GURPS Logarithmic ST and Powers

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.

What Is it and why should we care?

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.

ST vs Old ST

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*10^ST/10, and Old ST = 10^½+ST/20; every +10 points multiplies BL by 10, every +20 points multiplies Old ST.

Encumbrance Levels

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)

ST Damage

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

Damage remains on the same scale it always was

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:

• 1. 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.

  2. 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.

  3. 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.

Damage is placed on a Logarithmic scale as well

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).

Damage is placed on a log scale as well

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:

• 1. 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:

• 1. 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.

  2. 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.

  3. 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).