Thanks to quarantine, I've had plenty of time to indulge in a project that has interested me for some time: a grand unified theory of RPG design. Many years ago, I noticed two things: that GURPS proposed an easy-to-calculate average of 10 hit points (STR, in GURPS terms) while presuming an also-simple average of 1d6 damage per hit for swords (basically your standard weapon). I also noticed that, if you looked through Champions at premade villains and heroes who were in the players' power range, the average superbeing could hit themselves 3 times before falling unconscious--or 4 times, in the case of bricks and bruisers. It was remarkably consistent. So I got it in my head that, in general, players in most presumably-balanced games should expect to hit themselves 3 times if they were normal, or 4 times if they were tanks. (I used hitting themselves as the rule, because lightweight thieves tend to do less damage, but also to take less damage; fighters do more and can take more; and yet the ratio stays much the same, which--ahem--leads to simpler numbers.) No one as far as I know has ever decreed that this was the ideal way to handle PC health status; it just seems to have emerged. I had a theory as to why this might be--three hits gives you a standard narrative rule-of-three beginning, middle, and end--but I only had the two data points. What would happen if I poked other games further? It also raised other questions. What is the ideal (or at any rate most widely accepted) chance to hit an average opponent? What is the chance for a skill to succeed? How many skills are available in a healthy skill-based game, and what percentage of them is a player likely to possess? And so on. So today I actually went down a long list of games, and--by oversimplifying a lot and using the hit-yourself principle--I figured out the following rule of thumb: IN MOST GAMES, A PLAYER CHARACTER CAN SUCCESSFULLY HIT THEMSELVES 3 TIMES BEFORE DYING, GOING UNCONSCIOUS, OR DEVELOPING SERIOUS TROUBLE. A TANK TYPE OF CHARACTER CAN OFTEN HIT THEMSELVES 4 TIMES.
I know it's a little suspicious that I arrived at the exact conclusion I set out suspecting, but doggone it, I've included the math in my (admittedly sketchy) notes below. (And I realize my principles are so vague as to be ludicrous. For example, if a game had different character classes, I simply averaged them all to find the mean hit point value, on the probably-absurd assumption that all classes were equally likely to appear in any given game.) To put it another way, the average PC's damage roll is equal to 25-33% of their hit points. The implications of this for D&D are kind of interesting. It suggests that, if the average player does 7 damage (derived from assuming a +2 on average 1d8 martial weapons and 1d10 cantrips like eldritch blast), then the average player ought to also have 20 hit points. (21, actually, but 20's a nice round number.) Which roughly means that the ideal balance between offense and defense comes at third level (assuming a d8 hit die). Everything before that is harsher than is optimal, and everything after it is too lenient (and starts to take forever).
Oddly, though, the creatures that do 7 damage to the players (per DMG p. 274) are CR 1/2 and have 50-70 hit points. That...seems like a helluva lot of hit points for such a low CR. But then, I'm still a 3e baby at heart, and I'm not accustomed to all these high numbers. Next up, I'll be looking at the odds of success, for both to-hit rolls and skill checks. Later! *********************
Here's my work. Every game system I tested is followed by the % of the average damage to the player's hit points, endurance, or other survival stat. As you will see, with the exception of a few outliers (with Fantasy Age being exceptionally lenient and Fragged Empire especially harsh), my initial back-of-envelope suspicion seems to be confirmed. Note that even when an average hit goes as high as 40%, that still means a player takes three hits before going out. They just go down a little harder on that third hit.
BARBARIANS OF LEMURIA
39% Average HP: 10-13 Average damage: d6/d6+2
BLADES IN THE DARK
22.7% Average HP: 9 stress/4 trauma + 3 harm Average damage: 2-3 stress/2-3 harm (minus armor) [This was very hard to get a sharp bead on]
CALL OF CTHULHU/BASIC ROLEPLAYING
40% Average HP: 10-12 Average damage: 1d8
CONAN (MODIPHIUS 2D20)
37% Average HP: 7-9 Average damage: 3-5 (minus armor, 1-3)
CYPHER
35% Average HP: 7-10 (28 = death) [note; these pools are also used to adjust skill rolls, 2 at a time, so I assumed 2-3 uses of that too] Average damage: 2, 4, or 6 (minus 1, 2, or 3 armor)
D6
23% Average HP: 27-33(30) Average damage: 7 (the Wounds system causes problems at 3-5 wounds, for another average of about 4 hits)
DARK EYE, THE
23% Average HP: 30 Average damage: 8 (minus 0-4 protection)
FANTASY AGE
10% Average HP: 38 Average damage: 7 [minus 3-7/10 armor]
FATE CORE
25%-33% Average HP: 6 (Stress) Average damage: 2 [players may take consequences instead of tapping out at 0 Stress, and the first consequence is quite mild so most players take it]
FORBIDDEN LANDS
33% Average HP: 3 Average damage: 1 [assuming 3-4d Str + 1-2 skill +2 weapon]
FRAGGED EMPIRE/FRAGGED KINGDOM
66% Average HP: 3 [bleed at 0; death at -5] Average damage: 3-4 (minus 1-2 armor)
GUMSHOE
27% Average HP: 7 [unc at -6, death at -12] Average damage: 3-4 (minus 1-2 armor)
GURPS
32% Average HP: 11 Average damage: 1d6
HERO SYSTEM (CHAMPIONS)
33% Average HP: 35 (STUN) Average damage (after armor): 12 [25% for bricks]
HERO SYSTEM (OTHER)
37.5% Average HP: 10 Average damage: 1d6+1 to 2d6 (4.5-7) (minus 1-8 armor)
INDEX CARD RPG
35% HP: 10 Average damage: d6 (3.5)
PBTA (DUNGEON WORLD)
43% Average HP: 8 Average damage: 4.5 (minus 1-2 [3] armor)
PBTA (MONSTER OF THE WEEK/URBAN SHADOWS)
28.5% Average HP: 7 Average damage: 2 harm (1-3)
SAVAGE WORLDS
N/A [Wound system; not applicable...but it is a three-wounds-then-you're dead system]
SYMBAROUM
25% Average HP: 10 Average damage: 1d8 (minus armor of 1d4/1d6/1d8)
TINY DUNGEONS
16% Average HP: 6 Average damage: 1 (or 2; 10%)
TRAVELLER
33% Average HP: 7/14/21 Average damage: 2d6 (7)
WORLD OF DARKNESS (VAMPIRE, WEREWOLF, etc)
33% Average HP: 3 Average damage: 1 [very roughly, based on d10 dice pools]