Combat: Penetration and Damage Class

Diagram of ballistic gelatin test result for .308 Winchester soft-point (SP, similar to a Dum-Dum bullet) hunting ammunition, by former US Army surgeon Dr Martin Fackler (from http://www.firearmstactical.com/wound.htm).

The two most important stats for a weapon in Lead & Chrome are Penetration (PEN) and Damage Class (DC). These are explained in the Combat chapter under Armour and Penetration and Wounds, but an explanation of how the values of these stats are arrived at may be of interest, if only from the point of view of game design.

Background

In 1991 R. Talsorian Games published a book titled Edge of the Sword Vol. 1: Compendium of Modern Firearms by Kevin Dockery. The book was a generic supplement for various role-playing games, including R. Talsorian's Cyberpunk 2.0.2.0., but it also contained the kernel of an original RPG, in the form of a combat system. 

Kevin Dockery's system used a several complex mathematical formulae to calculate the effectiveness of various firearms against armour and cover, along with the size of the wound cavity created in the victim's body: in other words penetration and damage. 

For many years before I began the Lead & Chrome project in earnest I had been tinkering around with ways to calculate RPG damage for any firearm, by taking weapons defined in the rules, comparing the in-game damage with raw data like calibre, bullet weight and muzzle velocity, along with statistics derived from those numbers like kinetic energy, momentum and sectional density (much much mass is behind each square millimetre of frontal cross section area). I have compiled have a huge spreadsheet file full of data for all sorts of calibres, with the numbers 'crunched' in various ways.

In late 2011, when I had already started on a set of alternative rules for existing RPGs that would become Lead & Chrome, I read Edge of the Sword in detail for the first time, finally paying attention to the formulae in the back of the book. Having played Megatraveller at school I was familiar with the idea of having separate stats for penetration and damage. It adds a layer of complexity, but it also solves the 'realism' problem of how to describe weapons which penetrate armour easily but cause only limited wounds (like the M16), versus those with low penetration but great wounding potential (like shotgun slugs or flintlock muskets).

I'd already found this interesting discussion of terminal ballistics and wound mechanisms (in terms of big game hunting), and I was working along the lines of using a calculation of wound cavity size as the basis for damage stats. 

So I took Kevin Dockery's formulae for penetration and damage and modified them in various ways, producing two new formulae for what I came to call Penetration and Damage Class. Developing that idea was one of the catalysts for the project of designing an original game.

Penetration (PEN)

PEN represents how well a weapon punches or cuts through body armour and cover materials. It is meant to correspond to real-world data on what class of armour will stop what calibre of bullet, artillery shell, anti-tank grenade etc. 

PEN corresponds to another game stat called Armour Value (AV). If the PEN of the weapon is less than the AV of the target's armour (or intervening cover) then the attack fails to penetrate. If PEN is greater than AV, the attack penetrates with its full DC. If PEN and AV are equal then the attack penetrates with a -4 modifier to the wound roll.

Low levels of AV correspond to the US National Institute of Justice (NIJ) rating for body armour. Type I armour (AV 2) will stop about 50 per cent of .22 LR and .380 ACP rounds. Type IIA (AV 3) will stop about half of .38 Special, .40 S&W and .45 ACP rounds. Type II (AV 4) will stop 9mm Parabellum and .357 Magnum rounds, Type IIIA (AV 5) will stop .44 Magnums, Type III (AV 7) will stop 7.62mm NATO rifle rounds and Type IV (AV9) will stop armour-piercing 7.62mm rounds, half the time.

PEN is calculated simply by multiplying the round's calibre by its muzzle velocity. The result is divided by a constant number X which gives a result of 2 for the .22 Long Rifle calibre, corresponding to the AV 2 value given to NIJ Type I body armour. 

This sounds like an unscientific 'rule of thumb', but it works very well for most handgun and rifle calibres. The results go askew for large-calibre, low-velocity, low-sectional density projectiles like musket balls or shotgun slugs, but merely dividing the PEN of those weapons by two (done by doubling the constant X) gets it back on track. 

Damage Class (DC)

DC expresses the wounding potential of a weapon. It is based on a calculation of how wide and deep a hole the bullet (or arrow or knife) will make in the victim's body.

The formula is quite complex: the round's mass times velocity squared, times the cross-sectional area of the bullet (proportional to calibre/2 squared), all divided by Calibre times Velocity. The result is reduced to its square root to 'flatten out' the results into a manageable range, and then divided by a constant that gives a result of 1 for the .22 Long Rifle cartridge. This can be summed up as:

(Square root of (M x V0 squared x A)/(C x V))/X

Where M = mass, V0 = muzzle velocity, A = cross-sectional area, C = calibre and X = the magic constant.

Sounds complicated? Well, the spreadsheet does all the calculations for me, and I put the resulting stats in the book (or on the web page) for players to use. 

The result of all this algebra is that a Luger pistol has a PEN of 4 and a DC of 2, while a Colt .45 Automatic has a PEN of 3 and a DC of 3. What do you choose, better penetration or better stopping power? A .357 Magnum or .45 Long Colt revolver is seemingly the best of both worlds, with a PEN of 4 and a DC of 3, but you only get six shots and reloading takes longer. A .44 Magnum revolver trumps all of these with a PEN of 5 and a DC of 4, but the rate of fire is lower due to increased recoil. 

Thus we have a nice set of pros and cons for different weapons, which in turn makes the players think about their options.

Pleas leave any comments you have below this post.

Updates; Tasks and Stat Checks

John Dillinger, the famous depression-era bank robber

Today's updates 

Gangsters & G-Men: a new page on character backgrounds has been added, so never fear, source material is being written!

Equipment/Ammunition: tables now include the weight of ammunition (mostly thanks to http://www.pmulcahy.com/ammunition/ammunition.htm), and there is an extra section on how much magazines and ammo belts weigh.

Equipment/Machine Guns: I have clarified whether the listed weight is for a loaded or unloaded weapon, corrected the weights in light of this, and added the weight of ammunition belts to the appropriate weapon descriptions.

Tasks and Stat Checks

I'd now like to write something about the mechanics of the game, regarding Tasks and Stat Checks, the two main mechanisms for getting things done in the game.

A Task (or skill check) is used to decide whether a character successfully uses a skill. The player (or GM for NPCs) rolls 2D10 and adds the character's skill level (a number from 0-10) and relevant Stat for the skill (a number from 3-10), trying to equal or exceed a difficulty number, which is always a multiple of five. Negative and positive modifiers are applied to the dice roll depending on the situation.

A Task: 2D10 + Skill + Stat + Modifiers vs. Difficulty Number

An unmodified roll of 2 on the 2D10 is an automatic failure, and a fumble in most circumstances except a non-critical, no-stress situation. An unmodified roll of 20 is an exceptional success, and a third D10 is rolled and added to the result. If the roll of the extra D10 is a 10, roll a fourth (and so on and so on). This way success or failure are never automatic, unless the GM rules that no Task roll is needed to succeed or that the task is simply impossible.

The average human value for any Stat is six, and a skill level of three or four is considered competent. A task of Average difficulty has a target number of 20, so a character with a skill level of three and a stat level of 6 will succeed on a 2D10 roll of 11: slightly more than a 50 per cent chance.

The human maximum for any Stat (apart from Sanity, which is the sum of Geniality and Nerve) is 10, and a character can have only one Stat at that level. A Skill level of 10 represents the pinnacle of human achievement, and hardly anybody will have even one Skill at that level. For example, sprinting phenomenon Usain Bolt would have an Agility Stat of 10 and an Athletics Skill of 9 or 10, in game terms.

Originally I was going to use a roll of 1D10 + Skill + Stat + Modifiers (with all the difficulty numbers set five points lower), but on reflection I decided that there were advantages to a 2D10 roll. One is that the range of results is greater, making the outcome of any Task roll less predictable. 

Another advantage is that the probability of rolling a particular number is higher for numbers around the middle of the range (11 being the median and average) than it is for results at the extreme (2 or 20). This not only makes fumbles and exceptional successes less likely, but it encourages players to use their heads and role-play by stacking situational modifiers in their favour.

A Stat Check is a roll of 1D10 against the relevant Stat, trying to roll equal or less than the stat. Positive and negative modifiers are applied to the Stat, not the die roll. The exception is the Sanity Stat, which is the sum of Geniality and Nerve and so has a normal starting value from 6-20: A D20 is rolled for a Sanity check.

Stat Checks can be used as a kind of 'saving throw', or when no skill is relevant to the situation. For example, a character would have to make a Toughness check to see whether they recover from a disease or survive poisoning, or a Nerve check to stand up and shoot back when being shot at.

I hope that makes the rules a bit clearer and entices you to play the game. Please leave any comments you have below this post.

James