Friday, October 26, 2018

On Eggshells with Hammers

As I work on my GURPS Vehicles conversion, I get a lot of questions, and this is a common one for anyone who works with GURPS Spaceships. This post will be a deep dive into some basic assumptions behind GURPS and how it derives damage, HP and DR and how those relationships interact on the extreme ends of things like Spaceships and Ultra-Tech.

 The most common complaint leveled against GURPS Spaceships is that spaceships are "eggshells with hammers," that their firepower vastly exceeds their capacity to absorb damage, and fights ultimately come down to who fires first, who is more accurate, and who has better point defense, than who has better armor or who is bigger.  This may be realistic. It's certainly how battles play out in, for example, the Bobiverse, and it's pretty close to how combat plays out in the real world, where a single missile is generally enough to take out a major naval warship like a carrier (and one of the reasons we moved away from battleships and to carriers: better to project firepower far, far away from the ship than to try to absorb a single hit).  But it's not necessarily fun, and it creates some perverse incentives.  Where does it come from, who thought this was a good idea, and what can we do about it?


The Square-Cube Law


The Square-Cube law discusses how creatures scale up: the bigger you are, the more you weigh, and also, the stronger you are, but these factors do not scale with one another.  Your mass is proportional to your volume: if you double in size from, say, 2 feet long to 4 feet long and all other dimensions increase by the same amount (you go from 2 feet wide to 4 feet wide, you go from 2 feet tall to 4 feet tall, etc), then you are 8 times as heavy (2 × 2 × 2 = 8).  Your strength is based on the cross-section of your muscles: a thicker muscle is stronger than a longer muscle, so doubling your size will double the height and width of your muscle (which matters) as well as the length (which doesn't matter), giving you 4× the strength you had before.  This is why spiders and ants, vaunted for their incredible strength, are so mighty when compared, pound for pound, to humans.

What does this have to do with GURPS?  GURPS has a similar problem: it derives some values from the cube, and other values from the square.

Cube Traits

GURPS derives ST and HP from mass, and uses the cube root of your mass to determine your HP (see B558).  So, an ST person is, according to GURPS, about 125 lbs (125 ^ (1/3) * 2 = 10!).  This is one reason the Cult of Stat Normalization frowns on an ST higher than 15, as it's probably unrealistic (ST 15 = ~400 lbs, which is reasonable for an extremely large and well-muscled human, but probably your upper-limit).  Machines have twice as much HP for the same mass (125 lbs = ST 20) and homogenous objects have four times as much HP for the same mass (125 lbs = HP 40).

GURPS also beam weapon damage from the cube root of mass (see Pyramid #3/37 page 12).  This means that it scales with HP. If you look at GURPS Spaceships and compare the HP of a given ship size with the damage a ship of that size can do with a major battery, you see a consistent proportion: an SM +5 ship has ~200 HP and its major battery deals ~150 damage (or 75% of a kill-shot); an SM +15 ship has ~10,000 HP, and its major battery deals about 7,000 damage (or ~70% of a kill-shot).  The values bounce around, sometimes getting as low as 66%, and sometimes has high as 75%, but they always hover around 70% of your HP in one shot.  Similarly, if you track ST damage vs HP, it eventually evens out around 1 point of damage per 2 HP (or 50% of your HP in one attack; this is one reason I don't particularly like the KYOS rules, as they increase this to 1 damage per HP).

GURPS derives DR from the surface area of of the target.  The total weight of your DR is based on your desired DR × the mass of the armor per DR × the surface area of the target.  Even so, if we compare GURPS Spaceships armor to HP, we find that from SM +5 to SM +11, both HP and DR get a 10-fold increase.  We see a similar proportional rise in Force Screen DR.  I'm not sure how realistic this is, but we're discussing GURPS Spaceships currently, so we'll leave that alone.  In GURPS Vehicles, you may find DR follows a square, rather than cube, curve.

This means that if all we're concerned with is armor, beam weapons and HP, then it doesn't matter what size our ship is: everything will be proportional.  If an SM +6 ship with one nanocomposite armor slot takes 3 hits with a major battery to reduce to 0 HP (on average) then the same will be true of an SM +15 vessel (it comes to about 2.5 shots, give or take).

Square Traits

GURPS uses square roots to determine the damage of explosives (see B415)and firearms (I have no real rules for this in 4e, but I doubt the values have changed much since 3e's vehicles).  The net result is that 1 pound of homogeneous stone has about 8 hp, 1 lb of laser deals about 10 damage, and 1 lb gun deals about 4 damage, 1000 lbs of stone has about 80 HP, 1000 lbs of laser deals about 100 damage, and 1000 lb of gun deals about 120 damage, thus our laser and our HP are in near lockstep, but our gun goes from plainly inferior to plainly superior as our mass increases; our damage from explosives starts superior and just gets ridiculous.

It should be noted that the guns and missiles of GURPS Spaceships don't follow this trajectory.  For whatever reason, its guns and missiles get worse as they get bigger.  An SM +5 major gun vs an SM +5 craft with one nanolaminate armor section will take an average of over twice its HP from a single shot, while an SM +14 craft shooting at an SM +14 craft will need an average of ~18 shots to bring it to zero HP, and an SM +15 craft shooting at an SM +15 craft will fail to penetrate the armor.

Multipliers

Even if your traits are in lockstep, like with the example of the laser and homogenous HP, realize that different weapons and HP types enjoy different multipliers: homogenous items have 4 times as much HP as living flesh, and a pulsar or plasma weapon does about twice as much damage, lb for lb, as a laser or a blaster. Armor divisors further degrade armor, but armor tends to get a technological boost of its own (while HP never gets a technological benefit!).  Missiles and bullets tend to get a huge boost from vehicular speed in GURPS Spaceships, never mind the firepower of nuclear or antimatter weapons (REF is a classic example of a multiplier applied to damage)

A feature of ultra-tech combat is that the multipliers on everything except the target's HP has vastly increased.  A TL 12 soldier might wield a disintegrator that does 6dx10 damage while wearing a reality stablized force screen that provides 200 DR, while a TL 9 soldier might have a laser that does 6d(2) damage while wearing armor that provides a DR of 40, but both only have 10 HP: if you luckily roll maximum damage, the TL 9 target takes 16 damage and is still alive, if badly hurt, while the TL 12 soldier will take 160 damage, and be instantly vaporized.

Whiff vs Whittle

I had a long conversation about whiff vs whittle ages ago in regards to the new World of Darkness combat system (the old New World of Darkness as opposed to the new New World of Darkness?  Anyway...).  The problem there was that combat was all about "Whittle." Every attack would hit, and do a little bit of damage (usually 1-2), while the character had more than enough HP to endure quite a few hits (typically 6-10 HP).  This meant that fights were predicable affairs where the person with the largest dice pool always won, but also got slightly hurt.  It evoked images like a little old granny with a pistol who could barely aim, but still constantly hit you, but only for a single point of damage (her inaccuracy reduced the power of the gun to that of a beebee gun.

GURPS broadly has the opposite problem: it is more about whiff than whittle.  In GURPS, the trick is not to do enough damage to your opponent, but to hit them at all. More emphasis is placed on accuracy and defense, and attackers often cannot hit, and when they do, the defender often dodges, and when he doesn't, he usually has enough armor to reduce the damage to nothing.  If he doesn't, then he's dead. If granny with a gun gets a lucky roll. you're dead, but if she doesn't, you're fine, as though the fight never happened.

A lot of the "Eggshells with Hammers" problem stems from the fact that GURPS emphasizes whiff. With things like starfighters, the realism of combat vehicular fragility is fine, even desirable.  The reality of warships being destroyed with a single missile is less desirable. This comes because extremely large vehicles barely gain any HP compared to the firepower being directed at them, but are pretty easy to hit.  The net result is that if you can hit (and you will hit a large ship) and you can penetrate their armor (and you will penetrate their armor), then they're dead.

How to Fix It

There are several approaches you can take to solving these problems, once you understand what's going on.  It's important to understand what you want before you start implementing any of these changes.

Unify your curves

Either use the square or cube curve for everything.

Some people do this by ignoring the missile/gun table in Spaceships entirely and substituting beam-weapon damage for everything. If an SM +5 cannon deals 4dx10, then an SM+5 missile deals 4dx20.  Why would you use beam weapons rather than missiles in such a scenario?  That's up to you to decide.  You can come up with various trade-offs, but nothing really runs out of control.

Alternatively, you can use the Square Root of Destruction (Pyramid #3/34 page 9) to give everything equivalent damage. This doesn't help your HP or DR, though, unless you choose to rewrite how HP is derived, especially if you bring it back to a more 3e model.

The problem with this approach is that it makes size irrelevant. All things being equal, the bigger ship will win and armament is more a matter of flavor.  It also won't necessarily stop your eggshell-vs-hammer problem, depending on how you handle your multipliers.

For more on unifying curves, I highly recommend David Pulver's "Extreme Damage" in Pyramid #3/34.

Manage your Multipliers

Even if all your damage is proportional so you aren't reaching a point in combat where all shots vaporize your targets based on sheer size alone, the technological multipliers can easily get out of hand.  

One thing you can do is eliminate them entirely. I can't find the reference, but Pulver argues that you should consider reducing damage of ultra-tech firearms and replacing their extreme damage with extreme armor divisors, which is largely an approach he followed in GURPS Ultra-Tech. To use our disintegrator exmaple above, if our disintegrator did 6d(20) and our force screen was DR 20 (but with loads of hardening), the next result as far as disintegrator and force screen are concerned remain unchanged, but the result of an extreme roll remains... 16 damage to the target.  A similar approach means that ships can become much more survivable.

Alternately, instead of bringing weapons down to the level of HP, you can improve HP to scale with damage. Richard Burton and Timothy Ponce recommend giving large spaceships Injury Tolerance in  Pyramid #3/94's "So you wanna build a spaceship."  To go back to our disintegrator example, if our target has 100 HP, then hitting him with 160 damage is the equivalent of hitting a target with 10 HP with 16 damage.

This is most pertinent in GURPS Spaceships when it comes to extreme explosives or extreme projectile speeds.  If you want spaceships that stand up to such punishment, realistically, they would have some sort of "cosmic" or "indestructible" defenses, because realistically one does not build spaceships that can stand up to even small nukes unless we're building on a titanic scale.

Diminish Whiff and increase Whittle

If you want ships to take longer to kill, make them easier to hit, and easier to damage (less DR), but require more damage to defeat them.  This means every attack has some meaningful impact, and it's no longer and all-or-nothing affair.  

GURPS already has a few tools to do this.  Injury Tolerance: Damage Reduction, already mentioned, definitely does this.  If you're attacking someone with a disintegrator for 160 damage, and they have 100 DR and they have the equivalent to 600 HP (IT:DR (6)), then it'll take an average of 10 attacks to defeat them.  Ablative DR also fundamentally acts as increased HP: you must first defeat the force screen and then defeat the target.  Semi-Ablative DR acts like even tougher HP which is an interesting compromise between the two.  By the rules, Force Screens are semi-ablative, but personally, I think semi-ablative armor and ablative force screens make more sense.

Some combination of the above, with a justification based on "Super-heavy structures," or "Semi-ablative super-armor" or "Total compartementalization" can give you super-tough, but not unbeatable vehicles.

There is a danger here, though.  Just like too much "Whiff" can make for a boring game, so can too much "whittle."  A good combat system allows for a change in circumstances once a decision cycle (typically a turn, but longer than about 5 minutes of real time starts to get boring).  "My numbers got lower" is not a change of circumstances, it's a measure of time ("I'm taking 10 damage a turn, and I have 10,000 HP, so I'll be dead in 1000 turns...").  Make sure you allow for some tactical struggle, some way of getting around your opponent's defenses to leave a bigger mark or to damage some fundamental structure that forces your opponent to improvise, or ways of sacrificing some HP now for some advantage later.

Exploit the Tension between conflicting Systems

Having different proportionality curves is not necessarily a problem, especially if you manage your multipliers.  For example, if you missiles and beam weapons, the largest ships (your "Star Destroyers") will favor beam weapons out of the box, because those scale better than projectile weapons (at least according to GURPS Spaceships), which are "flatter" in their curve.  However, a small ship (like an X-wing) deals a disproportionately heavy blow with a missile: an SM +5 ship with a missile deals 6d×100; ignoring armor divisors or other multipliers, you would need 1 SM +13 Diamondoid armor system to take a hit like that, which means a TL 11 SM +5 fighter is a potential threat to an SM +12 or smaller ship.

This can be useful depending on what sort of genre you're trying to create.  In the real world, we have different sorts of military vehicles precisely because we want to exploit different niches.  Fighters vs battleships or helicopters vs tanks happens because of the tensions that exist between ground, sea and air and the assumptions necessary for each.  Sometimes, you want a glass cannon (a typical fighter) as long as you have the capacity to have tanky vehicles (a dreadnought).  If you want to make this sort of discrepancy even worse, use the "armor and volume" rules from Pyramid #3/34, page 4. This rule will let larger, heavier vehicles compound their natural toughness advantage, making larger and larger vehicles tougher but less dangerous, while smaller vehicles can be proportionately more dangerous, but tend to get less advantage out of armor and may well eschew it entirely.

Using the Toolbox

Ultimately, fixing the combat in your space game is a tricky exercise in manipulating values, and unfortunately, there's no way around that.  Psi-Wars currently exploits tension while minimizing multipliers (I use IT:DR on larger vehicles and vehicles tends to give larger vehicles a greater advantage when it comes to armor, while giving smaller vehicles high-impact missiles).  But there are other possible solutions, depending on what you want.
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