a Range/SPeed and size penalty. I find myself wanting a formula, Since I figure most of the other characteristics of a firearm based on formulas using muzzle energy, muzzle velocity, bullet weight, sight radius, weight, etc for Penetration, damage, snap shot penalty, recoil, Aim Time steps.

I have read through Understanding Firearms Ballistics, so I have a better grasp on the subject. I have also downloaded some ballistics programs that will let me calculate some drop charts but I haven't seen anything that will give me a solid formula to use. I know that using something based on the Ballistic coeffecient might work. But I was wondering if anyone else knew a good method to come up with this.

I guess the concept that your system embodies so far is that the shooter points the gun at the target and a virtual circle appears over the target representing where the shot may deviate to, with the area of the target on that circle representing the proportionate chance of a hit. As the shooter spends more actions pointing the gun the circle shrinks in size. A more "pointable" gun starts with a relatively smaller (but quite large)circle, while a more "aimable" gun ends up, after spending many actions with a much smaller circle. The ballistic accuracy of the weapon (and ammunition) increases the size of the circle, at first a very slight increase relative to all the other factors, but as the target diminishes in "size" (by being further away) and many actions are spent aiming this deviatation becomes extremely important.

Something like that?

One of the factors that, I think, is missing from this model is the "mean point blank range", which I assume you have come across in your reading (and can calculate with your ballistics programs). The trajectory of a bullet can be approximated to a straight line only to so far out, and this range is much longer for a rifle than for a pistol or submachinegun.

[RobMuadib]

I guess the concept that your system embodies so far is that the shooter
points the gun at the target and a virtual circle appears over the target
representing where the shot may deviate to, with the area of the target
on that circle representing the proportionate chance of a hit. As the
shooter spends more actions pointing the gun the circle shrinks in size. A
more "pointable" gun starts with a relatively smaller (but quite large)
circle, while a more "aimable" gun ends up, after spending many actions
with a much smaller circle. The ballistic accuracy of the weapon (and
ammunition) increases the size of the circle, at first a very slight increase
relative to all the other factors, but as the target diminishes in "size" (by
being further away) and many actions are spent aiming this deviatation
becomes extremely important.

Something like that?

That's one way of looking at it, yeah.

One of the factors that, I think, is missing from this model is the "mean
point blank range", which I assume you have come across in your reading
(and can calculate with your ballistics programs). The trajectory of a
bullet can be approximated to a straight line only to so far out, and this
range is much longer for a rifle than for a pistol or submachinegun.

Well, I went through with one of the ballistics programs I had and came
up with some accuracy values based on mean point blank range (actually
I used the root mean square of point blank and Max point blank range, to
err on the conservative side). Converting them to Accuracy values to use
with the game system, I got

PISTOLS

.44 Magnum ACC:12 (effective Range of 30 meters)
.357 Magnum ACC:12 (effective Range of 30 meters)
.357 SIG ACC: 12 (Effective Range of 30 meters)
.45 ACP 230 Grain ACC:9 (Effective range of 15 Meters)
.45 ACP 185 Grain ACC:10 (effective range of 20 meters
10mm Auto ACC:11 (effective range of 25 meters)
9mm Luger ACC:12 (effective range of 30 meters)
.38 Special ACC:11 (effective range of 25 meters)
.380 ACP ACC:10 (effective Range of 20 meters)
.22 LR ACC:11 (Effective range of 25 meters)[/list:u]


RIFLES
AK-74 (5.45X39mmS) ACC:22 (effective range of 300 meters)
AK-47 (7.62x39mmS) ACC:21 (effective range of 250 meters)
M16 (5.56x45mm Nato)M855 Ball ACC:20 (Effective range of 200 meters)
M16A2 (5.56x45mm Nato) SS109 ACC:22 (effective range of 300 meters)
M14 (M80 Ball) ACC:23 (Effective Range of 400 meters)
.308 Sierra ACC:21 (effective range of 250 meters)
.30-06 180 grn. SI SPBT ACC:19 (Effective Range of 150 meters)
.50 BMG 700 grn M33 Ball ACC:22 (Effective Range of 300 meters)
M40A1 Sniper Rifle (7.62x51mmN M118 Match) ACC:22 (effective Range of 300 Meters)
SVD Dragonuv Sniper Rifle 7.62x54mm Soviet ACC:22 (Effective Range of 300 Meters)[/list:u]

(I guess this would be with iron sights, using a rule similar to GURPS,
adding the square root of the scope magnification to the ACC would give
the M40 an ACC of 25: Good for an effective Range of 600 meters. (It has
a 10x scope). Meaning a skilled shooter could make a 600 meter shot with
the weapon with a high degree of success. The dragonuv has the PSO-1
4x optical sight, adding two to this would give it an ACC of of 24, good for
an effective range of 500 meters.)


Effective range means where the attacker would have +0 modifier for
range, so shot would be at even odds based on skill.


These values are pretty good. They would be lowered for snub nose
pistols, guns in poor condition, etc. Most likely by 1 or maybe 2 or 3 on
outside. Optionally adding 1 for longer barrels, etc.


Combining this with aim times we would have



M16A2 (5.56Nato SS109) PEN:22 DMG:10 RCL:1
AT    ACC
1       -5
2       +0
3       +1
4       +3
5       +5
6       +7
7      +10
8      +13
9      +16
10    +19
11    +22[/list:u]


Glock 17 (9mm) PEN:7 DMG:5 RCL:2
AT      ACC
1        -1
2        +1
3        +3
4        +6
5        +9
6        +12[/list:u]
These would be going against the Speed/Range (SIZE) table



R/S         SIZE          Linear Dimension
0   0   2.0 m
+1   -1   2.5 m
+2   -2   3.0 m
+3   -3   4.0 m
+4   -4   5.0 m
+5   -5   6.0 m
+6   -6   8.0 m
+7   -7   10.0 m
+8   -8   12.5 m
+9   -9   15.0 m
+10   -10   20.0 m
+11   -11   25.0 m
+12   -12   30.0 m
+13   -13   40.0 m
+14   -14   50.0 m
+15   -15   60.0 m
+16   -16   80.0 m
+17   -17   100.0 m
+18   -18   125.0 m
+19   -19   150.0 m
+20   -20   200.0 m
+21   -21   250.0 m
+22   -22   300.0 m
+23   -23   400.0 m
+24   -24   500.0 m
+25   -25   600.0 m
+26   -26   800.0 m
+27   -27   1000.0 m
+28   -28   1250.0 m
+29   -29   1500.0 m
+30   -30   2000.0 m[/list:u]

So what do people think of this system? Any problems people see with it?
For very long aim times, short range shots approach 100% success, which
I see no real problem with. You aim long enough and straight enough you
can hit stuff pretty good. I guess I could include a rule that you can't gain
an Accuracy bonus of more than twice your Firearms Skill Score. (This
would penalize low skill shooters, keeping them from getting a sure shot.
And save the maximum accuracy of the weapon for those character's
skilled enough to take advantage of it. )

So what do people think of these rules? I think they are shaping up as a
pretty good simulation of the factors involved, and I have a method to
come up with the values for Accuracy, snap shot penalty, Aim Time Steps,
& Recoil. Figuring the Opposing score requires a bit of modifier crunching
but isn't too difficult, no more difficult than GURPS, which I am ripping off
in large part:).


As for Recoil. You apply the RCL modifier for consecutive shots made with
a firearm. The aim time system meshes with this in that you have a set
aim time for a group of shots, with the OS being modified for consecutive
shots by the Recoil modifier. To avoid recoil you have to start aiming over
again, reorienting the weapon and drawing a bead on the target.
Resetting your aim time to 0 and requring a new cycle of aim time being
applied to the shot.

The next thing I need to do is come up with Damage drop off rule for
firearms, which would reduce the PEN: and DMG: of the firearm by a
certain amount after a certain range. I think the simplest way to
implement this would be to come up with a Damage Drop Off range GP
Score, corresponding to the drop off range. You would subtract the GP
score from the GP Score corresponding to the range this would give you
your PEN/DMG Modifier, which you subtract from the PEN/DMG of the
weapon. It would probably be 1/2 the result of the Range minus the
Damage Drop off score. I would just need to come up with the right range
for the damage drop off.

Best