This is the start of a multi-blog series on the basic and secondary attributes in GURPS. If you're new to the system, what are some things you'll want to think about? GURPS is point buy, so it's not the dice but you that decides what level your stats are. Here are some things you'll want to know about Strength and Hit Points.
Also see posts on Gaming Ballistic, Ravens 'n' Pennies, and RPG Snob on this same subject, and the GURPS 101 page.
How Much Strength Do I Need?
As much as you can afford. No one ever complained they were too strong. But you rarely have unlimited points, so you need to make some decisions.
If your character depends on muscle for damage (melee weapons, thrown weapons), there are breakpoints you need to know.
Thrust Damage: ST adds one point of thrust damage for every two points of ST, on the odd numbers. (So ST 11 and 12 do 1d-1 thrust, but 13 and 14 do 1d). Since adding more dice to your rolls helps in a lot of ways (see below), three breakpoints to keep in mind are:
ST 13 (1d thrust) - not the first time you do 1 die, but the first time you do 1d without penalties.
ST 19 (2d-1 thrust) - the first time you do 2 dice.
ST 27 (3d-1 thrust) - the first time you do 3 dice.
Thrust damage doesn't go up very quickly, so people who depend on thrust (people with stabby weapons, unarmed strikers, and biters) tend to want to look at maximizing their bonuses, not their raw ST score.
Swing Damage: ST adds one point of swing damage for every point of ST, so any ST score makes you do more damage with swinging attacks. Still, the "more dice" points are worth knowing.
ST 13 (2d-1 swing) - the first time doing 2 dice. This makes ST 13 a really sweet spot for ST for a cut-and-thrust low tech warrior.
ST 17 (3d-1 swing) - the first time you do 3 dice.
ST 21 (4d-1 swing) - the first time you do 4 dice.
These breakpoints for more dice are important because there are advantages (like Weapon Master), skills (like Karate or Brawling), maneuvers (All-Out Attack Strong), and techniques (Jump Kick) that add damage per die. So +1 per die adds +1 to a ST 13 thrusting attack, but adds +2 to a ST 19 thrusting attack.
An example of this big shift came up in my DF game recently - a character with net ST 16 (2d+2 swing), a swing+4 weapon, and Weapon Master (+2 per die) went up to ST 17 (3d-1). That is a 1 point shift in average damage, but the dice shift meant that he went from 2d+10 to 3d+9 (+4 for the weapon, +6 for Weapon Master). That's 12-22 (av. 17) to 12-27 (av. 20.5). Now, there are optional rules for converting bonuses to additional dice (p. B269) that would take this character's damage from 2d+10 to 4d+3, and 3d+9 to 5d+2, but either way, the jump in +1 ST made for +3 in additional Weapon Master bonuses which is really where it matters. Plus, All Out Attack (Strong) would do +3 damage (+1 per die) not +2 (the flat bonus for AOA Strong).
Weapons ST - Weapons have a ST stat, usually (but unofficially) called Min ST. Basically, you need that much ST to use the weapon without penalties. Weapons are also limited in damage to 3x their ST stat, which is why stronger folks need sturdier weapons.
For high-tech weapons, ST is rarely a determining factor . . . but the more ST you have the more powerful firearms you can use, and the further you can chuck a grenade. At a high enough ST you can start using heavy weaponry like light weapons (MGs fired off the tripod or bipod, one-handing assault rifles like Arnie in The Terminator), etc. And there is always a need to carry more ammo . . .
Basic Lift - This is a figured characteristic of ST. The next thing you want to be aware of for ST is the often-overlooked BL. This is another spot where every point of ST really matters. Each bit of ST you add makes you able to lift more, which means more weight carried at less encumbrance.
In my DF game, even a heavy fighter like Vryce is at Light encumbrance (max 2xBL) because of his high BL. He's got a bit more than 100 pounds of weapons and armor and can still move freely around the battlefield and not get too fatigued after a fight.
BL also makes a difference in some strong guy moves like Piledrivers, and makes a difference in how far you can throw things, too. A high BL character is a great asset to have around. Check the chart on p. 17 and you can see how a little more ST can make a loadout that much easier to deal with. And for rapid-fire modern weaponry, you need to expend a lot of weight on ammo.
What about Striking ST and Lifting ST? You can buy up Striking ST if you really just want to improve damage (it's 5/level), and Lifting ST (3/level) if you only care about picking stuff up (or grappling, with Technical Grappling). If one part of ST is of critical important to you, those are worth considering. These tend to be limited as well, but they give you yet another option for narrowing in on the characteristics you want for your character.
How Many HP Do You Need?
First, just note that HP = ST initially.
Crippling Injuries: Crippling in GURPS for limbs is more than HP/2, and more than HP/3 for extremities. That means HP 12 takes 7 damage to cripple a limb and 5 damage for a hand, HP 15 takes 8 and 6, and so on. Eyes are more than HP/10, which means 2 points up to HP 19 and 3 at HP 20.
Maxima: - The limit on extra HP for non-supers/non-nonhumans is +30% over your ST, although some perks in later books let you bring it up to +50% over ST (such as Special Exercises), or even +100% (Mountain of Meat, which is totally unrealistic but fun). One thing about GURPS is that you can suffer a large amount of damage in a single blow. High hit points can mitigate the effects a bit but even a nearly-supernatural level of HP won't matter in the face of a rifle bullet to the vitals. So HP aren't a panacea.
But they make it hard to die, and give you a wider margin of failure when you do blow a defense. You die at -5 x HP no matter what, so even a single extra HP gives you 6 more damage you can suffer before automatic death.
Healing: - If you have a lot of HP, you heal faster (to scale to healing effect to you.) At 20-29, you heal twice as much. From 30-30, triple, and so on. See High HP and Healing, p. B424 for more.
Slams: - HP are a proxy for mass in GURPS for rules where mass matters. Slams are collisions, so your HP (multiplied by your current speed) are the factor that determines how much damage you do on a slam or a charge. You can also easily get damaged slamming folks, so you really need to increase your HP if your mode of attack is putting people down. The more HP you have the better for you, offensively and defensively. This is why sumo wrestlers qualify for extra HP in GURPS Martial Arts!
The more HP you can get, the merrier. And in a combat-heavy low-tech game, they are critically important. You can probably get away with just staying with what you get from ST, but if you're going to fight a lot give getting some extra a look.
So, does this mean I should only buy odd-numbered ST scores, hunt for breakpoints, and otherwise min-max my ST and HP score? If that makes you happy, do it. But it's not necessary (or, in my experience, especially common). It's a good set of things to know when you're making a decision where to drop some points, or when you're thinking about the edge cases. ST and its related characteristics are too useful to shave down just to save points and stay at the breakpoints. I look at those breakpoints as things to strive towards ("Get at least ST 13 if you can!") not the only scores worth buying ("ST 14 is useless, stay at ST 13.")