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Firearms, joules and damage dice


Thot

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Looking at the various weapons in the BGB, I wondered what the formula behind damage is. Obviously, it is some sort of logarithmic scale, but how can it possibly be computed for new weapons?

After having played around with the available numbers a bit, the following seems to work:

Starting at 400 J, which I put equivalent to 1 point of average damage, each additional point of damage requires a multiplication of the muzzle energy by 1.225.  So 400 for the first point of damage, a total of 490 Joules for 2 points of damage, 600 J for three, and so on.  (Those numbers 1.225 and 400 are sort of arbitrarily chosen via trial-and-error, but should be close enough.)

As a formula, that is (average damage)=1+ Logarithm [to the base of 1.225] of (400-number of joules). Or, in a LibreOffice spreadsheet:

1+(LOG(A1/400;1,225))

... where "A1" is the field in which you put the projectile's muzzle energy. That formula will give you average damage - maximum damage will probably be 30-50% more than that. Translating this average damage number into damage dice is probably not done via a formula, but I guess selecting a die type (d4, d6, d8, d10 or d12), dividing by the expectation value for that die and keeping any rest as a bonus to the damage dice should do the trick.

Now, projectile muzzle energies you can find all over the Internet for a given type of ammo, but if you don't find it or want to use a fictional weapon, you could simply do the E=0.5mxv², equation, which, if you set m as the mass in kilograms and v as the velocity in m/s, gives you the correct joule value.

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Hm. Energy weapons would work completely differently, I would reckon. We don't have any real-world examples to compare the BGB's sample energy weapons with, so we'd have to use fire as a reference. A small candle fire is supposed to do 1 point of damage per turn (which is 12 seconds).

Edit: In the following I try something that in the end doesn't work. So don't spend too much effort on trying to work with this.

According to http://www.thenakedscientists.com/HTML/questions/question/1857/ , a candlelight has a power of around 80 watts (joules per second), so 1 point of damage across 12 seconds apparently equals 960 Joules. We can simplify this to 1000 joules, but as joules to damage isn't a linear conversion, that doesn't help us much.

A torch supposedly does 1D6 (3.5 average) of heat damage per turn, a large bonfire 1D6+2 (5.5 average), molten lava or a rocket 3D6 (10.5 average).

A torch might be worth, well, about 30 times the volume of a candlelight. That's a very rough estimate, but that would mean increasing energy by a factor of 30 increases damage by a factor of about 3.5. Adding one point of damage then should then require an increase in energy by about a factor of (very roughly) 5.5. (Lots of very, very, very rough estimates here!)

Thus, the spreadsheet formula would be

(average damage) = 1+ LOG((Energy/1000); 5.5)

A pool of lava would would then inflict just short of 4.6 billion joules on a human body over a time of 12 seconds. Lava has a temperature of about 700 to 1200 degrees Celsius. Inflicting that kind of temperature on a (very muscular or very fat, but in either case more easily computable) human body of 100 kg at 37 degrees Celsius would require

(energy required to heat a gram by 1 degree) x (number of degrees) x (number of grams).

Now, the amount of energy needed to heat given piece of matter by one degree increases with the temperature of that piece of matter, but we'll just ignore that for simplicity. Just over 4 Joules are needed to heat one gram of water by 1 degree at human temperature ranges, so the above formula at the lower end of the range for lava temperature would be:

4x700x100.000=280.000.000

or 280 million joules per second, times 12 for a full combat round is 3,36 billion Joules.  But a ton of TNT contains about 4.1 gigajoules.

So the simple logarithmic formula doesn't work here, I would say.

Edited by Thot
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Yes. There is no link between damage in a roleplaying game and the number of joules. GURPS - which you also know - may be closer from such a manner of calculating damage but, even with GURPS, there are a lot of problems like that. For one simple reason: roleplaying games are not reality simulators. They are designed to have fun. So, damage that weapons inflict are just calculated by comparing weapons with each others and with average Hit Points of a character.

A broadsword inflicts 1D8+1+db damage (8 in the average, for a good warrior with +1D4 bonus) because the authors wanted it to kill a man in about two blows and to often make a Major Wound. A shotgun inflicts 4D6 (14 in the average) because authors wanted it to kill a man in one point-blank range blow. And that's also why an assault rifle only inflicts 2D6+2 damage (9 in the average): to let victims have a fair chance of surviving the first shot ... Suppose you are playing a soldier, in an open war. A foe is aiming at you and pull the trigger ... If damage was calculated by a joule formula compared with broadsword, it would just be zap, you're dead ... and it wouldn't be fun at all.

Note that it wouldn't really be realistic either, actually. Sometimes, people survive assault rifle bullets. And sometimes, the first strike of a broadsword kills.

So, that is why roleplaying game authors prefer comparing weapons with each others and with Hit Points rather than using a joule/momentum formula. And they also do it because it is much more easy! ;)

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14 minutes ago, Gollum said:

Yes. There is no link between damage in a roleplaying game and the number of joules.

There basically is one for firearms. See the OP.

It does not work for energy weapons, at least not in a way I have found yet, but for firearms, yes, it does. The formula in the OP works for a Derringer, a Colt or a tank gun alike.

And that is practical and useful.

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GURPS - which you also know - may be closer from such a manner of calculating damage but, even with GURPS, there are a lot of problems like that. For one simple reason: roleplaying games are not reality simulators. They are designed to have fun. So, damage that weapons inflict are just calculated by comparing weapons with each others and with average Hit Points of a character. [...]

Yes, of course RPG's are simulators, in that they are models of the way the game world works. They don't need to be very precise in their simulation (so for many weapons and damage types, a guess for damage will do), but they do deliver consistent results that allow for planning and are generally thought to be somewhat mirroring the way things work in the real world.

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So, that is why roleplaying game authors prefer comparing weapons with each others and with Hit Points rather than using a joule/momentum formula. And they also do it because it is much more easy! ;)

 

No, the reason is because it is a complicated and difficult undertaking, and each type of damage would require different formulas. It is just easier to go by gut feeling in many cases, while getting just-as-good results.  But for firearms, it is more practical to have a formula.

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19 minutes ago, Thot said:

There basically is one for firearms. See the OP.

It does not work for energy weapons, at least not in a way I have found yet, but for firearms, yes, it does. The formula in the OP works for a Derringer, a Colt or a tank gun alike.

And that is practical and useful.

Yes, you're right. I was speaking about guns compared with other kinds of weapons ... Revolver, medium, 1D8; Longbow, 1D8+1+½db. Sorry for not having clarified it

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Yes, of course RPG's are simulators, in that they are models of the way the game world works. They don't need to be very precise in their simulation (so for many weapons and damage types, a guess for damage will do), but they do deliver consistent results that allow for planning and are generally thought to be somewhat mirroring the way things work in the real world.

They could be named "simulators" because they give plausible results for a fictional story, yes. But they are not simulators in that their purpose is not calculating what would really happen, like scientific simulators would do it. Light club, 1D6+db. Pistol, medium, 1D8. In reality, a medium pistol is far much more dangerous than a light club. Especially when dealing with armors.

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No, the reason is because it is a complicated and difficult undertaking, and each type of damage would require different formulas. It is just easier to go by gut feeling in many cases, while getting just-as-good results.  But for firearms, it is more practical to have a formula.

Yes, I fully do agree here. But you also have to take into account the type of bullet. The FAMAS, for instance, uses bullets with hollow points, which increases damage inside the body ...

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26 minutes ago, Gollum said:

They could be named "simulators" because they give plausible results for a fictional story, yes. But they are not simulators in that their purpose is not calculating what would really happen, like scientific simulators would do it. Light club, 1D6+db. Pistol, medium, 1D8. In reality, a medium pistol is far much more dangerous than a light club. Especially when dealing with armors.

The BGB sais you should halve any pre-modern armor vs firarms. ;) And while 1D8 isn't much against plate armor (which will protect with 4 against it), a medium pistol isn't a particularly deadly weapon and could conceivably be stopped by full plate half of the time. An assault rifle could not really avoid to penetrate it, though (except under very rare circumstances).

26 minutes ago, Gollum said:

Yes, I fully do agree here. But you also have to take into account the type of bullet. The FAMAS, for instance, uses bullets with hollow points, which increases damage inside the body ...

 

You could do that, of course. But that is a level of detail that, at least in my opinion, just isn't worth it in a game.

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10 hours ago, Thot said:

So the simple logarithmic formula doesn't work here, I would say.

Aha, I see. Perhaps this kind of formula isn't as useful here either, as we have very few real world energy weapons. Still enjoyed your reasoning though : )

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29 minutes ago, clarence said:

Aha, I see. Perhaps this kind of formula isn't as useful here either, as we have very few real world energy weapons. Still enjoyed your reasoning though : )

 

It does work for all weapons that I looked at, and that includes the "tank gun" given in the BGB. Any one that it doesn't cover?

 

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The thing about "damage" is that is isn't the same thing as energy. A weapon can have a lot of energy than another but end up doing less damage to a human body fr several reasons. 

First off, how that energy is spread over a body makes a big difference. Case in point, if you poke someone with a finger or stick them with a pin, you are apply the same amount of energy (and force for that matter), but the pin will do more damage. The poke spreads the energy out over an area the size of your fingertip, whereas using the pin concentrates the energy over an area the size of a pin, and can pierce the skin and do more "damage". 

Conversely, concentrating the damage too much can reduce the damage! This is often the case with bullets. A larger, heavier bullet will usually inflect more damage than a smaller, lighter one, even if both have the same amounts of energy, as the lighter bullet can go right though the body and expend most of it's energy on something (or someone) behind the target. 

Another big factor, in fact probably the most important one, is just where on the body that the energy is applied to. The human body is not just a block of stuff. It is filled with various organs, and some are far more resistant to damage than others. A powerful attack that hits bone or an extremity might do more "damage" in terms of the amount of tissue, nerve, and bone damage, but. for a "quality" standpoint, that damage might be less than a lower energy attack to a more vital location. For example, a .600 Nitro-Express round is superior to a .25 ACP round, as far as "damage" goes, in just about every conceivable way, yet a .25 bullet though someones eye is probably go to end up doing more "damage" in game terms than a .600 round that takes off a pinky. 

 

So if's more complicated than just the amount of energy or force. Then there are things like armor, range, inertia (heavier bullets tend to keep their energy longer in flight), shape, and energy over time to consider (basically spreading out the energy over time actually can reduce the amount of "damage" inflicted. It's also why old style armors aren't as effective against firearms)

 

Edited by Atgxtg
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Well, for such variances, we do have the damage dice, which allow for a wide range of actual results. The formula in the OP just gives you the average damage.

Of course, you could still argue with the details, such as energy vs. shape of the bullet. But do we need it that precise? What we need is a plausible number to distinguish a 5.56 mm from a 7.62 mm cartridge, and a way to figure out what the 40mm ship gun can do.

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Thot,

Do you have a spreadsheet with the firearms statted up? I have some doubts about your formula. Back when the firearms stats were done up (in Call of Cthulhu, I believe), most 9mm Parabellum rounds had more energy than most .45 ACP rounds. So, if firearm damage was determined strictly by energy,  then 9mm weapons would have damage ratings as good or better than .45 ACP weapons - but they don't. 

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https://en.wikipedia.org/wiki/9×19mm_Parabellum

570 to 680 Joules. (3 to 4 points of average damage according to the formula)

https://en.wikipedia.org/wiki/.45_ACP

Depending on manufacturer and subtype (of which there are many), 483 to 835 Joules (2 to 5 points of average damage according to the formula)

I would reckon that the discrepancy you see stems from comparing different manufacturers' rounds.

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Just now, Thot said:

Well, for such variances, we do have the damage dice, which allow for a wide range of actual results. The formula in the OP just gives you the average damage.

Of course, you could still argue with the details, such as energy vs. shape of the bullet. But do we need it that precise? What we need is a plausible number to distinguish a 5.56 mm from a 7.62 mm cartridge, and a way to figure out what th 40mm ship gun can do.

Sure, but those details can be very important in terms of gameplay.

For instance, a musket ball from an old muzzle loader should do more "damage" to a person than a modern 9mm pistol round, yet the 9mm round is probably going to end up doing more damage if the target is wearing body armor, since the smaller bullet concentrates all than energy over a smaller area.

 

Another thing to consider is what the hit point and armor rating progressions are. For example, a 5 ton giant (or elephant ) might have 65 times the mass of an average man, but he wouldn't have 65 times the hit points. Probably closer to around 5 times as many. So if you want a elephant gun to be about as effective against an elephant as a rifle would be against an average man, it should do about 5 times the damage is game terms...but that would probably make the elephant gun too effective against men. 

 

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16 minutes ago, Thot said:

https://en.wikipedia.org/wiki/9×19mm_Parabellum

570 to 680 Joules. (3 to 4 points of average damage according to the formula)

https://en.wikipedia.org/wiki/.45_ACP

Depending on manufacturer and subtype (of which there are many), 483 to 835 Joules (2 to 5 points of average damage according to the formula)

I would reckon that the discrepancy you see stems from comparing different manufacturers' rounds.

But that's the point. Back in the 80s when the weapons were first written up, .45 ACP rounds weren't that powerful, nor could most .45 ACP firearms actually be able to for those rounds safely. 

 

And the 1D10+2 damage given to the .45 ACP in CoC (which is where BGB got them from) would have an average damage of 7.5, which would require about 1500J of energy (which would be great if the 1D10+2 was for a .44 Mag).

 

Edited by Atgxtg

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1 minute ago, Atgxtg said:

Sure, but those details can be very important in terms of gameplay.

For instance, a musket ball from an old muzzle loader should do more "damage" to a person than a modern 9mm pistol round, yet the 9mm round is probably going to end up doing more damage if the target is wearing body armor, since the smaller bullet concentrates all than energy over a smaller area.

Hm. According to this:

http://historum.com/war-military-history/37754-kinetic-energy-ancient-modern-weapons.html

"Matchlock Full Musket - 1,943"

That is above the level of 5.56mm NATO, and should produce an average of 9 points of average damage. Works fine for me.

 

1 minute ago, Atgxtg said:

 

Another thing to consider is what the hit point and armor rating progressions are. For example, a 5 ton giant (or elephant ) might have 65 times the mass of an average man, but he wouldn't have 65 times the hit points. Probably closer to around 5 times as many. So if you want a elephant gun to be about as effective against an elephant as a rifle would be against an average man, it should do about 5 times the damage is game terms...but that would probably make the elephant gun too effective against men. 

An elephant gun that shoots a 130 gram bullet at a speed of 430 m/s, which are numbers I get from:

https://en.wikipedia.org/wiki/Elephant_gun

will do an average of 18 points of damage (damage given by the BGB is 3D6+4, or an average of 14.5, but that may be a smaller gun than I used in my computation now - there were many types of 'elephant guns', apparently). Head hit location hitpoints are one third of total hit points, so an elephant with no more than 54 hitpoints should be a somewhat safe kill - for stubborn elephants, history seems to indicate that many needed more than one shot.

 

 

 

 

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20 minutes ago, Atgxtg said:

But that's the point. Back in the 80s when the weapons were first written up, .45 ACP rounds weren't that powerful, nor could most .45 ACP firearms actually be able to for those rounds safely. 

 

From where do you get the notion that those weaker weapons were more powerful than 9mm parabellum? I'd be very interested in reports about the actual penetration of those bullets that you deem more powerful than the energy amount would indicate.

I would be inclined to subsume this under http://tvtropes.org/pmwiki/pmwiki.php/Main/KatanasAreJustBetter , if you get my meaning.

 

That said, yup, the formula doesn't work here.  The .45 ACP comes out as too light, and for the

https://en.wikipedia.org/wiki/.500_S%26W_Magnum

which one could also understand as a "heavy revolver" round, it gives too high a value.

 

20 minutes ago, Atgxtg said:

And the 1D10+2 damage given to the .45 ACP in CoC (which is where BGB got them from) would have an average damage of 7.5, which would require about 1500J of energy (which would be great if the 1D10+2 was for a .44 Mag).

Hm. Personally, when in doubt, I'd prefer something deriving the stats from the energy over some cinema-induced gut feeling.

 

But yes, some firearms in the table apparently don't follow the formula.

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2 minutes ago, Thot said:

Hm. According to this:

http://historum.com/war-military-history/37754-kinetic-energy-ancient-modern-weapons.html

"Matchlock Full Musket - 1,943"

That is above the level of 5.56mm NATO, and should produce an average of 9 points of average damage. Works fine for me.

Doesn't work fine for me, or for the existing weapon damages.  That musket ball is going to to be stopped by armor that the 5.56 NATO round will penetrate. 

 

Also, your source uses energy in foot-pounds, not Joules, so that Musket rated at 1943ft-lbs would be rated at 2643 Joules for an average damage of about 10.30 points by your formula . For comparison a .58 Springield rifle has a damage rating of 1D10+4 (average of 9.5) and a muzzle energy of around 1355J (for an average damage of 7 by your formula).

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1 minute ago, Thot said:

But yes, some firearms in the table apparently don't follow the formula.

Yes, because they didn't use your the formula to assign damages scores. I believe Sandy Peterson based his values more on the force of the weapons rather than the energy. Then those values were tweaked a bit, by eye for the BGB. So I don't believe your formula is going to hold up over a wide range. 

I do agree that I prefer to go with some sort of formulatic approach over a gut feeling, but I don't think just going by total energy is going to match up with the existing weapon stats. If you want to do up a new table of weapon stats that is close to what exists you can (and some people did just that for a BRB supplment  a few years back), but that's something else. 

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6 minutes ago, Atgxtg said:

Doesn't work fine for me, or for the existing weapon damages.  That musket ball is going to to be stopped by armor that the 5.56 NATO round will penetrate. 

There was no "standard musket", and especially not a standard load. The musket shown in he BGB may be of a different type, or simply loaded differently when they tested it.

6 minutes ago, Atgxtg said:

Also, your source uses energy in foot-pounds, not Joules, so that Musket rated at 1943ft-lbs would be rated at 2643 Joules for an average damage of about 10.30 points by your formula .

Ah, didn't catch that. Thanks for the hint.

6 minutes ago, Atgxtg said:

For comparison a .58 Springield rifle has a damage rating of 1D10+4 (average of 9.5) and a muzzle energy of around 1355J (for an average damage of 7 by your formula).

But... there is no .58 Springfield rifle in the BGB?

 

 

 

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2 minutes ago, Atgxtg said:

Yes, because they didn't use your the formula to assign damages scores.

Of course they didn't. The formula is just an approximation, of course. It does work for the weapons I used for playing with the numbers, and seems like a good approximation for me.

2 minutes ago, Atgxtg said:

I believe Sandy Peterson based his values more on the force of the weapons rather than the energy. Then those values were tweaked a bit, by eye for the BGB. So I don't believe your formula is going to hold up over a wide range. 

 

I tested it with the assault rifle, various handguns and the tank gun, liked the result, and reported back here. A range from a light pistol to a 120mm tank gun is a wide enough range for me.

 

The force and the energy are equivalent in amount, so I do not see any relevant difference here?
 

2 minutes ago, Atgxtg said:

I do agree that I prefer to go with some sort of formulatic approach over a gut feeling, but I don't think just going by total energy is going to match up with the existing weapon stats. If you want to do up a new table of weapon stats that is close to what exists you can (and some people did just that for a BRB supplment  a few years back), but that's something else. 

Well, nothing is going to be completely the same as the gut-feeling stats. Not even another person's gut feelings. ;)

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15 minutes ago, Thot said:

But... there is no .58 Springfield rifle in the BGB?

 

 

 

No, but there is in Call of Cthulhu, which was the source for the BGB firearm stats Compare:

COC: .58 Springfield Rifle Musket

Base Chance: 25%   Damage: 1D10+4  Base Range: 60 yards  Rate of Fire: ¼  Ammo: 1

Hit Points: 12  Malfunction: 95-00

 

BRP Rifle, Musket

Skill: Rifle  Base: 25%  Damage: 1D10+4  Attk: ¼  Special: Impaling  Range: 60  Hands: 2H

Hit Points: 12 Parry: No  STR/DEX: 9/5  Mal: 95-00

 

it's the same weapon. 

Edited by Atgxtg

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4 minutes ago, Thot said:

Of course they didn't. The formula is just an approximation, of course. It does work for the weapons I used for playing with the numbers, and seems like a good approximation for me.

 

I tested it with the assault rifle, various handguns and the tank gun, liked the result, and reported back here. A range from a light pistol to a 120mm tank gun is a wide enough range for me.

 

I think you should have tested it out with more weapons. Just because it matches up well for a handful of weapons doesn't mean that it will hold up well for most of them, and certainly doesn't prove that the  formula works. For one thing firearms with less that 400J of energy will do negative damage by the formula. 

 

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The problem is that most weapons in the BGB table cannot be easily identified (or at all) with any certainty. So we could probably both find weapons that fit or don't fit with the formula, but you are right that the formula fails for the really small guns like a Derringer or other .38 calibre weapons.

 

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1 hour ago, Thot said:

The problem is that most weapons in the BGB table cannot be easily identified (or at all) with any certainty. So we could probably both find weapons that fit or don't fit with the formula, but you are right that the formula fails for the really small guns like a Derringer or other .38 calibre weapons.

 

Actually they can. Pretty much all of the weapons in the BGB table came from other Chaosium RPGs,, Pretty much all of the firearm stats came from Call of Cthulhu. Jason "filed off" the names, gave them generic names such as "medium pistol". but it's easy enough to backtrack it. In a few instances he adjusted a weapon a little for some reason or another, but they are still the weapons from CoC.  Some examples:

BGB Light Pistol  is a CoC .22 Short Automatic

BGB Heavy Pistol is a CoC .45 Automatic

BGB Assault rifle is a CoC AK-47 (with an extra point of damage)

BGB Bolt Action Rifle is a CoC .30-06 Bolt Action Rifle

 

You can go through the weapon tables in both RPGs and see which weapon is which. 

 

 

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