# Inherent burst size and full-auto fire

When +Hans-Christian Vortisch wrote Tactical Shooting, we came up with the Minute of Angle rule, which states that the maximum skill you can have with a firearm, including all modifiers except for range and size, can’t exceed 22 + 2*Acc. This was a calculation where I looked at the typical spread of a weapon in bench-rest mode, and converted it to a round target, usually at extreme range. As it turns out, if you know the spread of a weapon, you know it’s Acc, and there’s a very straightforward correlation between the two. Acc 5, for example, is about 1.5″ of shot spread at 100 yards.

And as a matter of fact, you can simply find the spread of a shot pattern at 100 yards by looking up -2*Acc on the Size table. Acc 4 firearm? Look up -8, and find that equivalent (in this case, 3.6″, or 0.1 yds) and that’s the circle that 90% of the shots will be in. Note that this means that the SM of that target is actually -10, but with +2 for being circular.

Showing the full work: 22+2*Acc = 22+2*4 = 30

At 100yds = -10 range penalty; Target Size penalty = X

90% chance to hit is 14 or less

So 30 – 10 + X = 14; X = -6

SM of -6 is a 3.6″ circle, because the SM of something 3.6″ in dimension is -8, +2 for being circular, thus -6. Therefore, the shot spread of an Acc 4 weapon is 3.6″ at 100 yds.

OK, so given that, how big is your burst (say, from a shotgun, where all the pellets are released at once) at any given range?

No problem. The spread can be found by taking -1* (10+2*Acc+Range Modifier) and looking that up on the Size table.

Acc 5 at 200 yards? (10+10-12 = 8*-1 = -8; SM -8 = ) 3.6″.

Acc 1 at 30 yards? 10.8″

Acc 2 at 25 yards (typical benchrest accuracy for a self-defense pistol of mediocre quality)?

It’ll produce a 5.4″ group (a little smaller, actually, but 25 yds rounds up to 30 yds on the Range table).

What does that have to do with anything?

Well, there’s a huge thread over in the SJG GURPS Forum about controlled bursts, shot spread, and all the usual stuff. As I ponder this, I think that the natural place to start is to figure out how disperse your bullets are, somehow compare that to the SM of your target, and roll to see if you hit.

Now, of course, combat isn’t about clamping a gun into a perfectly stiff and firm mount and pulling the trigger. Skill enters into it, and recoil, and motion, and . . .

But if we abstract all of that into a degradation of skill, perhaps what we wind up with, instead of using the Rcl mechanic, is an expression for the size of the burst due the inherent spread of the weapon, plus spread due to waving the thing around (control of recoil and steadiness, or purposeful lack of steadiness, of the mount), offset by a margin of error for misplacing the centerpoint of the target. Then you might compare that number to the SM of the target, which would give you a percentage of overlap between the shot pattern and your target. That should be a fairly straight-forward table lookup, perhaps. That would give you the percentage chance to hit with any one shot, and you could then find the chance to hit with many shots by rolling 3d6.

I actually did this in excel a while ago. So if, for example, you find that your pattern overlaps your target by 35%, and you fired three shots, you hit with one shot on a 12-, two shots on 8- and all three on a 5-.

If you fire 60 shots in one second (!!), you’ll hit with 13 shots on the worst roll of 17, all the way down to rolling a 3 and hitting with 31 shots.

The trick is to come up with the right way to get spread and displacement from the ideal aimpoint, and convert that to a hit chance. Then it’s just math.

Would you REALLY do this in play?

Not without a computer, no. But then, that’s getting more and more common, and all of this is just easy if what you’re entering into your tablet is a skill, a weapon (for Acc), a Range, and a number of shots for the attacker, and the SM of your target region for the defender.

Figuring out where specific shots hit would be a secondary complication, but that’s actually fairly doable. I’ve done something like it in the past, with an overlay that shows (with a d12 roll, sorry) where a shot might go depending on margin of success of a shot. That really only works for single shots, though.

Parting Shot

Finding a mechanic that is both playable and realistic is tricky. What I might try and do is invoke agency, and players could perhaps take a penalty to skill to purposefully widen or narrow (!) their shot pattern (which might increase your odds of even being able to roll a hit, or compensate for a high-recoil/high-spread gun), and then the actual die roll is for how close the center of aim is to the target. You’d still wind up with, for rapid fire, multiple die rolls (bad), but I think you’d wind up with fewer edge cases. Open up on a SM+13 battleship, you’ll hit with every shot unless you completely biff the roll. You’ll even know how far from the ideal aimpoint you diverted, and how spread out your shots were. Assuming you care.

High skill individuals might purposefully take a penalty to spread shot around (saturation fire, hoping for suppression using the Fright Check rules from Tactical Shooting) or to control the shot spread, tightening the burst. Instead of Rcl being a MoS factor, it would be an increase in spread that occurs on multiple shots as a penalty to skill. You’d have to burn skill to compensate for it, which would impact your ability to keep your center of aim where you want.

Clearly this needs more fleshing out, probably tons of issues with it, etc. But it’s a potentially viable approach to the matter. I’ll have to see where this goes.

And just for fun, here’s the Acc to MoA table, which might be useful

## 7 thoughts on “Inherent burst size and full-auto fire”

1. If you're involving a computer anyway, and are willing to not use physical dice, there's something to be said for just pushing all the grunt work off on the computer. All you need to know are your expected error based on skill, and your shot dispersion. The computer generates error once from your skill, and once per bullet from your dispersion.

I think that may be solvable for an optimal hit chance, though; ideal dispersion is probably proportional to your skill.

1. True enough, and unsurprisingly, I did this a long time ago as well. I wasn't so attached to the Size and Speed/Range table back then, I think I calculated spreads based on Acc, Skill, and 3ed Recoil numbers to generate a location for each shot.

I do think there's plenty of room for gameable abstraction though, that doesn't require calculating the fall of every shot.

2. I really like it when there is internal consistency between things like Acc and the size/range table.

With all the die roller apps and VTTs around now I think it would be a good thing to include in a supplement (GURPS via computer?) or perhaps in some future 5e.

3. I don't mind some automation at the table (especially for tedious tasks like character creation) but I don't like mechanics that have to be done by computer. I think it's because I don't like having this black box that I can't tell what it's doing, or if it's doing it correctly

1. Yeah, and eventually, you're playing a video game, and that's not what I signed up for. If I wanted to do that, I could play X-Com on my computer. What I want to do is play X-Com in GURPS.

4. I think some of it's a head-up vs head-down thing: if my head's down in a computer, I will miss at least some of the social aspect of the game. Paper character sheets (if well-designed) simply work better for finding small amounts of information quickly, at least for me, so I can stay in the social game.