Tuesday, February 7, 2012

Falling Damage and Hit Point Inflation

For the moment, I'm not going to wade further into the question of whether real world physics has much to teach us on the question of falling damage of Dungeons & Dragons. However, in thinking about this, I thought it might be worth taking note of the maximum hit points possible for a 10th-level character in three successive versions of old school D&D: LBB-only OD&D, Supplement I OD&D, and pre-Unearthed Arcana AD&D. In each case, I assumed the character to have 18 Constitution.

Dungeons & Dragons (LBBs Only)
Class (10th Level + 18 Constitution)
Maximum Hit Points
Cleric (7d6 + 2 Hit Dice)
51
Fighting Man (10d6 + 1 Hit Dice)
71
Magic-User (7d6 Hit Dice)
49

In LBB-only OD&D, all characters have D6 Hit Dice and bonuses for Constitution are limited to +1 per die. What's of particular interest to me is that clerics and magic-users have very similar maximum hit points figures at this point.

Dungeons & Dragons (LBBs + Greyhawk)
Class (10th Level + 18 Constitution)
Maximum Hit Points
Cleric (8d6 + 1 Hit Dice)
73
Fighting Man (9d8 + 2 Hit Dice)
101
Magic-User (10d4 Hit Dice)
70
Thief (10d4 Hit Dice)
70

Supplement I begins the game's hit point inflation, first by increasing adding giving every class a full hit die at each level (and bumping the fighter's dice type to D8) and second by granting a +3 bonus per die for 18 Constitution. What's especially interesting is that, at this stage, all classes but fighters have roughly the same maximum hit points at 10th level, which was also true in LBB-only OD&D, though the numbers have gotten much large.

Advanced Dungeons & Dragons
Class (10th Level + 18 Constitution)
Maximum Hit Points
Cleric (9d8+2 Hit Dice)
92
Fighting Man (9d10+3 Hit Dice)
129
Magic-User (10d4 Hit Dice)
60
Thief (10d6 Hit Dice)
80

Here's what we get in AD&D. All classes but the magic-user get a bump in their hit dice types, but the bonus for 18 Constitution is knocked down to +2 per die for non-fighters, while fighters get it increased to +4 per die. All classes except magic-users see an increase in their maximum hit dice at 10th level.

These are all quick calculations done in my age-addled and math-impaired head, so I'm sure someone will point out an error or five in my sums. Regardless, my essential point remains: with each new revision of D&D, the overall number of hit points increased, particularly with regards to fighters (whose maximum potential at 10th level increased by over 40%). In addition, AD&D abandons 3D6 in order as the default method of generating ability scores and counsels that characters need at least two scores of 15 or above to be viable, leading to a much greater likelihood that a character will have a significant number of hit points.

Thus, it's my feeling that most, if not all, of the hand wringing regarding the "realism" of 1D6 per 10' fallen is consequence of the fact that it was a rule introduced when a high-level fighter would, at best, have 71 hit points. By the time of AD&D, most classes had seen a significant boost in their hit point potential (aided by ability score inflation) and thus the odds that a character could brush off a fall from a very great height were increased. The problem, then, is not that 1D6 per 10' is, on the face of it "unrealistic," it's that it was a rule from a time before fighters could have well over 100 hit points.

42 comments:

  1. ... And let's not forget that, in the LBBs, you only take falling damage for a 10-foot pit on a 1 or 2 in 6 (according to U&WA p5, note 8) or on 1 in 6 per 10 feet fallen (U&WA p32, note 2.) So the original rules are kind of forgiving when it comes to falling damage, which makes the desire to make falling more deadly very interesting...

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  2. I've never been a fan of a linear increase in damage from falling. At higher levels it allows characters to fall 100s of feet in relative safety. Instead, I increase the number of dice after each 10' fallen. A 30' drop would then be 1d6 for the first 10' plus 2d6 for the second 10' plus 3d6 for the third 10' or 6d6 for a 30' drop. It's simple and turns falling into a more significant threat.

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  3. I know you didn't want to introduce real world physics, but I thought it worth mentioning that IRL a fall of 30'+ onto stone generally results in death or maiming, so even the LBB magic user is superhumanly hardy at 10th level.

    d6 per 10 feet fallen would be realistic applied versus a typical con score or for a <4th level PC. YMMV

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  4. D&D 3.x
    Fighter lvl 10 with Con 18
    Max. 140
    Avg. 90.5 (10+9d10+40) // Maximum hit points from the first level

    D&D 4th Edition
    Fighter lvl 10 with Con 18
    97 (15+Con+9*6) // no rolling, no ability modifier to hitpoints, falling damage 1d10 per 10'

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    1. Don't forget, in 3rd edition you could take feats which could also potentially increase your hit point total. I forget how they work, but I'm sure there's a way for a 3rd edition character at 10th level to have more than 150 hit points.

      p.s. - I'm not familiar with 4th edition at all.

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    2. Yes, in 3.0 and 3.5 you can have +3 hp from Toughness and +1 per level from Improved Toughness. In Pathfinder you get +1 per level from Toughness and possibly +1 per level from taking a level in your favored class. It's also possible to raise your constitution score as you level and boost it with spells or magical items. A human fighter 10 could easily have a Constitution 24(+7) if he had started with Con 18 and wished to boost it.

      Still, in all my years of DMing 3.x, I haven't seen anyone really focus on maximizing his constitution.

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  5. Let's add some clarifications:
    In 3.x you can negate 1d6 falling damage with a successful skill check. Maximum falling damage is 20d6.

    In 4th edition you can make an Acrobatics check if you are trained in the skill, and reduce the amount of falling damage you take by one-half the check result. Maximum falling damage is 50d10 (Rules Compendium) and as a fast alternative, you take the average 25 damage per 50 feet fallen, plus 1d10 damage for each 10 extra feet.

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  6. Good analysis, totally agreed (and you can say the same thing for the d6-damage from fireballs and lightning bolts). It's another case where Original D&D has a cohesiveness that got lost in later iterations.

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  7. I can overlook a lot of un-realism in regard to falling (in any addition) to simplify game play. To some extent we do want heroic actions regarding terrible heights. However it pains me when a player makes the decision to leap a great distance to the ground with impunity to save time running down the stairs, and then drink a potion to 'fix' the damage. I only let that happen once before I began using a massive damage rule which requires a save or lose all your HPs.

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  8. Hit point inflation also affects monsters' ability to meaningfully harm the PCs. Over the course of the editions (at least through 3.5, anyway), there seemed to be a HP arms race, to the point where monsters had to be beefed up to keep up with the PCs.

    The ultimate design question would seem to be: how many "average" hits should an "average" PC be able to sustain at a given level? It would seem that the designers moved in the direction of longer combats and reduced PC mortality.

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  9. Another interesting angle is how hit points are an abstraction concerning an adventurer in battle. The plausibility of them is stretched a little, but most gamers I have met are okay with it. A warrior surviving the blast of a fire breathing dragon. There is something heroic to that scenario. But when it comes to a warrior, willfully jumping off a cliff, the abstraction of hit points drops in its believability if there is no risk of death (for some gamers). Maybe it is a psychological factor of combat, where we can easily abstract away a battle between two opponents. But it is harder to do when there is nothing to fight, such as falling off a cliff or a giant stone block crashing down upon a hapless adventurer.

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    1. @Random Wizard

      I think you've correctly identified the problem.

      In almost all level-based RPG character systems, only a character's 1st-level hit points represent the amount of actual physical damage that character can take. All 2nd-level & up hit points represent the character's fantastical ability to AVOID taking actual physical damage.

      And that system works great for playing out heroic combat -- where we not only can easily imagine many possible ways how a character could avoid taking actual physical damage, but we also want them to do so -- because it's heroic.

      But, unless we're playing a game about superheroes or some such, we not only can't easily imagine many possible ways how a character could likely avoid taking any actual physical damage from a great fall, but we also don't want them to be able to do so because that's not heroic -- it's super-human.

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    2. Agreed. To me, any use of hp outside of combat—or at least something that at least looks vaguely similar to combat—is questionable.

      The d6 roll to see if the trap works. A saving throw or Dex check to see if the character manages to avoid falling or grab the edge or something. Then a roll on my injury table modified by distance fallen. That’s the direction I’m going.

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  10. I grew up playing AD&D 2nd edition, and my main group had a house rule that if you fell a distance greater than 100 feet you had to make a System Shock roll or die instantly, and if you survived that THEN you rolled for damage.

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  11. How about replacing randomly rolled damage per 10 feet with a % of (full) hit points per 10 feet? For those wanting "realism" simply add a roll for the chance of instant death (perhaps equal to the same % score above). Done this way, no matter what the character level, all will take the same damage, relatively speaking of course. Given that hit points are an abstract concept in D&D and don't represent actual wounds, this should work quite well.

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  12. >so even the LBB magic user is superhumanly hardy at 10th level.

    And well he should be, he's a 10th LEVEL WIZARD after all!!! (if you can imagine the excuse being some arcane reason...)

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  13. I actually don't have a problem with a character realising that they can take the damage from leaping off a castle wall and continuing on, simply because hit points don't actually represent physical damage in D&D, but rather are more akin to plot immunity.

    So you are not going "leap - *splat*" but rather doing that epic leap for that deep part of the moat or that tree or that tent or hay cart, just like in the movies. Just as hit points in D&D allow you to keep fighting for longer, presumably because of ability, having a large amount of hit points to expend in such activities implies a certain amount of ability to make that leap, or realise that tree can break your fall, and so on.

    Essentially hit points are your defensive skill. For an accidental fall, plot immunity comes back into play.

    On the other hand if you have a fixed amount of hit points (frex Runequest) then they do represent the ability to sustain physical damage, and most such systems have a wound system to cope, so falling damage becomes more realistic.

    [Personally I represent physical damage in D&D by taking actual CON damage. This replaces the "not dead until -10" It also heals a lot more slowly (frex each die of healing magic only heals 1 CON wound point). Critical hits and surprise attacks can do CON damage directly. I once played with physical damage slowly leaking through but it really wasn't worth the effort, and a much better result is that when your luck (hit points) runs out you start taking CON damage. When I used the leak rule falling damage did no CON damage on a "1," 1 point on a "2-5," and 2 points on a "6" for an accidental fall, halved for a purposeful leap. But I think a better approach is let the hit points represent situational luck.]

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    1. @Reverance Pavane

      I play stuff like that much the same way you do whenever anybody there can concoct any even remotely plausible explanation how somebody could possibly avoid taking any significant physical damage from whatever a character's hit points would allow them to avoid.

      But, if nobody can come up with any even remotely plausible explanation, then...

      SPLAT!!!

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  14. "...most, if not all, of the hand wringing regarding the 'realism' of 1D6 per 10' fallen is consequence of the fact that it was a rule introduced when a high-level fighter would, at best, have 71 hit points. By the time of AD&D, most classes had seen a significant boost in their hit point potential (aided by ability score inflation) and thus the odds that a character could brush off a fall from a very great height were increased. The problem, then, is not that 1D6 per 10' is, on the face of it 'unrealistic,' it's that it was a rule from a time before fighters could have well over 100 hit points."

    I think you're right. 1d6 per 10' is a good enough approximation when no human can ever have more than 71 hit points.

    (Though 1d6 cumulative per 10' still is a better approximation even in that case.)

    But, when a human could possibly have over 100 hit points, then 1d6 per 10' just isn't a good enough approximation anymore.

    So, what it comes down to is that we need to use a system for determining falling damage that's in line with whatever maximum hit points we're going to allow.

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    1. I was wrong about 1d6 per 10' cumulative being a better approximation than 1d6 per 10'.

      It turns out that ALL OF US have been thinking about this incorrectly.

      The equation for calculating the instantaneous velocity of a falling object that has fallen a certain distance is:

      Instantaneous Velocity = √(2 x Gravitational Constant x Distance)

      And that's neither linear nor arithmetic nor geometric nor exponential.

      It's INVERSE exponential.

      That means the impact velocity of a falling person increases as the SQUARE ROOT of the distance they fall.

      So falling 4 times as far results in only twice as much impact velocity and, presumably, damage.

      And falling 9 times as far results in only 3 times as much impact velocity and, presumably, damage.

      And falling 16 times as far results in only 4 times as much impact velocity and, presumably, damage.

      And so on.

      So a more "realistic" (*GASP!*) falling damage rule would be:

      Falling Damage Dice = √((Distance Fallen/10')Rounded Down)

      That'd result in:

      A fall less than 10' = no damage

      A fall from 10' to less than 40' = 1d damage

      A fall from 40' to less than 90' = 2d damage

      A fall from 90' to less than 160' = 3d damage

      And so on.

      To make falls more potentially deadly to characters with lots of hit points, just include a save or die with a penalty of however many dice of damage the fall inflicts.

      To make falls very deadly to just about everybody, make the save or die penalty however many POINTS of damage the fall inflicts.

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    2. I was wrong again. I didn't think it through far enough. Even though impact velocity varies as the square root of distance fallen, damage isn't due to merely velocity. Damage is due to energy. And energy varies as velocity squared. So impact energy, and the resulting damage, actually does vary linearly with distance fallen. So 1d6 per 10' fallen is exactly right after all!

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    3. ^ Thanks to Ed for entirely recreating the Dragon #88 article-rebuttal. :-)

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    4. Damn! If I had Dragon #88, I could've just read that article instead of doin' all that freakin' math!

      But, I suppose, if I had just read the article, not actually done the math myself, I probably wouldn't understand either the math or the physics as well as I do now.

      And I wouldn't have provided a such valuable service to the OSR community! ;o)

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  15. I differentiate between what I call HiP and HeP. HiP are the base 1st level Hit Points, while HeP are Hero Points, or the points accumulated with every level thereafter. Where they differ is that HiP are reduced by combat, falling, poison, etc the usual way. HeP, however, are not reduced by falling, but can be reduced by other forms of Heroic damage such as taken in combat, and can also be burned as luck points for skill rolls or for MUs and Clerics to access spells when they are tapped out for the day. It is a bit foolish of us to talk about 'reality' in a fantasy game, but this rule and ones like it (i.e. Shields Shall Be Broken) do add verisimilitude, which is what allows us to predict how the game world will function and thereby engage with it mentally.

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  16. Guys, why do you keep over-complicating the hit points mechanic?

    Hit Points are a measure of how much damage a character can take before he dies. It's so simple as that. It has nothing to do with how adept the character is at *avoiding* damage.

    Just like a big, strong body-builder can take more damage from clubs, punches or even poisonous substances than a child, woman, or a skinny guy. Whether or not that body-builder would be able to avoid the hit by a club would be another question entirely.

    The D&D characters are no exception. Hit Points show you how much direct damage you can take before you die.

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    1. @The Beyonder

      The reason why many (most?) of us don't treat all character hit points as representing capacity to withstand actual physical damage is because we want to play characters with merely fantastically heroic capabilities, not super-human superheroes.

      But, if you want to play characters who can withstand several times as much actual physical damage as any normal person, then have fun.

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    2. Because if you treat HP as ability to take damage, you are saying that a character can actually be stabbed tens, even hundreds of times. You are saying that even a first level fighter can stab himself in the head with a dagger and survive, with no lasting effect.

      If you're not going to introduce critical hits to D&D, in order to keep things remotely plausible you either need to treat most HP as the kind of Hero / Fatigue / Fate that keep you from being stabbed until that last, deadly blow runs you through, or treat combat as completely abstract and 'board-gamey', rather than a narrative - a succession of dice rolls rather than a series of character and monster actions and reactions.

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    3. Because the DMG specifically says hit points aren't simply a matter of how much damage a character can take, but are an abstraction representing all of the different resources available to turn a killing blow into a minor scratch, cut, or bruise.

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  17. A friend of mine (and a DM) has always maintained that D&D (at least in AD&D and later) *is* a supers game, and plays everything accordingly. I mean, how many people in real life run around with the real world equivalent of 15s (and often higher) in more than one "ability score"? He's got a point, especially when it comes to falling damage.

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    1. 3d6 in order? Nevertheless, while Geoff Capes might have had Str 18, but he couldn't fall 30 foot without injury, or fight on punctured by a quiver full of arrows, nor did he have any 'super powers'. He was just the World's Strongest Man - at the maximum of the normal human range in strength, or 'Str'.

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  18. Here's an idea for falling damage that makes great falls a significant threat to even characters with lots of hit points, but short falls not too much of a threat to characters with few hit points, and still stays realistically almost linear too:

    1d4 damage for the 1st 10 feet fallen.
    1d6 damage for the 2nd 10 feet fallen.
    1d8 damage for the 3rd 10 feet fallen.
    1d10 damage for the 4th 10 feet fallen.
    1d12 damage for the 5th 10 feet fallen.
    1d20 damage for each additional 10 feet fallen.

    No maximum.

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  19. I seem to recall there being a percentage chance associated with CON in AD&D called "System Shock". It was rolled for instances where a great "shock to the system" must be survived. I think we mostly used it in conjunction with resurrections, but doesn't it seem to follow that this would be a better way to handle falling damage? The PC must roll a system shock check after falling X amount of feet, and if he fails, splat. If he succeeds, apply the amount of HP damage as written.

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  20. Hit points are merely a conceit that we accept when playing D&D. As far as falling damage goes, I once again would point out to everyone the little story of poor Vesna Vulovic in the AD&D2 PHB. Some knights fall off their horse and die while some stewardesses fall 10 km to Earth from the sky and survive. She was 22 at the time, which would make her no more than 3rd level. If we assume that she was a member of the Dedicated Hero class from d20 Modern, even with an 18 Constitution, her maximum hit points would be 30. This fall would do 20d6 damage. Statistically speaking, the likelihood of the fall doing 40 or more points of damage (bringing her to -10 hit points; instant death) is 99.9984%. But she survived.

    So, who's to say that a name level fantasy warrior couldn't survive such a fall?

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  21. @Slerotin

    "So, who's to say that a name level fantasy warrior couldn't survive such a fall?"

    That sounds like an ideal example for an argument in favor of using System Shock or some sort of "save or die" roll.

    FTR, I like Ed Dove's a couple of comment above, with the caveat that I'd add a SS roll after 100 feet.

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    1. In this case, Vesna would have a 99.998416% chance of instant death. If her Constitution was 18 (when she was 22), she had a 99% System Shock roll. There's a 1% chance of dying outright coupled with the 99.9984% chance of dying from the damage instantly. It's gone from a 1 in 62,500 chance to a 1 in 63,131 chance of living.

      This stuff warms my monomaniacal statistics loving heart. Sorry, Gary!

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    2. @Anthony

      Thanks for saying!

      I thought about suggesting a saving throw or System Shock roll at some point, too. But, because a 100-foot fall would, on average, do about 75 points of damage, I figured that alone would be enough.

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  22. I find it immensely amusing how this thread demonstrates again that few things can stir up a D&D debate faster than "is falling damage correct?" and "what are hit points, really?" Thus it was at the beginning, and thus it shall be at the end.

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  23. A few people have asserted something like Ed does above:

    "In almost all level-based RPG character systems, only a character's 1st-level hit points represent the amount of actual physical damage that character can take. All 2nd-level & up hit points represent the character's fantastical ability to AVOID taking actual physical damage."

    Okay, I can certainly see how that could be the case. But just to be clear, it's officially contradicted for AD&D by Gygax in the DMG where he lays out that actual hits taken do increase up through at least level 7 (linearly so, in fact):

    "Furthermore, these actual physical hit points would be spread across a large number of levels, starting from a base score of from an average of 3 to 4, going up to 6 to 8 at 2nd level, 9 to 1 1 at 3rd, 12 to 14 at 4th, 15 to 17 at 5th, 18 to 20 at 6th, and 21 to 23 at 7th level." [AD&D DMG p. 82]

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    1. "Furthermore, these actual physical hit points would be spread across a large number of levels, starting from a base score of from an average of 3 to 4, going up to 6 to 8 at 2nd level, 9 to 1 1 at 3rd, 12 to 14 at 4th, 15 to 17 at 5th, 18 to 20 at 6th, and 21 to 23 at 7th level." [AD&D DMG p. 82]

      Yeah...I know. :o)

      I've always found that idea to be unplayably vague, though.

      For a while, I tried to approximate it by treating both all 1st-level hit points and all Constitution bonus hit points as actual physical hit points. But I eventually gave up even that because it was more trouble to keep track of than it was worth.

      So, now, I treat only 1st-level hit points as actual physical hit points because that's not only playable and makes sense, but it also seems more like what almost all level-based character systems really assume, despite what Gygax wrote in the DMG.

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  24. Maximum hit points are actually an irrelevant metric: if you play by the book (roll for hit points) no mid to high level character will have anywhere near maximum hit points. For example, 10% of 1st level AD&D fighters would naturally roll maximum hit points, 1% of 2nd level fighters would have the maximum, 0.1% of 3rd level fighters, and so on until only 0.000001% of 9th level fighters would roll the 9 consecutive 10s required. Only 0.1% will roll a total of 80 or more, and just over 1% will roll a total of 70 or higher.

    The median metric is a better representation of expected hit points. This also makes the effects of constitution even more pronounced. For example, a 9th level AD&D fighter with a 10 constitution will expect to have 45 hit points. With an 18 constitution, add an extra 36 hit points, which almost doubles the total to 81.

    The LBB median hit point total with 18 constitution would only be 45, which is a little over half of what the 18 AD&D equivalent gets. However, if you assume average constitutions, the difference between 10d6 and 9d10 is 35 versus 45, which is a much more modest difference.

    The change in dice used to generate hit points from edition to edition did not alter hit point totals in that dramatic a fashion, but the piling on of ability score bonuses had a huge effect.

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  25. Oops, I screwed up the math: the average for a 9th level AD&D fighter without constitution bonus is 55, not 45, so the spread is a little larger than what I originally wrote. It is in the Greyhawk suppelement (and Moldvay/Cook) that the median is 45, with maximum constitution bonuses of 18 and 27 respectively. So the disparity between editions from changes in dice is more significant, but constitution bonuses are still the overriding factor.

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  26. Since 1977 I've always assumed that hit points represent the hero's will to survive, physical capacity to sustain damage, ability to avoid damage, and luck/supernatural favor all rolled up into one messy ball of wax. I also assumed that hit points only apply when you are attempting heroic actions, engaged in the day-to-day activities of your class, and/or are able to actively try to prevent what someone/something is trying to do to you. In any other case, the Ref is allowed to apply damage directly to your CON.

    Under these assumptions falling damage becomes very easy to adjudicate...if you were chased to the edge of the cliff by the chittering horde of ratmen after beheading their leader *and* there's no where to go but down *and* there are plenty of trees/a lake or river/a bunch of giant birds then go ahead and jump, the falling damage will come off your hit points; however, if those same ratmen catch you, tie you up, and toss you off the cliff...well, you're pretty much dead.

    Same goes for combat. In the thrust and parry of a sword fight your hit points are used to track your damage. If you're hanging from a pair of manacles in a dungeon while being tortured, damage is coming off your CON. Tied up with a knife to your throat? If the knife cuts, you die.

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