Great Umbrage
First Post
I want to address the issue of Strength, and its correlate statistics, in the 3E D&D game.
By necessity, I will touch on the idea that the gargantuan creatures of myth, as realized in the D&D game, cannot exist in the proportions that they do, but nevertheless accept the premise that they do indeed exist and that we must therefore give a treatment of their attributes. What I am referring to is the fact that giants, for instance, cannot have the same relative proportions as humans and be able to support their body weight, due to the observation that with an increase in height, mass increases by that height factor cubed, while cross-sectional area of a supporting appendage, such as a leg, only increases by that height factor squared, if it keeps the same proportions as a human.
Example: A 12-foot tall giant is twice as tall as an average 6-foot tall human, but weighs EIGHT times as much (volume being a cubic function of height). However, his legs would only be FOUR times as thick (area being a square function of height) and therefore be subject to twice the pressure (say, in pounds per square inch) as a human. Assuming that the giant is made of flesh and bone as is a human, then it would not be able to support itself. This is even more pronounced if the height factor is greater...a 60-foot tall giant would be putting 10 times the pressure on its frame, etc.
However, I am not trying to denounce the existence of giants--they don't exist; this is a fantasy game. I am trying to look at the relationship between Strength, hit points, and damage in D&D. I will work under the premise that giants can somehow support their weight.
The Monster Manual and other books have detailed the relationships between different size categories and listed recommended Strength, hit dice, etc., as well as a height and weight range. In short, each size category includes creatures twice as tall or long as the creatures in the size category before it. That is, a Small creature is half the height/length of a Medium-sized creature, which is half the height/length of a Large creature. As well, the corresponding weight ranges go up in factors of 8, as it works under the assumption that creatures in a type are made of the same kinds of matter and in relatively similar proportions of each kind of matter.
Looking at the recommended Strength values, they increase by either +8/category or +4/category. Aberrations, Animals, Beasts, Dragons, Magical Beasts, Monstrous Humanoids, and Vermin get +8/category above Medium (mostly Quadrupeds, or creatures with a greater horizontal than vertical face), while Constructs, Elementals, Fey, Giants, Humanoids, Oozes, Outsiders, Plants, Shapechangers, and Undead get +4/category above Medium (essentially Biped creatures, or creatures with a greater vertical than horizontal face). This is equivalent to approximately a x2 carrying capacity for Bipeds and about a x4 capacity for Quadrupeds per category. Factor in a x2 for carrying capacity per size category (page 142 in PHB), and thus Bipeds carry x4 more weight, and Quadrupeds, x8.
However, we note that bipeds do not increase carrying capacity as quickly as they do mass (x4 vs. x8). In addition, the method by which the designers arrived at these values is somewhat erroneous. They should be x4 for both bipeds and quadrupeds, because cross-sectional area of bone/muscle is squared, not cubed; thus for a x2 increase in height, the carrying capacity should only increase by x4 for both bipeds and quadrupeds.
One might argue that quadrupeds divide their load between four limbs instead of two, but that applies for quadrupeds of all sizes, and therefore, the multiplier between sizes should still be 4, not 8. A quadruped of the same size as a biped should have twice the carrying capacity that the biped does (though not twice the Strength).
In short, the Strength increase between categories should be +4 (actually, +5), and not +8 for quadrupeds.
However, we are operating under the premise that creatures can somehow carry the same relative weight (especially body mass) regardless of size in this fantasy setting; that is, a 12-foot giant should be able to carry the same size object relative to his body that a 6-foot tall human can.
In nature, real life nature, that is, the thickness of a creature's limbs increase by more than a factor of 2 when the height is increased by 2...it is increased by about 2.8 (square root of 8) so that the cross-sectional area is increased by a factor of 8 and the creature is able to support its body mass.
In fantasy, we can assume that the physical or magical laws operate differently. The easiest assumption is that larger creatures are made of sterner stuff than smaller ones...that is, stronger bones, muscle tissue, whatever, by about 1.4 times (square root of 2). In which case, they should have a Strength increase commeasurate to their mass increase, or x8 (+10 STR/category), so that they can lift the same things as their size that smaller creatures can at theirs.
Now, with regards to the Hit Dice suggestions, they increase by a factor of 2 per size category for most creatures...a Medium-sized humanoid has 1d8 hp, a Large humanoid has 2d8, a Huge humanoid has 4d8, etc., except between Huge and Gargantuan sizes, wherein they quadruple. The exceptions are Dragon and Elemental subtypes, which have different ratios, but we'll deal with the increments used for most creatures, as described above. The Hit Dice recommendations should be considered alongside Constitution recommendations. These increase by 4 per size category, or a +2 hp bonus/category starting from Medium-size, which has a 10-11 recommendation, or 0 modifier.
The Hit Dice ranges therefore look something like M: 1d8, L: 2d8+4, H: 4d8+16, G: 16d8+96, C: 32d8+256, or average hp of M: 4.5, L: 13, H: 34, G: 168, C: 400. The difference is about 2.5 times per category, except for the irregularity between Huge and Gargantuan, where it is about 5 times. In general, HD increase as a direct function of height. But with the CON modifiers factored in, they increase a bit faster than height...This is nevertheless quite different from the increase in mass.
However, there is nothing to indicate that hit points are anything but linear. Yet, a creature twice as tall and 8x as massive as a another creature should be able to take 8x the damage. They should therefore have 8x the number of hp.
Another indication of the disparity is the damage recommendations for various attacks. Let us assume that the damage inflicted is a function of momentum, or mass times velocity. The Slam attack, for instance, should inflict 16x the damage per size category...it is a function of mass (8x) times the velocity achieved (2x, a function of height). Even accounting for the Strength bonus to damage (+2 or +4/category), it is insufficient.
Thus, hp cannot be a linear function of mass, but a function of height. Damage is therefore scaled as hp, which is not linear, or straight line function comparing damage and mass, but exponential. That doubling of hp between Medium and Large creatures is representative of 8x the mass. 1hp means a lot more to a Large creature than it does to a Medium or Small creature. However, weapon damage remains the same, regardless of what you are striking...
These are some of the problems integrating the D&D system into a setting where you wish to set benchmarks for what every statistic represents. This is especially of interest when designing a Supers game that requires consideration of ability scores, especially Strength, that reaches high numbers. What is the relationship between hp and Strength, damage and size, etc.?
By necessity, I will touch on the idea that the gargantuan creatures of myth, as realized in the D&D game, cannot exist in the proportions that they do, but nevertheless accept the premise that they do indeed exist and that we must therefore give a treatment of their attributes. What I am referring to is the fact that giants, for instance, cannot have the same relative proportions as humans and be able to support their body weight, due to the observation that with an increase in height, mass increases by that height factor cubed, while cross-sectional area of a supporting appendage, such as a leg, only increases by that height factor squared, if it keeps the same proportions as a human.
Example: A 12-foot tall giant is twice as tall as an average 6-foot tall human, but weighs EIGHT times as much (volume being a cubic function of height). However, his legs would only be FOUR times as thick (area being a square function of height) and therefore be subject to twice the pressure (say, in pounds per square inch) as a human. Assuming that the giant is made of flesh and bone as is a human, then it would not be able to support itself. This is even more pronounced if the height factor is greater...a 60-foot tall giant would be putting 10 times the pressure on its frame, etc.
However, I am not trying to denounce the existence of giants--they don't exist; this is a fantasy game. I am trying to look at the relationship between Strength, hit points, and damage in D&D. I will work under the premise that giants can somehow support their weight.
The Monster Manual and other books have detailed the relationships between different size categories and listed recommended Strength, hit dice, etc., as well as a height and weight range. In short, each size category includes creatures twice as tall or long as the creatures in the size category before it. That is, a Small creature is half the height/length of a Medium-sized creature, which is half the height/length of a Large creature. As well, the corresponding weight ranges go up in factors of 8, as it works under the assumption that creatures in a type are made of the same kinds of matter and in relatively similar proportions of each kind of matter.
Looking at the recommended Strength values, they increase by either +8/category or +4/category. Aberrations, Animals, Beasts, Dragons, Magical Beasts, Monstrous Humanoids, and Vermin get +8/category above Medium (mostly Quadrupeds, or creatures with a greater horizontal than vertical face), while Constructs, Elementals, Fey, Giants, Humanoids, Oozes, Outsiders, Plants, Shapechangers, and Undead get +4/category above Medium (essentially Biped creatures, or creatures with a greater vertical than horizontal face). This is equivalent to approximately a x2 carrying capacity for Bipeds and about a x4 capacity for Quadrupeds per category. Factor in a x2 for carrying capacity per size category (page 142 in PHB), and thus Bipeds carry x4 more weight, and Quadrupeds, x8.
However, we note that bipeds do not increase carrying capacity as quickly as they do mass (x4 vs. x8). In addition, the method by which the designers arrived at these values is somewhat erroneous. They should be x4 for both bipeds and quadrupeds, because cross-sectional area of bone/muscle is squared, not cubed; thus for a x2 increase in height, the carrying capacity should only increase by x4 for both bipeds and quadrupeds.
One might argue that quadrupeds divide their load between four limbs instead of two, but that applies for quadrupeds of all sizes, and therefore, the multiplier between sizes should still be 4, not 8. A quadruped of the same size as a biped should have twice the carrying capacity that the biped does (though not twice the Strength).
In short, the Strength increase between categories should be +4 (actually, +5), and not +8 for quadrupeds.
However, we are operating under the premise that creatures can somehow carry the same relative weight (especially body mass) regardless of size in this fantasy setting; that is, a 12-foot giant should be able to carry the same size object relative to his body that a 6-foot tall human can.
In nature, real life nature, that is, the thickness of a creature's limbs increase by more than a factor of 2 when the height is increased by 2...it is increased by about 2.8 (square root of 8) so that the cross-sectional area is increased by a factor of 8 and the creature is able to support its body mass.
In fantasy, we can assume that the physical or magical laws operate differently. The easiest assumption is that larger creatures are made of sterner stuff than smaller ones...that is, stronger bones, muscle tissue, whatever, by about 1.4 times (square root of 2). In which case, they should have a Strength increase commeasurate to their mass increase, or x8 (+10 STR/category), so that they can lift the same things as their size that smaller creatures can at theirs.
Now, with regards to the Hit Dice suggestions, they increase by a factor of 2 per size category for most creatures...a Medium-sized humanoid has 1d8 hp, a Large humanoid has 2d8, a Huge humanoid has 4d8, etc., except between Huge and Gargantuan sizes, wherein they quadruple. The exceptions are Dragon and Elemental subtypes, which have different ratios, but we'll deal with the increments used for most creatures, as described above. The Hit Dice recommendations should be considered alongside Constitution recommendations. These increase by 4 per size category, or a +2 hp bonus/category starting from Medium-size, which has a 10-11 recommendation, or 0 modifier.
The Hit Dice ranges therefore look something like M: 1d8, L: 2d8+4, H: 4d8+16, G: 16d8+96, C: 32d8+256, or average hp of M: 4.5, L: 13, H: 34, G: 168, C: 400. The difference is about 2.5 times per category, except for the irregularity between Huge and Gargantuan, where it is about 5 times. In general, HD increase as a direct function of height. But with the CON modifiers factored in, they increase a bit faster than height...This is nevertheless quite different from the increase in mass.
However, there is nothing to indicate that hit points are anything but linear. Yet, a creature twice as tall and 8x as massive as a another creature should be able to take 8x the damage. They should therefore have 8x the number of hp.
Another indication of the disparity is the damage recommendations for various attacks. Let us assume that the damage inflicted is a function of momentum, or mass times velocity. The Slam attack, for instance, should inflict 16x the damage per size category...it is a function of mass (8x) times the velocity achieved (2x, a function of height). Even accounting for the Strength bonus to damage (+2 or +4/category), it is insufficient.
Thus, hp cannot be a linear function of mass, but a function of height. Damage is therefore scaled as hp, which is not linear, or straight line function comparing damage and mass, but exponential. That doubling of hp between Medium and Large creatures is representative of 8x the mass. 1hp means a lot more to a Large creature than it does to a Medium or Small creature. However, weapon damage remains the same, regardless of what you are striking...
These are some of the problems integrating the D&D system into a setting where you wish to set benchmarks for what every statistic represents. This is especially of interest when designing a Supers game that requires consideration of ability scores, especially Strength, that reaches high numbers. What is the relationship between hp and Strength, damage and size, etc.?
