Forward: some content on this page is quite old, but as of Pyramid #3/83: Alternate GURPS IV logarithmic ST has been introduced into the 'standard' for GURPS, so I decided to update this. It appears that they came up with the same overall scaling that I did.
Logarithmic ST is a rescaling of the GURPS ST attribute to place it on an exponential scale, where +X ST has the effect of multiplying lifting ability, damage, and so on, by some constant value, rather than the current formula where it adds a fixed amount. In particular, the system uses a scaling where 10 points of ST increases lifting ability by a factor of 10. There are a number of purposes for this, but the basic reason is the same reason many other game systems have used logarithmic systems: it lets you fit a very wide range of power levels onto a simple chart, without dealing with huge numbers or awkward fractions, and it lets you compare ST values by subtraction rather than division. In vanilla GURPS, an ant (with the ability to lift 0.0002 lb) has a computed ST of 0.03; a giant monster with the ability to lift 10,000T has a computed ST of 3,162. Under logarithmic ST that becomes ST -40 and ST 60. In addition, this makes such things as a contest of ST relatively easy to manage: a critter that's twice as strong will always have a +3 advantage in such a contest, whereas in standard GURPS, even over the human range of 7-20, the bonus can range anywhere from +3 to +6.
The new ST chart is as follows. On this chart, ST is ST by this rule, Old ST is the ST you would have in GURPS 4th edition, and BL is the same as it is in GURPS 4th edition. For people who like equations, the equation is that BL = 0.2*10ST/10, and Old ST = 10½+ST/20; every +10 points multiplies BL by 10, every +20 points multiplies Old ST.
While it's possible to use multiples of BL, as in traditional GURPS, doing so misses the value of logarithmic ST. It's far easier to say:
No Encumbrance: carry up to (mass listed for ST)
Light Encumbrance: carry up to (mass listed for ST+3)
Medium Encumbrance: carry up to (mass listed for ST+5)
Heavy Encumbrance: carry up to (mass listed for ST+8)
Extra-Heavy Encumbrance: carry up to (mass listed for ST+10)
If you're putting lifting ability on a logarithmic scale, it's natural to want to do the same thing with damage. Unfortunately this runs into a big problem: while logarithms make multiplication and division easy, they make addition and subtraction hard, and any treatment of armor is basically a problem of subtraction. Let's say our new scale is that New DR and New Damage are equal to 10 x log10( Old DR/Damage ). Thus, a 1,000 point hit Damage 30, and DR 200 becomes DR 23.
If we expect it to behave anything old GURPS, after going through a layer of DR 200 armor, a 1,000 point hit has DR 800 of penetration left, which converts to Damage 29. So somehow, DR 23 became DR 1.
There are three basic ways around this: you can decide you don't care, you can convert to a linear value before applying DR, or you can have a table of DR vs Penetration interactions.
The first option is pretty easy. Say, just use the existing ST damage table. Unfortunately, it has the problem that, say, a battleship with under old rules has armor enough to withstand ST 500d attacks (equivalent to ST 64, or about DR 25) and a 1,000d attack (equivalent to ST 70, or 8d damage), if it first hits Ensign Expendable (cover DR 10) is no longer able to penetrate another battleship.
The second option requires table lookup, but at least it can be the same table as before. There's two choices: lookup in character creation, or lookup in play. For lookup in character creation:
Damage: look up Old ST on the table above, and divide by 10. That's your Swing damage dice.
Hit Points: look up Old ST on the table above. That's your hit points.
For lookup in play we instead have:
Damage: make a ST roll and look up your margin of success on the table above. That's your Swing damage.
Hit Points: look up Old ST on the table above. That's your hit points. To determine your threshold for shock and stunning, modify ST as follows:
Shock (-1): -20 to ST
Shock (-2): -15 to ST (should be -14, but -15 is a pretty number)
Shock (-3): -10 to ST
Major Wound: -5 to ST (should be -6, but again, pretty numbers)
The drawback of this method is that we still wind up needing to do multiplication and division for armor divisors and wounding modifiers.
The third option requires a table, and is thus ugly in its own way. Give each attack a penetration rating, and for each barrier you have a lookup table that indicates how it modifies incoming attacks, based on their penetration rating. If we're using the Old ST method, DR 100 would have a table that looks a bit like this:
Once all layers of armor have been applied, take the remaining penetration, add a wounding modifier, and compare to the target's ST to figure damage. This lets us cut down on multiplication quite a bit -- AP(10) is +20 to penetration, -20 to wounding -- at a cost of fairly significant table lookup requirements.
For example, make a ST roll, and look up your margin of success on the ST table above. Your damage is the corresponding Old ST. Likewise, look up your ST on the table above and that's your
This means that 1 point of damage in classic GURPS is equal to 1 point of damage in Logarithmic GURPS. This has the immediate benefit that you can simply use gear from all your existing GURPS products, with no changes. It has three immediate drawbacks:
You need to come up with a new mapping from ST to Damage; someone who can lift a hundred tons should probably punch for more than 5d+2 and have more than 50 hp.
Damage suffers from the same scaling problems as lifting; GURPS can't handle fights on the small scale at all due to granularity problems, and has playability problems at the high end of ST.
GURPS damage has a number of anomalous effects anyway, so if we're redesigning the system, maybe we should try and fix those things as well.
None of these problems are impossible to deal with. If you choose to do so, the simplest solution is something like the following:
Hit Points: equal to Old ST
Damage: for ST <23, use 4e values. For ST 23+, Swing is Old ST/10, Thrust is Old ST/20 (you can use the ST 23+ formula for lower ST values, but it winds up with resolution issues).
You can fix some of the resolution issues with table lookup:
Alternate Damage: make a ST roll, at -6 for Thrust, and look up your margin of success on the ST table above. Your damage is equal to the resulting Old ST -- e.g. if your ST is 10 and you Swing and roll a 17 (fail by 7), you'd do 1 damage; if you rolled a 4 (success by 6) you'd do 6. If between two values, use the lesser; thus, something with a ST of 7 or lower can actually do zero damage with an attack.
In this assumption, damage is placed on a logarithmic scale, just like lifting.
This is an intuitive option, and a number of systems, such as Champions, have done this: change the meaning of damage points. Say, use the range/speed chart; damage stays the same up to 2d, and beyond that each step on the range/speed chart acts like +1d damage. A 10d attack becomes 6d, a 100d attack 12d, a 1,000d attack 18d.
This... does not actually work well. Consider armor that will stop a 6d attack (DR 35 in classic GURPS; DR 21 here). Three sheets of that (DR 105 in classic GURPS) will stop an 18d attack (3,500 damage).
If we put damage on a logarithmic scale, this has the obvious benefit of scaling quite cleanly whether you're talking about ant vs ant or kaiju vs kaiji. Unfortunately, it runs into one really difficult problem: armor. Let's say we convert damage via the ST to Old ST table given above, so 1,000 damage (Old) becomes 50 damage (New). Our target is a tank with Old DR 500, which is presumably New DR 47.
If we subtract one from the other, the result is 3 points of damage -- so the armor which stopped half of the attack under the old system subtracts 94% under the new system. Worse, let's put Ensign Expendable (cover DR 10) in front of the attack. Now our giant attack doesn't do any damage at all; it would take an attack doing 6,300 damage to scratch the paint on our DR 500 target. We also run into an opposite problem: lightly armored targets get chewed up with remarkable speed. Even in vanilla GURPS 4e, sinking a container ship (something like 1k hp, DR 10) with an assault rifle isn't all that hard; when you're instead doing 15 damage vs DR 10, and the target has 50 HP, it becomes easy to do by accident.
There are a couple of ways around this, but they have an annoying flaw that they tend to require table lookup. For starters, you can simply use the procedure mentioned above for Alternate Damage -- convert damage to a linear value (as per Alternate Damage above), subtract any barriers that are in the way, and then convert back. This works, but eliminates much the the value of log damage to start with.
Another alternative, somewhat more complex, is to give attacks two values, penetration and wounding; targets have corresponding armor and toughness. To resolve an attack, you would go through the following procedure:
For each barrier, compare penetration and armor, and find the result on a chart. That chart will give a modifier to further attacks. A chart that works out equivalent to the Alternate Damage system above would be something like:
There are a couple of ways around this, but they have an annoying flaw: attacks require table lookup. Simply assign each attack a damage and a penetration.
At Old DR 100 (New DR 30), it would take 20 damage. At Old DR 10 (New DR 10), it would take 40 damage -- twice as much. By comparison, in our original GURPS
Now, with DR 100 it would take
This means that we change the meaning of damage; 1 point of damage is no longer a fixed quantity. This has considerable benefits for scaling (if done properly, battles between ants and battles between kaiju work equally well), but has historically always caused problems for games. Consider a model where we convert damage via the ST to Old ST rule above; thus, a tank gun doing 6d*25 (average 525) damage winds up doing 44 damage.
Barriers: let's say we convert damage via the ST to Old ST rule above, so a tank gun doing 6d*25 (average 525) damage now does 45 damage, and the target tank's DR 1,680 becomes DR 53. FIrst o
Hit Points: equal to Old ST.
Damage: Swing is 1d per 10 Old ST. Thrust is 1d per 20 Old ST.
Some of the options are:
Use classic GURPS scaling, possibly without the anomaly with how swing progression changes for ST 26+. This is decently balanced within the human-normal ST range, but it breaks down pretty badly for superhuman ST scores -- they do far too little damage, and (assuming HP are based on ST) can also take far too little.
Use classic GURPS scaling, but based on Old ST. This means superhuman ST can do and take superhuman damage, but it runs into some known anomalies with how ST damage works in GURPS, and also has balance issues unless you dramatically up the cost of ST.
Damage and HP are linear in Old ST.
There are several ways of doing ST damage, but the simplest one is probably this: for any ST-based weapon, make a (modified) ST roll to use it. For every point by which you succeed, increase basic damage by 10%; for every point by which you fail, reduce it by 10%. Heavier weapons require more difficult ST rolls, but have higher basic damage. Note this as something like ST+n(xx cr).
To determine the statistics for an improvised weapon, look up its weight on the table above. The corresponding ST is the penalty to your ST roll to use the weapon, the corresponding HP is the basic damage (crushing). Thus, a 2 lb weapon requires a ST+0 roll and has a base damage of 3. If you use two hands, you get +3 to your ST roll. Anything designed as a weapon is treated as a higher ST penalty for damage purposes only -- typically +0 if the base damage type is Impaling, +2 if Cutting, +4 if Crushing, with an additional +2 for an Unbalanced weapon. Thus, a normal 3 lb object would be ST-2(4 cr), while a 3 lb sword would be ST-2(4 Imp) or ST-2(5 Cut).
-- e.g. a sword is ST+2, Cut, which means a 2 lb sword (ST+0) has its damage computed for a ST of 2 (=4), but still rolls against ST+0, not ST-2. Particular weapons:
Axe: +4 to ST, Cutting, Unbalanced. Mace: +6 to ST, Crushing, Unbalanced.
Boxing, Brawling, Karate, or DX: ST modifier = SM x -5. Punch: -5 to ST. Kick: -2 to skill. Consider +1/die as being worth +2 to your ST roll.
Broadsword, Knife, or Shortsword: +2 to ST, Cutting, or +0 to ST, Impaling.
Flail: +4 to ST, Crushing, Unbalanced, -2 Enemy Parry, -4 Enemy Block.
Knife: +2 to ST, Cutting, or +0 to ST, Impaling. A small knife is ST+10(1 Imp), a large is ST+4(2 Imp).
For a basic melee weapon, the difficulty of the ST roll is equal to -1 x (ST required to lift as 1xBL) and the basic damage is (HP for that ST) -- i.e. a 2 lb weapon requires rolling ST+0 and has basic damage 3, a 3 lb weapon requires rolling ST-2 and has basic damage 4, a 5 lb weapon requires rolling ST-4 and has basic damage 5. This is the damage for improvised weapons; things actually designed as weapons will do a bit better, as follows:
Axe/Mace: treat axes as 2 ST heavier for damage purposes; treat maces as 4 ST heavier.
Brawling, Boxing, Karate, or DX: typical effective weapon weight is
Unbalanced Weapon: treat unbalanced weapons as 2 ST heavier than they actually are for damage purposes.
The entire way ST is
The point cost for ST is (LV-10)*10, and abilities that have or modify ST are also based on the LV or change in LV. Thus, Telekinesis (ST -20, LV 1) costs 5 points. Due to changes in load and damage scaling, lifting ST is increased to 6 points per level (which is more expensive for BL below 160 lb, cheaper above), striking ST is reduced to 2 points per level (which remains 20 points per d6). Extremely high ST characters (ST 25+, or less if other scaled powers are wanted) should take Power Scaling:
Adds +1 per level to ST; if multiple advantages affect ST, apply this one last. Also adds +1 per level to any other abilities with a ST score. For these purposes, any ability that has DR or HP has a ST score (for that purpose) equal to the ST for that LV, any ability that affects a specific mass has a ST score equal to the ST required to affect that mass, any ability that does damage has a ST score equal to the ST required to do that much damage, and the HP, DR, Mass, or Damage should be recomputed after applying Enhanced ST. A number of limitations may be applied:
Not for Damage (-25%): does not scale damage.
Not for Lifting (-25%): does not scale mass affected.
Not for Toughness (-25%): does not scale HP or DR.
Only for Damage (-50%): only scales damage.
Only for Toughness (-50%): only scales HP and DR. You may take Accessibility limitations, as per DR.
Only for Lifting (-50%): only scales mass affected (and ST rolls).
Powers Only (var): take a Temporary Disadvantage (reduced ST) so your ST does not change.
Size (-10%): your Mass is at least 19+Rank, your SM is at least Rank/5. Apply mass, damage, and toughness scaling to your gear, and multiply cost by the ratio of mass. Size may also be taken as a limitation on ST, if desired.
Thus, if you buy a 5d innate attack and have enhanced ST 5, you determine that 5d is a ST of 31, increase ST to 36, and determine that real damage is 7d+2. Note that if you take the Size limitation on Enhanced ST, you can't take it on your normal ST. You may take Enhanced ST even if your actual ST is less than 20, though this is only worth doing if you have other abilities that would be enhanced (usually, enhanced ST will break even when you have spent more than 50-100 points in affected abilities).
If you want the exact equivalent of existing 4e ST stats, they can be done as follows:
The cost difference, while non-zero, is probably small enough that it can be ignored.
While it is possible to use the table in Basic for HP, there is another way. First, compute the object's Mass. That is just the ST corresponding to the item's Mass on the table above. If the object is Living, subtract 8 from Mass to determine effective ST. If the object is Unliving, add 1; if the object is Homogeneous, add 10. In all cases, the object's HP are equal to the HP for the computed effective ST. In most cases where an object is resisting ST with its weight, use Mass-10 in place of ST. Note that this computes hit points, not ST. For a creature following the ST to mass curve in Basic, lifting ST is mass*2/3 - 2, striking ST and toughness are both mass-8. For a realistic creature, lifting ST is roughly Mass * 0.8 - 4, striking ST (and toughness) are roughly Mass * 1.1 - 10. For a cinematic giant monster, lifting ST is Mass - 8, striking ST (and toughness) are Mass * 1.5 - 17.
An object's mass can be computed from SM; it's roughly SM*5 + 20 for living creatures. Add up to 15 for particularly compact shapes (a 2 yard sphere of flesh would be around 3 tons). Add 5-8 for stone, 9 for iron, 13 for gold.
The invention of the Mass stat allows improvements in the collisions rules; realistically, object HP should have no direct relevance to collision damage, though relative hardness should make a difference as to which object takes the damage. The recommended system for collisions is very simple: find ST for LV equal to speed (e.g. 10 yards per second is ST 10). Add either the larger mass -10, or the smaller mass, whichever is less (for collisions with an immovable object, use smaller mass). This is the effective ST of the collision; collision damage is normal for that effective ST (in the simple case of a velocity of 10-18, one object much smaller than the other, damage = mass+speed). Thus, a Mass 18 unliving object (20 hp) at move 10 (ST 10), hitting a wall, collides with an effective ST of 28 (4d), which is the same as the current rules. Now, modify based on shape: a dense, compact object (such as a rock) has a normal armor divisor, an object that is dense or compact but not both has an armor divisor of 1/2, an object that is neither dense nor compact (e.g. a human) has an armor divisor of 1/3. Finally, in any collision, the harder object takes less damage: add the difference in DR to the effective DR of the higher DR object.
When throwing an object, start by figuring out the damage. The damage ST of a thrown object is (ST) if the object has a mass of at least (your mass)-15 (mass 4 for an average person), and is reduced by 1 for every 3 points or fraction the object's mass is lower. To determine speed, take (damage ST) - (Mass) and look up LV for that number. To determine max range, double that number and subtract 10. Thus, a ST 15 person throwing a baseball (mass -8) has a damage ST of (ST-4) or 11, and will throw the baseball at a speed of 20 with a max range of 40. Note that an object that's large compared to the target will have to use the collisions rule above, rather than computing ST directly.
A difficulty with standard GURPS is that the system loses granularity at the low end; there isn't really much to distinguish attacking a SM -7 mouse from attacking a SM -18 ant, and there isn't really any option for moderate injuries. There is a very simple fix for this:
Negative Toughness: 0 point feature
When building your character, you gain Enhanced ST (Toughness Only) equal to your level. When you are hit by an attack, add your Negative Toughness to the ST of the attack.
Thus, if we have a small rat (mass -6, lifting ST -9, damage ST -16) vs a large rat (mass -4, lifting ST -7, damage ST -14) we might give them both NT 30 and resolve a fight as 1d+1/14 hp vs 1d+2/16 hp, which is far more meaningful than base scaling, where both would be doing 1d-6 with 1 hp. In general, any creature with a ST below about 5 should probably use negative toughness.
An interesting feature of logarithmic systems is that you can interpret power advantages as simply adding or subtracting ST; by the scaling we have, a 10% enhancement is about as good as +1 ST. This offers an interesting and reasonably balanced way of increasing flexibility:
Tradeoff Technique: Add Advantage (average, default -5, cannot exceed base skill)
Adds an advantage to a ST-modified power. In addition to the difficulty modifier to the skill check, each 10% gives -1 ST. Multiple tradeoff techniques can be stacked, all modifiers are cumulative; thus if you have tradeoff technique (AP/2, -5 to ST) at Skill-3, and tradeoff technique (increased range x2, -1 to ST) at Skill -1, you combine them for a total of -6 to ST, -4 to skill. If applied to a power with no associated roll, apply the technique modifier to the ST of the attack, so Hardened would be a total of -7 ST instead of -5 skill, -2 ST, and could be learned up to -2 ST.
Tradeoff Technique: Add Limitation (average, default -5, cannot exceed base skill)
Adds a limitation to a ST-modified power. In addition to the difficulty modifier to the skill check, add +1 ST per full 10% limitation; thus the technique Melee Reach C has a base difficulty of -3 and grants +3 ST. If applied to a power with no associated roll, apply the technique modifier to the ST of the attack, so Only Vs Fire would be a total of -1 ST instead of -5 skill, +4 ST, and could be learned up to +4 ST.
Tradeoff Technique: Change Damage Type (average, default -5, cannot exceed base skill)
Alters the damage type of an attack. Certain types modify ST, as follows: Corr (-9), Cut (-3), Fat (-9), Imp (-6), Pi- (+6), Pi+ (-3), Pi++ (-6), Tox (-2). Subtract the ST modifier of the original type, add the ST modifier of the new type.
Tradeoff Technique: Weapon (average, default -3, cannot exceed base skill)
As another tradeoff technique, but you can only perform the technique with a weapon or object that plausibly grants the technique -- i.e. you can only change damage type to impaling with a stabbing weapon, you can only change damage type to corrosive if you can get a bottle of acid, and so on. You still suffer all normal ST modifiers.
Tradeoff techniques normally only work for powers such as Innate Attack, but may be used for equipment at the GMs discretion. Tradeoffs on advantages requires the same action as is required to activate the power, so generally a turn of concentration; reduced time is rarely an appropriate technique. Tradeoffs specifically cannot be used to remove power limitations.
As an interesting trick, it is possible to buy 'super-punch' as a crushing innate attack, and then pick up the ability to use weapons, etc, as tradeoff techniques, most of which would be weapon techniques. The common tradeoff techniques would be:
Close Attack: melee C, 1, ST +2.
Weapon, Cutting: change damage type Cut, ST -3
Weapon, Large: area attack, ST -5
Weapon, Long: melee reach 1-4, ready action to change reach, ST +2.
Weapon, Stabbing: change damage type Imp, ST -6
Weapon, Thrown, Heavy: range 10/20, ST +1
Weapon, Thrown, Light: range 50/100, ST -1
Most of the time, you would be using Close Attack to do crushing damage. If you bought a 10d attack, you would do 12d with a punch (close attack), 9d+1 with a sword (close attack, cutting), 7d+2 with a spear (long attack, stabbing), 7d+2 with a car (large, long attack), 7d-1 with a thrown car (heavy thrown, large).
In many games, it is useful to limit the total power level of PCs. A typical setup would be along the lines of:
Damage Scale: max 20 - Skill. +30 if D-scale, +60 if C-scale, +90 if M-scale.
Toughness Scale: max 25 - Dodge - Highest Active Defense. +30 if D-scale, +60 if C-scale, +90 if M-scale.
This usefully allows choosing between power and skill -- 20 ST/20 skill (22 hp, 2d damage) vs 30 ST/10 skill (46 hp, 4d+2) is actually a sensible enough fight.