Bell Curve on 1D6 [math]

[JCurwen3]

Originally Posted by ericthered

I'm enough of a math nerd that the changing of the curve shape even from 3d to 5d bugs me. I've tried a variant where damage is read as an "average" amount (1d becomes 4) and everything is multiplied by (2d-2)*.2. It requires a bit of math, but most of my play is by post, so it yields really nice results, if you don't mind worrying about tenths of points of damage (I don't, but your milage may vary).

Also, what do you do to fix the curve shape to that of 3d for rolls of 5d? Or, as a generalization, to Nd? I'm curious because these sorts of things bug me too.

[ErhnamDJ]

The variability issue has come up before. I even suggested this same solution, though after thinking on it I no longer think that's going to work.

I think armor as dice is the way to go for handling armor, so that only leaves wounding.

What is the purpose of variability in wounding? To represent that not all wounds are the same. If you imagine a sword strike, on any given hit it can go from being a minor scratch to a grievous wound. At least for any creature strong enough to swing a sword fit for a human.

The big problem I've been dealing with here is figuring out how to represent that. If someone hits you with a sword, then is there any way for that sword to only deal one point of injury? It seems to me like that should be possible. So what I would like to do is figure out what the minimum injury is and also what the maximum injury is and to go from there.

Maybe I'm wrong, though, and that's not what an hit is supposed to represent. If you look at the weapons, a lot of them have something like +1 or +2 damage. They can't ever deal a single point of injury. A two-handed katana deals a minimum of 4 injury on any hit. That's always a crippling blow to a normal person's hand. They can't ever deal a less severe blow than a crippling one. The katana can't ever deal only one, or two, or three points of injury. And that same issue occurs with lots of different weapons.

We know it's possible to deal one point injury wounds with a katana. A ST 8 person is able to do so. But a ST 10 person isn't.

I'm left wondering what that's supposed to represent. I would expect that variability to represent sword placement and the different amounts of energy someone might put into an attack. Sometimes you swing harder than others. Humans aren't machines with exact control of their muscles like that. Olympic athletes don't get exact precision and they're not in combat.

But with either of those assumptions it should be possible to deal the entire range of injuries. If it's about wound placement, then sometimes you should hit a place where the wound's not as severe. If it's about the energy put into the attack, then that should vary by quite a lot as well. Sometimes a ST 10 man will get a swing that's only as hard as one from a ST 8 man.

Actually trying to figure out a way to do this isn't so easy, though. One idea I had was to sort injuries into different categories and to then roll to see which category of injury you got, maybe with your damage being some sort of modifier on the roll, using something akin to the reaction table.

If you try to do this with straight rolls of the dice, then you're going to run into problems. And this also applies to firearms as well. A giant rifle round could probably nick my hand and deal only a single point of injury if it hit just right, but that's not represented in the rules. The minimum injury on a 6d rifle round is six. You never get lucky. And it's the same with any weapon that doesn't have a minimum injury of one.

And that's only looking at the minimum injury. Sometimes you get some pretty questionable results from rolling the maximum injury as well. You roll a six on a hit from a small animal or a child or something and whatever verisimilitude you might have had going disappears in an instant.

[ericthered]

Originally Posted by JCurwen3

Wouldn't 1d become 3.5?

yes, 3.5 is the average value. I choose 4 because it means every damage step increases damage taken by 1 point with no .5 steps and it make the math cleaner. It increases the damage, but not by much,

Originally Posted by JCurwen3

Also, what do you do to fix the curve shape to that of 3d for rolls of 5d? Or, as a generalization, to Nd? I'm curious because these sorts of things bug me too.

What I said above. I use the 2d for all damage. if the table says 5d, its an average 20 damage, multiplied by (2d-2)*.2. 3d is 12*(2d-2)*.2.

If you want everything to be a 3d shaped curve (for when damage should be more consistent) take the average damage and multiply it by (3d *.1). That will increase the damage by a little bit, but if that effects your HP-Damage-DR balance, you're walking a tightrope as it is and the change in the curve shape will hurt you as much as the increase in damage.

[jeff_wilson]

Originally Posted by ErhnamDJ

We know it's possible to deal one point injury wounds with a katana. A ST 8 person is able to do so. But a ST 10 person isn't.

Late in the 3rev era, it was floated on the Pyramid forums to allow glancing and grazing wounds: If the roll to-hit is made exactly, wounding is limited to 1 pt per die, but in exchange, a miss by one allows a wound limited to 1 pt regardless of dice.

[ErhnamDJ]

Originally Posted by jeff_wilson

Late in the 3rev era, it was floated on the Pyramid forums to allow glancing and grazing wounds: If the roll to-hit is made exactly, wounding is limited to 1 pt per die, but in exchange, a miss by one allows a wound limited to 1 pt regardless of dice.

That's only one example, though. It's a general problem that you end up with lots of numbers that you're not able to deal as injuries.

The way I look at, whatever gets hit by a weapon is usually destroyed. Wherever a sword's blade hits on a person's body is getting hacked to pieces. A solid blow through the middle of their torso might cleave them in two, but a blow that doesn't catch as much flesh will deal a significantly less damaging injury.

It's not as obvious when you're looking at the torsos of high HP heroes, but once you start dealing with smaller people with fewer HP, or with body parts with fewer HP, then it becomes an obvious problem.

With a six HP character, it becomes quite obvious that there's no chance in the wounding mechanics for them to get lucky and have less important parts of their bodies hit with weapons. A twelve HP character can take a three injury attack (which might well be the minimum injury on that weapon) to the torso and you can explain that as a hit to something other than arteries or organs. They can get hit in the muscles or they can have their ribs bruised or whatever. But there's never a commensurate injury to the lower HP person. Weapons never miss the organs of someone with six HP. There's no way, with most weapons, for them to take a single point of injury to their torso.

I don't think this is because the overall damage is too high. The problem here is that there are results that you can't get in the game that you would expect to be able to get (at least some of the time) in real life.

You can read about people getting stabbed five or six times and walking away from it with all the attacks having missed anything important. Each attack still did something. It was painful (probably incredibly so if the person didn't see it coming and already have their adrenaline going). It pierced flush and possibly severed muscle and tendon, and caused bleeding, but if it didn't hit an organ or an artery, then it's probably not stacking up the way GURPS would handle injuries.

The same sort of thing occasionally happens with gunshots too. It was fairly common when police officers carried smaller caliber weapons. You'd have people survive getting shot ten times with a .38, since none of them got them in an important organ or severed an artery. Well, those .38s deal 2d-1 or 2d damage in GURPS, so that's incredibly unlikely to happen.

I think a lot of this has to do with the fact that all we're doing is tallying up numbers from these attacks rather than figuring out what actually happened to the person's body. This has been a big problem in my games with things like hands getting attacked. You can chop at someone's hand, but that hand really only has three conditions: Normal, Crippled, or Dismembered. You don't ever happen to chop off a finger (or fingers) or hit their thumb or catch your blade under their nail or pierce their palm anything like that. You tally up numbers that are so large that you almost certainly immediately move to at least the Crippled state and usually to the Dismembered one.

It's the same with all the wounds. They're nothing more than numbers that don't give you very much information about what actually happened, but you can infer from what the rules say happened that the vast majority of attacks from even the weakest attackers deal significant injuries. No one ever gits hit a few times in a fight and walks away with a broken rib and a few stomach lacerations. The sort of defensive wounds you see on people's hands in real life when they're trying to protect themselves from a knife attack don't happen either. In real life, I would expect lots of really weak attacks being thrown around and received, but in GURPS it's always like samurai duels to the death in movies where the first guy to get hit is immediately dead in an incredibly gruesome fashion.

[jeff_wilson]

Originally Posted by ErhnamDJ

No one ever gits hit a few times in a fight and walks away with a broken rib and a few stomach lacerations.

How often should a blow deal one of these petty injuries?

[ErhnamDJ]

Originally Posted by jeff_wilson

How often should a blow deal one of these petty injuries?

I don't know. I've tried to find some data on knife injuries and gunshot wounds, but nothing I've been able to find lists the information we would need for determining that.

I can find some specific cases and we can generalize from those, but we'd still need to make assumptions about what's going on in GURPS. Are those what GURPS calls hits that hit and didn't do much, or are they misses that would have some grazing result applied?

We'd have to figure out what a 'hit' is supposed to represent in GURPS first. I don't know how much skill goes into that kind of thing. I can easily imagine a skilled gunman or swordsman hitting someone with an attack that doesn't cause a lot of damage. The way I would be inclined to represent that would be with a low damage roll. If Musashi has skill 18, then he's not going to miss very often. But does that mean that he always gets a particularly grievous injury out of those hits? That's not how I would intuitively expect that to work, but that might well be the underlying assumption in GURPS. Maybe a hit represents a well-placed hit to one of the body's more vulnerable areas, and so that's why you don't get those minor injuries (I don't think I would call them petty--we are talking about getting stabbed or shot). But if that's the case, then it doesn't make any sense to me what the damage roll is for. If the damage roll doesn't represent hit placement, then what does it represent? There's essentially no energy variability in a gunshot. It always hits with the same force. If the damage roll doesn't represent hit placement, then I have no idea what it does represent.

[martinl]

Originally Posted by ericthered

I'm enough of a math nerd that the changing of the curve shape even from 3d to 5d bugs me. I've tried a variant where damage is read as an "average" amount (1d becomes 4) and everything is multiplied by (2d-2)*.2. It requires a bit of math, but most of my play is by post, so it yields really nice results, if you don't mind worrying about tenths of points of damage (I don't, but your milage may vary).

If I was using charts and/or multiplication there are lots of interesting options, I agree. A lot of the GURPS damage system is constrained by the granularity of Xd6+Y.

[Gnomasz]

Originally Posted by ErhnamDJ

If the damage roll doesn't represent hit placement, then I have no idea what it does represent.

I'm quite sure that they do represent hit placement. I've learned this after playing with a couple of people that described a hit based on MoS, before rolling damage (Those blows straight to the heart dealing 3 points of injury! Hilarious). Energy input may have something to do with this, too, but I don't think it would have such an impact.

Originally Posted by ErhnamDJ

Maybe I'm wrong, though, and that's not what an hit is supposed to represent. If you look at the weapons, a lot of them have something like +1 or +2 damage. They can't ever deal a single point of injury. A two-handed katana deals a minimum of 4 injury on any hit. That's always a crippling blow to a normal person's hand. They can't ever deal a less severe blow than a crippling one. The katana can't ever deal only one, or two, or three points of injury. And that same issue occurs with lots of different weapons.

This, I think, is a matter of simplification. There is nothing wrong with system using logarithmic tables or multiplications of decimals, but most players prefer easier solutions, even if they cause headaches to their more analytical friends. That's why Modifying Dice + Adds, which deals a bit with flat bonuses, is an optional rule. And it's still a simplification.

The minimum injury on a 6d rifle round is six. You never get lucky. And it's the same with any weapon that doesn't have a minimum injury of one.

My houserule derived from Modifying Dice + Adds: keep subtracting flat bonuses and adding dice until minimal roll is as close to 1 as possible. That rifle gets +2d-7 (average 0) for 8d-7 of damage. My players don't seem to like it, though. You know, dealing 6 points of damage at minimum is fun. Verisimilitude is meh.

Originally Posted by ErhnamDJ

With a six HP character, it becomes quite obvious that there's no chance in the wounding mechanics for them to get lucky and have less important parts of their bodies hit with weapons.

I think that GURPS just wasn't tailored for 6HP characters (which makes me, a gnome at heart, very sad). It could have been less granular in this range of values, but this would mean bigger, scarier numbers above 10, where most of the game takes place, thus deteriorating overall experience (see that thing about simplicity above).

You can read about people getting stabbed five or six times and walking away from it with all the attacks having missed anything important [...] it's probably not stacking up the way GURPS would handle injuries.

I have to agree. At a minimum of 2 points of injury per (torso) stab it means 0 or -2 HP, which kinda excludes "walking away." I'd change the rule on minimal damage (Damage Roll, p. B378) to minimal injury of 1 if you roll less then 1 damage and target has no DR. This makes walking away after 6 (minimal) stabs possible, if unlikely (if it happens a couple of times in a 6 billion population, it should be unlikely).

I think a lot of this has to do with the fact that all we're doing is tallying up numbers from these attacks rather than figuring out what actually happened to the person's body. This has been a big problem in my games with things like hands getting attacked. You can chop at someone's hand, but that hand really only has three conditions: Normal, Crippled, or Dismembered. You don't ever happen to chop off a finger (or fingers) or hit their thumb or catch your blade under their nail or pierce their palm anything like that. You tally up numbers that are so large that you almost certainly immediately move to at least the Crippled state and usually to the Dismembered one.

I think that chopping off a finger is a matter of Hit Location (in system terms) and not damage, thus calling for a Hit Location Subtable (let's say, on a hand hit, roll 1d: 1-3 palm, 4-5 finger, 6 thumb). As for lack of slight cuts - a matter of minimal damage, above and below.

No one ever gits hit a few times in a fight and walks away with a broken rib and a few stomach lacerations. The sort of defensive wounds you see on people's hands in real life when they're trying to protect themselves from a knife attack don't happen either. In real life, I would expect lots of really weak attacks being thrown around and received, but in GURPS it's always like samurai duels to the death in movies where the first guy to get hit is immediately dead in an incredibly gruesome fashion.

This is a matter of power creep in my opinion. In real life most of the people* have ST 10, DX 10 and maybe a point in Brawling, which doesn't increase damage. Half of the punches don't even deal damage - average roll is 0.5 cr. If a knife appears, it's probably small one, which again deals 1 point of damage (drop fractions = 1 point of injury on a cut) half of the time. Those defensive wounds are probably just a matter of unsuccessful unarmed parry. The one thing that doesn't fit here is a fact that in game attacker could always choose to hit his original target and not parrying arm. I'd maybe give him that option only if defender failed by more than 3†.
But in games most of the people are in heroic category. They are stronger and more skilled, so their attacks are more effective. Sometimes it's restricted to PC's. But sometimes average mooks become ST 12 Brawling DX+2 not-really-so-average-people. And if common people in the game world aren't built realistic, why would effects of fights be?


* not based on any statistical research. But that's my understanding of Word of Kromm.
† I don't have Martial Arts, so I'm making it go in line with galerus, as described in Fantasy p. 223.

[martinl]

Originally Posted by ErhnamDJ

If you look at the weapons, a lot of them have something like +1 or +2 damage. They can't ever deal a single point of injury. A two-handed katana deals a minimum of 4 injury on any hit. That's always a crippling blow to a normal person's hand. They can't ever deal a less severe blow than a crippling one. The katana can't ever deal only one, or two, or three points of injury.

I think you are trying to make an issue of fidelity (fitting varying damage amounts from ST and weapon into Xd6+Y) into an issue of deliberate modelling.

If it was a modelling issue there wouldn't be rules for converting 1d+5 into 3d-2.