Logarithmic Damage

Note: this page was written quite some time ago, but Pyramid #3/83: Alternate GURPS IV motivated me to adjust it.

While there are some distinct advantages to linear damage scales, they tend to break down outside of a fairly small range of game scales; GURPS damage is inconvenient when dealing with vehicles or giant monsters, and completely unusable when dealing with small animals (there just isn't enough resolution in the game system to distinguish between a mouse and a grasshopper). One traditional solution to this has been some sort of logarithmic damage system, converting an extreme range of damages into a simple linear measure. There are a number of difficulties with logarithmic systems as well (in particular, barrier penetration can be an issue, and invariant hit points can be puzzling), but at times they can be easier to handle than the linear problems. The method below is slightly complex in setup, but should be fast enough in actual play.

Setup: Computing Required Stats

Attacks

All attacks have a penetration of 3d6±n and a wounding modifier. This is noted as, for example, 3d6+5[+1]. They are calculated as follows:

Penetration and Wounding (non-ST based weapons)

For weapons that do fixed damage, unaffected by ST, basic penetration is directly computed from GURPS damage, by the formula 3d6 + 20 x log10( damage dice ). For those who don't want to use a calculator, here is a table:

Basic wounding is based on damage type: [+2] for Pi++ and Imp, [+1] for Pi+ and Cut, [-2] for Pi-, and [0] for all other types. You should still list the damage type for other effects (discarding any +s on Pi), but it has no direct effect on wounding.

Then, modify both penetration and wounding by armor divisor, as follows (note: the combined effect of these two is no change in wounding against an unarmored target).

Penetration and Wounding (ST-based weapons)

The ST damage tables are, for historical reasons, something of a disaster, but a not completely horrible formula is:

    • Thrust: equal to 3d6 - 10 + ST/2.

    • Swing: equal to 3d6 - 5 + ST/2.

    • Weapons: if damage bonus ≤ 3, double the bonus. Otherwise, add 3.

    • Damage Type: adjust for damage type as above.

    • Weapon Scaling: you may use heavier or lighter weapons. Every +2 Min ST gives +1 damage.

Thus, a broadsword now does Sw+2[+1] Cut/Thr+4[+2] Imp. At ST 10, that's 3d6+2[+1]/3d6-1[+2].

Defenses

All likely targets have Wound Thresholds. This indicates the amount of damage required to inflict a specific effect.

Unarmored Wound Thresholds

Unarmored wound thresholds are very simple, as they are computed directly from ST, as follows:

    1. If the victim does not have a wound at the level of the current wound, add one. If the victim does have a wound of that level, remove (or mark out) that wound and add a wound of the next level up. Continue upwards if the victim also has higher level wounds. If the attack was did not require a death check, but this upgrades the wound to one that does, roll one death check (this is significantly less cumulative than normal GURPS wounding; it takes 32 level 1 wounds to create a level 6 wound and 64 to force a death check.

    2. The victim suffers cumulative effects based on the total wound level. Apply all effects for the worst wound the victim has, and everything above it, but penalties do not stack, wound level 9 is -4 to consciousness, not -7.

Precomputed Tables

It is possible to compute the effects of step 4, steps 6-7, or the combination of step 4, 6, and 7, ahead of time; doing so can save time in combat but requires more preparation. If you're just replacing step 4, that's a pre-computed penetration table -- just list a table with the initial penetration on the top row, the final penetration on the bottom row. For an armor value of 0, it looks like this:

For armor values other than 0, just add the armor value to every cell except the (-2) and (-1). Tables for armor values 0-60 (DR 1-100) are given here (including some values that do not actually occur in vanilla GURPS, but occasionally it's nice to have DR options between 1 and 2). If you're replacing steps 6-7 it's even easier, as each wound level is just toughness+level*5+0-4, so it looks like this (since attacks can have large negative wound modifiers, listing levels above 10 does have meaning).

Armored Wound Thresholds

For armored wound thresholds. you need two values: your unarmored wound thresholds (as above), and your armor value (equal to 20 x log10(DR)). For those who aren't using a calculator, armor value table (use the highest value ≤ your DR)

Now, take these DR values and combine them with your unarmored threshold, as follows: take the higher value, and add a bonus based on the difference between higher and lower value, as follows:

As a worked example, consider a ST 10 man wearing DR 6 plate (armor value +16). Unarmed wound level 1 is at 0, so to get armored value we note that 16 > 0,

Note that the armor combine rules above can be used in play to cover situations such as barriers. You may want to list more than one set of thresholds.

Damage Resolution

Basic Damage Resolution

    1. Roll Damage (as above)

    2. Compare with the target's wound thresholds. Basic wound level is the largest threshold that is ≤ the damage roll.

    3. If the attack has a Wounding Modifier, adjust the wound level by the wounding modifier of the attack. This is the modified wound level.

    4. If the target has any types of Injury Tolerance that are relevant, adjust the wound level.

    5. Apply the immediate effects (shock, disabling, major wounds, death checks) of the indicated wound level.

    6. If the victim has not previously suffered a wound of this severity, mark off this wound level. Otherwise, there is a chance to cascade. Cascading works as follows:

      1. Roll 1d. On a 1-3, mark off the highest blank wound ≤ your wound level. On a 4-6, increase wound level by 1, and mark it if it is unmarked.

      2. Continue until you reach an unmarked wound level, or roll a 1-3.

    7. Apply lasting effects (consciousness checks, slowed due to injury) for the highest wound level you have suffered.

Advanced Damage Resolution

Most advanced rules are just additional wounding modifiers

    • Bleeding: any wound capable of bleeding has a chance to worsen. Every five minutes, make a HT roll. On a failure, apply a wound equal to the size of the bleeding wound; this wound has a chance to cascade.

    • Healing: healing works just like damage, only in reverse: make a healing test and erase the appropriate wound. This is capable of cascading up or down, as normal.

    • Hit Location: Arm or Leg. Add -2 wound modifier to Impaling or Piercing damage. If modified wound level is 4 or higher, treat as 4 and the location is disabled. If modified wound level is 6 or higher, the limb may be destroyed.

    • Hit Location: Eye. Add +3 wound modifier. If modified wound level is +1 or higher, the eye is disabled.

    • Hit Location: Face. Add +1 wound modifier to corrosive attacks.

    • Hit Location: Hands or Feet: Add -2 wound modifier to Impaling or Piercing damage. If modified wound level is 3 or higher, treat as 3 and the extremity is disabled. If modified wound level is 5 or higher, the extremity may be destroyed.

    • Hit Location: Neck. Add +1 wound modifier to corrosive, crushing, or cutting attacks.

    • Injury Tolerance: Diffuse. Single-target attacks are limited to a modified wound level of 1 for Impaling or Piercing attacks, 2 for all other attacks.

    • Injury Tolerance: Homogeneous. Add a -4 wound modifier to Impaling or Piercing damage. Does not stack with the modifiers for hitting limbs.

    • Injury Tolerance: Unliving. Add a -2 wound modifier to Impaling or Piercing damage. Does not stack with the modifiers for for hitting limbs.

Basic Combat Sequence

The basic combat sequence for LDS is as follows:

    1. Determine the attack you are using, and look up its Penetration Bonus and Wound Modifier.

    2. Penetration starts at a value of 1d6+Penetration Bonus.

    3. If any barriers are in the way, look up Penetration on the Initial Pen row for the barrier, and read down to the Final Pen. The result is the penetration after passing that barrier; Nil means that the attack is stopped, NC means that Penetration is unchanged. Repeat this process for each barrier.

    4. Look up Penetration on the target's Penetration Chart, and read to the Wound Depth. This will be the basic wound level of the attack.

    5. Check for blowthrough. The maximum basic wound level is 6 for the legs, 5 for the arms and feet, 4 for the hands.

    6. Add hit location modifiers (+3 for the vitals, +4 for the brain)

    7. Determine the target, and look up its Penetration Chart.

    8. Roll 1d6 and add Penetration

    9. Roll 3d6 and add the weapon's Penetration Bonus to get Penetration.

    10. Compare penetration to the barrier's armor rating, and modify penetration based on the difference: If between two values, use the lower. If the difference is zero or less, no penetration occurs.

    11. If multiple layers of armor are present, repeat this process.

    12. Subtract the target's Toughness.

    13. If the result is less than zero, the attack is too shallow to apply. Otherwise, the basic wound level is equal to remaining penetration/5 (can be 0 at this point).

    14. Add wound modifiers for the weapon. The bonus cannot exceed the basic wound level, there's a limit to how dangerous a shallow wound can be.

    15. Modify for hit location: +2 wound levels for the neck, +3 wound level for the vitals, +4 for the brain. The brain and vitals are both located behind a fair amount of tissue, so again, the bonus cannot exceed the basic wound level; the neck is not limited in that way. Max wound level is 3 on the hands, 4 on the arms or feet, 5 on the legs, +1 for cutting weapons. Optionally, piercing and impaling attacks to the torso (only) add 1d-4; this produces the extremely variable results seen from real stab and bullet wounds.

    16. Discard any wound levels below 0, and increase any level 0 wounds to level 1.

    17. Apply immediate effects of wound level. Effects are as follows:

If you're replacing steps 4, 6, 7, precompute the penetration as above, and then simply work out the actual wound level for each penetration result, as per steps 6 and 7; you may want to consolidate multiple columns into one. This only works for the last layer of armor, and is probably not worth doing if you have complex armor setups. For armor level 0, toughness 0, a chart looks like this:

Determining the Stats of an Attack or Character

For pre-existing GURPS abilities, it is necessary to compute their effect levels. Attacks and defenses are computed with the following table

Attacks

Start by looking up the attack on the table below:

Find the cell for the attack's damage, and read down for the attack's penetration. If damage exceeds the maximum shown here, each x10 damage is +30. D-damage is also +30, C-damage is +60, and M-damage is +90. This will be the basic penetration of the attack. It starts with a wound modifier of 0.

If the attack has an armor divisor, it modifies both penetration and wounding, in opposite directions, as follows:

This will produce no net change to damage on unarmored targets. It's plausible to consider some weapons to be semi-AP (+5 penetration, -1 wounding), but that's up to GM discretion, no normal GURPS attacks have that property.

Finally, apply wounding modifiers for damage type. For cutting attacks, this is +1; for impaling attacks it is +2. For innate attack piercing attacks, pi- is -2 wounding, pi+ is +1, pi++ is +2. I don't recommend doing this for other powers, though -- realistically, all attacks are likely to be wider as damage increases, so rather than giving every weapon type a bonus to wounding, it's a lot easier to figure that the default is that wounds get wider as damage increases, and alter piercing attacks to follow the same paradigm. Therefore, the wounding modifier for bullets is as follows:

    • Bore Size < Damage Dice: -2 wounding. Rare, mostly ultra-tech gauss weapons.

    • Damage Dice >= Bore Size < 2x Damage Dice: -1 wounding. Most rifles.

    • Damage Dice x2 >= Bore Size < 4x Damage Dice: +0 wounding. Most pistols.

    • Damage Dice x4 >= Bore Size < 8x Damage Dice: +1 wounding. Heavy, low velocity pistols, such as .45

    • Bore Size >= 8x Damage Dice: +2 wounding. No weapons I'm aware of.

    • If ammunition modifies the normal damage type of a bullet up or down, apply that modifier to wounding. Thus, AP munitions apply the +10[-2] for AP, with an additional -1 for the would type reduction, or a total of +10[-3].

Weapon damage should be listed in the form ±Penetration[±Wound Modifier], so an assault rifle (5d) is listed as +28[-1].

ST-Based Attacks

While you can just compute ST-based damage per the above method, ST-based damage, per RAW, actually has a lot of anomalies -- +1 damage has different significance on 1d and 3d, damage isn't linear in actual ST score, and so on. Completely fixing this is a lot of work, but a basic tweak is as follows. First of all, look up your ST on chart for HP (below) (this will be equal to ST-10 over the range 8-18). This is your ST damage bonus. Then add the basic penetration of the weapon; this is 0 + (damage bonus*3) for thrust weapons, 8 + (damage bonus*2) for swing weapons. That only applies to the base damage bonus for the weapon, any other damage bonuses should be treated as a flat +1 per level (yes, this reduces fine/very fine weapons by quite a bit). This doesn't perfectly match standard stats, but it comes close, and has the virtue that x1.5 ST really does translate to x1.5 damage. This has slight effects on reasonable point value of ST, but ST is already a very good deal in settings where ST damage is relevant.

Defenses

Characters normally have Toughness and Armor. Toughness is computed from HP, per the table below, using the 'Tough' column. Armor is converted in the same way, but based on DR and using the 'Armor' column. Realistically, objects with inherent DR are also usually internally reinforced, if armor rating is greater than toughness, add half the difference (this does not apply to characters).

For objects, it may be more convenient to work out toughness by weight:

Add +30 for weight in kilotons, +60 for megatons, +90 for gigatons, etc. Add +9 for unliving, +18 for homogenous. If weight is shown as X×10Y kilograms (typical for scientific references), look up X tons and add Y*10-20; thus, the planet earth, at 6×1024 kg, has toughness 20(6T), +240(exponent), -20, +18 (homogenous), or 258. The sun, at 2×1030 kg, has toughness 313. It may be convenient to list computed toughness by weight (not adjusted for unliving/homogenous); call this mass.

Realistically, Toughness should not be a pure variable in weight anyway, a one ton steel ingot isn't tougher than a one ton sandstone boulder simply because of higher DR. Many homogenous objects don't really have DR at all, treating that boulder as having a toughness of 20-30 and no DR at all won't produce silly results.

Special Cases

Ablative and Semi-Ablative Armor

Ablative and semi-ablative armor have their own Toughness value, and are not protected by their own armor value. For armor bought as an advantage, the toughness is Armor-40 for ablative armor, Armor-20 for semi-ablative armor (items might have whatever toughness the GM feels is appropriate; armor value/2 is a decent estimate for human size armor). Armor that is damaged has two effects: add its damage level to any rolls to target chinks in armor, and at high damage levels it loses armor rating.

This is cumulative, a level 6 and 7 wound give -3 to barrier rating. Armor that's just barely penetrated will take a level 6 hit if semi-ablative, level 10 if ablative. Real armor frequently also has a toughness score and is damaged in the same way, but its toughness score is generally higher and it's usually homogenous; compute as per Barriers. It's difficult to use pre-computed tables with ablative and semi-ablative armor.

Afflictions, Side Effects, and Symptoms

The existing rules for regular (not blood agent or malediction) afflictions are quite bad, so I recommend these rules instead.

    • Affliction: afflictions have penetration and wounding as an innate attack with dice equal to their level, but do not cause wounds. Instead, make a HT roll at a penalty equal to the wound they would cause to resist the affliction. The wound level is also the level of the affliction for other effects based on the affliction level. This makes afflictions somewhat more potent than they are in standard GURPS, a level 1 affliction averages a -3 on a ST 10 character, but regular (non-followup, non-Malediction) afflictions are notably bad in GURPS.

    • Side Effect: as Affliction, but reduce wound level by 2.

    • Symptoms: automatic effect on delivery of a level 3 wound (3x cost), level 4 wound (2x cost), or level 5 wound (1x cost). The pricing is dubious, I would actually make the cheapest form require a level 6 wound.

Area Powers

Area attacks and explosions, realistically, cause more damage to larger objects. For explosions, add the SM*5 of the target, and add -15 at one hex, -25+RM*5 at 2+ hexes; this cannot increase damage over the base damage for the explosive. This actually affects penetration as well as wounding, due to how blast waves interact with objects. For area attacks, damage is normal as long as the area attack is at least equal to the size of the target; add -2 wounding per SM by which the target is larger than the area effect.

The explosion scaling in GURPS is dubious. More realistically, look up the net explosive weight (quantity * REF) on the toughness chart for weight and add 58; thus, 1 lb (toughness -21) does +37 damage, equivalent to a 12d attack (no change), but a ton only does +70 damage, not the +87 it would do per RAW.

Attacking through Barriers

Barriers have an armor rating, like other armor, that functions in the same way against attacks passing through the barrier. GURPS has fairly poor rules for barrier resistance to penetration, so I suggest computing DR based on thickness and material, as follows:

Barriers function in the same way as ablative armor. This toughness figure is for a SM +0 wall (one hex of a typical wall), add SM×2.5 for larger walls. In typical wall materials, the width and depth of holes are similar to one another. Note that, while walls can be fairly easily damaged, it takes 128 level 1 wounds to demolish a wall.

Bleeding and First Aid

I find the standard GURPS rules for bleeding unduly complex; I like these rules instead. Bleeding occurs at four times: 5 minutes, 15 minutes, 30 minutes, and 1 hour after the injury that is bleeding, and produces a wound each time, with a wound level equal to the triggering wound -1. A successful HT roll reduces this wound level by one. Bandaging also reduces bleeding by one (this is cumulative). Successful first aid stops bleeding outright, and may result in healing (per healing and recovery), but cannot reduce wound level by more than one step.

Blowthrough

Realistically, attacks beyond a certain power will simply pass through the target. For piercing and impaling attacks, any attack doing more than 6 wound levels base damage loses half of its remaining wound levels. Realistically this should probably occur after step 6, attacks that pass through armor easily usually pass through flesh pretty easily too, but doing so makes armor piercing munitions unreasonably ineffective -- an assault rifle normally does 27[-1] and averages 6 wound levels without blowthrough, 5 with; using AP ammunition it's 37[-4] and averages 5 wound levels without blowthrough, 3 with -- so either increase the wound level of AP ammunition (realistic enough, the main reason AP rounds are less lethal is because of blowthrough) or apply blowthrough after step 7 instead.

Blunt Trauma

Crushing, cutting, and impaling weapons that hit flexible armor but don't penetrate, or only barely penetrate, can instead be treated as applying blunt trauma. Resolve (base) damage against Toughness, but apply an addition -4 wound level modifier to Crushing, -5 to Cutting, and -6 to Impaling and Piercing.

Collisions

To match the existing GURPS rules, take the toughness of the object, add -5x its speed modifier, and subtract 14. Personally, I find those rules bizarre in several cases. If you don't think homogenous/unliving should affect collision damage, work out the mass score (as per toughness based on mass) of the less massive object, add -5x speed modifier, and subtract 5.

Corrosive Attacks

If you're using rules for armor damage, corrosive attacks have a +4 wound level bonus vs armor. Otherwise, treat armor as having a toughness of (armor value - 30).

Edge Protection

Realistically, cutting weapons usually don't penetrate hard (metal or ceramic) armors. Unless the blade beats the armor rating by 10 or more, only crushing damage gets through: reduce wounding modifier by 1, treat as a crushing attack for purposes of bleeding and first aid, and carrier effects such as poison don't do anything.

Healing and Recovery

Realistically, it takes a very long time for most wounds to heal (three to five weeks for a broken finger, which is a one or two point injury in GURPS), and high tech medicine can't do much except reduce the likelihood of complications. Unless you're planning on a particularly gritty game, this usually isn't a good idea. The standard is that it takes points of healing (including any healing from resting) equal to your current wound level to reduce all your wounds by one level.

Injury Tolerance and Other Advantages

Most forms of injury tolerance are quite obvious, but some require further discussion:

    • Extra Head: with two heads, head injuries blow through at level 6; every doubling reduces this by 1.

    • Injury Tolerance (Damage Reduction): reduces wounds by its level, but not below 1 unless Cosmic. Cosmic may be interpreted as +5 Toughness, to simplify math.

    • Injury Tolerance (Diffuse): reduces piercing and impaling wounds to level 1, and all other wounds to level 2.

    • Injury Tolerance (Homogenous): reduces impaling and piercing wounds by 4 levels, but not below 1.

    • Injury Tolerance (No Vitals): in addition to the normal effect, if you're using the rule of adding 1d6-4 to impaling and piercing wounds to the torso, it doesn't apply.

    • Injury Tolerance (Unliving): reduces impaling and piercing wounds by 2 levels, but not below 1.

    • Supernatural Durability: you cannot be killed by any hit that doesn't do at least a level 11 wound. A level 10 cumulative wound gives a -8 to consciousness checks.

    • Unkillable: you do not roll death checks, and do not die until you reach wound level 11.

Knockback and Knockdown

Normally, knockdown may occur for any major wound, and otherwise isn't much of a factor, while knockback tends to be more cinematic than realistic. However, it can occur realistically with collisions, or with ridiculously tough characters hit by large weapons. For any attack, resolve knockback as (raw penetration) + (knockback modifier for the attack) - (mass). If the result is positive, knockdown occurs; a result of 5+ results in knockback, with a distance of (result/5)-2 on the size chart. Collisions have a knockback modifier of 0, melee weapons have a modifier of -25 (and also lose any armor piercing modifier), other weapons typically don't have knockback worth noting (usually around -65 for rifle bullets, -55 for pistol bullets).

Large and Small Weapons

Small weapons have two effects: they typically aren't as durable and are thus prone to breaking, and they might not be able to reach far enough into the target to really cause damage. Assume a weapon has a maximum penetration roll equal to its Toughness+40; typical weapons have Toughness between SM*5 and SM*5+5 (treat as homogenous objects at their weight). Also, small weapons may simply not be able to reach deeply into targets, the maximum possible basic wound level is 10+SM difference for most weapons, 9+difference for a shortsword or similar small weapon, 7+difference for a large knife, 5+difference for a small knife (these last can create issues even at human size).

Maneuvers and Skills

Various abilities can modify the damage of weapons and other attacks. Usually there's an obvious comparison, and some of these examples are in fact obvious, but included here for completeness:

    • +1 damage per die (brawling, karate, blunt claws, weapon master): +3

    • +2 damage per die (karate, weapon master): +6

    • All Out Attack (strong): counts as a flat +3 bonus.

    • Breaking Blow: will break a brittle object with a level 5+ wound. Using the anti-armor rule, gives a +20[-4] modifier to damage, like any AP(5) effect.

    • Chinks in Armor: grants a +10[-2] modifier, like AP(2).

    • Power Attack: on an attack, grants a +10 modifier, or a +15 modifier when taking skill-30 turns. If you want more granularity, it takes (bonus*2)-skill turns of concentration, minimum 1 (this eliminate the magic numbers at skills 20 and 30).