mplindustries mentioned that two of the sticking points with using DnD for this sort of thing were that both jumping distances scaled with the hard numbers on a sheet and falling damage scaled independently of them entirely. I had time on my hands, so I set out to see whether or not I could address the falling damage for high-level characters who are more experienced and more skilled, but not literally tougher.
What Measure Is A PC?
As such, I set out to calculate the lowest and highest HP values one could have in the game at any given level.
The lowest value belongs to the wizard, invoker, and the assassin, iirc. Assuming an 8 in Constitution and no other stat boosts, feats, features, or items related to increasing HP, you have the following advancement.
Level: 1 - 2 - 3 - 4 - 5 - 6 - 7 - 8 - 9 - 10
HP: 18 22 26 30 34 38 42 46 50 54
Level: 11 - 12 - 13 - 14 - 15 - 16 - 17 - 18 - 19 - 20
HP: 59 63 67 71 75 79 83 87 91 95
Level: 21 - 22 - 23 - 24 - 25 - 26 - 27 - 28 - 29 - 30
HP: 100 104 108 112 116 120 124 128 132 136
The highest values one could have belong solely to the Warden. The example Warden will be a Dwarf Warden MC Fighter/Dreadnught/Demigod, taking Toughness at level 1, increasing Constitution at every opportunity, and gaining a Brooch of Vitality of level+4 at every available level (11/16/21/26). This gives us the following advancement.
Level: 1 - 2 - 3 - 4 - 5 - 6 - 7 - 8 - 9 - 10
HP: 42 49 56 64 71 78 85 93 100 107
Level: 11 - 12 - 13 - 14 - 15 - 16 - 17 - 18 - 19 - 20
HP: 135 142 149 157 164 176 183 191 198 205
Level: 21 - 22 - 23 - 24 - 25 - 26 - 27 - 28 - 29 - 30
HP: 225 232 239 247 254 266 273 281 288 295
Now, the overall rate of increase for the two is slightly different. The minimal hp character has increased 7.55... times, while the maximal hp character has increased 7.02 times. This may causes a problem, in that balancing for the weaker character's survivability means the tougher character actually gets diminished returns, while balancing for the tougher character to remain the same means the weaker character gets inexplicably more resilient to falling.
As such, I think that balancing for all PCs to get more resilient to falling is the better option, so we should scale falling damage at a lesser rate than either. A front-loaded version of the Warden above (retraining Toughness at a later level, removing the ability score increases, Dreadnought PP, and the Brooch of Vitality) ends up with increasing his HP total 6.12 times from 1st to 30th. (It's worth mentioning here that taking the Wizard and boosting his HP as much as possible gives him 10.44 times as much hp as when he started. Corner cases are screwy.) As such, I think the maximum scaling of falling damage should be a factor of six at thirtieth level.
If A PC Falls In The Forest...
For a moment, let us consider whether or not falling 1d10 damage is consistent enough at 1st level to utilize with the scaling. If the aforementioned wizard falls a mere twenty feet, he could be lying there dying until someone comes along. This is not entirely unreasonable, as falls from that height can be lethal if you land poorly. However, it cannot even knock out the Warden (the one in the example, or any other Warden ever). The example Warden must fall at least 50' to have any chance of getting killed. Further, the wizard must fall 180' to guarantee that he will be dying when he hits the ground, and 270' before it kills him outright without fail. The Warden must fall 420' to guarantee "dying", or 630' for "killed outright".
I think a spread ranging from 160' to 580' for what could constitute a lethal fall is too large. This is purely an opinion, of course, but I think narrowing the lethal range will help guage just how well the scaling is at higher levels. The only method I see to restrict the lethal range is by decreasing the range of results. Since the default range is a d10, the lower ranges available are 1d4, 1d6, 2d4, and 1d8. 1d4 gives us the least range, but also makes longer falls far more survivable. 1d8 minimizes the difference in lethality, but still gives us large ranges. 2d4 gives us more lethal falls and a smaller range than 1d8, along with having an average close to that of 1d10, but involves rolling lots of dice when falling long distances. 1d6 wishes I had something that it could be special at here, and in that I have nothing to recommend it over any other option, that does make it special. Poor 1d6.
Minimum Lethal Fall Distance
1d4 1d6 2d4 1d8 1d10
Ex. Warden 110' 70' 60' 60' 50'
Ex. Wizard 50' 30' 30' 30' 20'
Guaranteed Lethal Fall Distance
1d4 1d6 2d4 1d8 1d10
Ex. Warden 420' 420' 210' 420' 420'
Ex. Wizard 180' 180' 90' 180' 180'
Lethal Fall Range (GL - ML)
1d4 1d6 2d4 1d8 1d10
Ex. Warden 310' 350' 150' 360' 370'
Ex. Wizard 130' 150' 60' 150' 160'
Based on these numbers, I think using 2d4 as our base will give the best evidence of scaling effectiveness over time.
All things entail rising and falling timing.
Now we consider at which points the increases should take place. As it must rise to a factor of six at thirtieth level and presumably not before, the final incresae must come at level 30. Since there are five increases spread across thirty levels, and the last one must occur at level 30, the simplest solution is to have the increase at every multiple of 6, and we get the following chart.
Level: 1 - 2 - 3 - 4 - 5 - 6 - 7 - 8 - 9 - 10
Damage: 2d4 4d4
Level: 11 - 12 - 13 - 14 - 15 - 16 - 17 - 18 - 19 - 20
Damage: 6d4 8d4
Level: 21 - 22 - 23 - 24 - 25 - 26 - 27 - 28 - 29 - 30
Damage: 10d4 12d4
However, the scaling is not terribly smooth. However, our base damage die is not singular, and thus can be split across the intervening levels as well. If we do this as evenly as possible, we get the following chart.
Level: 1 - 2 - 3 - 4 - 5 - 6 - 7 - 8 - 9 - 10
Damage: 2d4 3d4 4d4 5d4
Level: 11 - 12 - 13 - 14 - 15 - 16 - 17 - 18 - 19 - 20
Damage: 6d4 7d4 8d4
Level: 21 - 22 - 23 - 24 - 25 - 26 - 27 - 28 - 29 - 30
Damage: 9d4 10d4 11d4 12d4
With this chart, we have ten total increases resulting in a total value six times that of the original. We can compare HP values to the damage lines to see if resilience falls within a more limited increase.
Minimum Lethal Fall Distance
Level 1 6 12 18 24 30
Ex. Warden 60' 50' 60' 60' 70' 70'
Ex. Wizard 30' 30' 30' 30' 30' 30'
Guaranteed Lethal Fall Distance
Level 1 6 12 18 24 30
Ex. Warden 210' 200' 240' 240' 250' 250'
Ex. Wizard 90' 100' 110' 110' 120' 140'
Lethal Fall Range (GL - ML)
Level 1 6 12 18 24 30
Ex. Warden 150' 150' 180' 180' 180' 180'
Ex. Wizard 60' 70' 80' 80' 90' 110'
The first level distances are slightly higher than the sixth level distances because they are technically out of the pattern. The proper level to compare ought to be the zeroth. While the zeroth level doesn't exist in the system, you can reduce the hit point values to determine whether such a level would fall in the pattern, but you also have to figure out whether you want the Warden to have Toughness, which you can imagine skews things a bit. A 40' fall can kill a 0th level example Warden if he doesn't have the feat (30 hp), otherwise (35 hp) it must be 50'. The example wizard at 0th level (14 hp) can be killed by a 20' fall.
At any rate, the minimum lethal distance for the example wizard always remains at 30', and never exceeds 70' for the Warden. The guaranteed lethal ranges show more variation, but the range of values is only 80 (from 190' to 270') for the Warden and only 30 (90' to 120') for the Wizard. This is already a vast improvement for our stated premise, and the Warden's largest jump is easily explained: it occurs at level 11, when he gainst 28 hit points (Dreadnought +10, Con +1, Toughness +5, level +7, 15th level Brooch +5). If you want to create a spreadsheet to check my work, I used =ROUNDUP(/ROUNDDOWN(((/3)+2)))*10 for the guaranteed kill distance, and =10*ROUNDUP(/(4*ROUNDDOWN(((/3)+2)))) for the minimum lethal distance. These formulae only work for the 2d4 base increasing by 1d4 at every multiple of 3.
I believe that means there's only one thing left.
It's Not The Fall That Kills You...
That's going to be a constant.
The Endurance save to reduce the impact is used to simulate higher HP characters surviving falls easier (and the Acrobatics check to simulate agile characters landing better) and you could even combine the two for a double reduction, if you like.
You are trying to make sure falls in general stay deadly, while I'm trying to make sure the same fall stays roughly as deadly.
The six increment damage = Surge Value thing seems like a nice start.
My personal way of handling it would be to have four fall distances, rather than deal damage by the actual number of feet falling. I don't feel it necessary to figure out exactly how far drops are in feet, nor do I think it's especially important for the game to ensure that a 50' fall is actually distinct from a 60' fall.
I like the DMG's suggested ranges:
Painful would deal minor damage, Dangerous would deal moderate, Perilous would deal high damage (the kind that could easily knock you unconscious), and Deadly would deal, well, deadly damage. Now, exactly what fall distances would be which category would be up to the GM to call responsibly and consistantly. Don't worry about giving exact fall distances, actually, unless it's important to know if they have enough rope to climb back up, for example.
I don't know how exactly I'd work the numbers. My goal would be to keep those four fall differences roughly equal across the board. The "Surge Value" based idea could readily work with this, honestly, with Painful Falls dealing 1 surge value, Dangerous dealing 2 surge values, Perilous dealing 3 surge values, and Deadly dealing 4. Or, even up all those numbers by 1 surge value if you want falls to be even scarier.
No I mean dealing actual damage equal to that number of surges. Nobody ever has more then 4 surges worth of HP, so it means that you can be pretty certain that a 4 surge fall is going to knock out everybody who falls off, or kill everyone who falls off while bloodied.
Okay, I see how I was misunderstanding you. When you said dealing a number of Healing Surges in damage instead of HP damage, I thought you meant like the rules for extreme weather and such, where the PCs lose surges first, then their surge value in HP, until they either die or find shelter. My bad. Yes, this does make it simple.
As an aside, due to rounding, I think more characters walk around with just over four surges worth of HP than those who run around with exactly four.
I'm glad I can be an inspiration, but I think this is a little bit too complicated, not to mention it's not really aimed at what my target would be.
You are trying to make sure falls in general stay deadly, while I'm trying to make sure the same fall stays roughly as deadly.
Actually, my goal was to make falling damage scale at roughly the same rate as character HP, which would make the same character falling the same distance roughly as deadly at any level. I don't see that as inherently different from your goal, though from the latter half of your post, I think you mean for any characters, while I was looking obviously looking at simply for a given character.
It was just easier for me to establish a scale with a narrower area of "deadly". Using the default 1d10 damage as the scaling value left me with situations where the example Warden at level 5 had to fall 710' to guarantee death, but then at level 6 he only had to fall 390'. Being suddenly unable to survive falling 320' less than you might have before was a huge problem with the numbers. Even the Wizard loses 150' from advancing to level 6 using 1d10 scaling. While that level change is the biggest difference, there are others that are also significant, which meant falls had to have smaller ranges and start slightly more lethal.
The numbers I have above don't show the full expected range, but it is available here: spreadsheets.google.com/ccc?key=0AjkSNmp...
It has the Example Warden, Example Wizard, and a Wizard who started dumping Con and then picked every HP boost the Warden took. Each one has a column for level progression, hp progression, and minimum/average/guaranteed lethal fall distances. All in all, each character is rather static, which is at least what I was going for, even though it wasn't what you'd actually be looking for.
The six increment damage = Surge Value thing seems like a nice start.
My personal way of handling it would be to have four fall distances, rather than deal damage by the actual number of feet falling. I don't feel it necessary to figure out exactly how far drops are in feet, nor do I think it's especially important for the game to ensure that a 50' fall is actually distinct from a 60' fall.
I like the DMG's suggested ranges:
Painful would deal minor damage, Dangerous would deal moderate, Perilous would deal high damage (the kind that could easily knock you unconscious), and Deadly would deal, well, deadly damage. Now, exactly what fall distances would be which category would be up to the GM to call responsibly and consistantly. Don't worry about giving exact fall distances, actually, unless it's important to know if they have enough rope to climb back up, for example.
I don't know how exactly I'd work the numbers. My goal would be to keep those four fall differences roughly equal across the board. The "Surge Value" based idea could readily work with this, honestly, with Painful Falls dealing 1 surge value, Dangerous dealing 2 surge values, Perilous dealing 3 surge values, and Deadly dealing 4. Or, even up all those numbers by 1 surge value if you want falls to be even scarier.
That does seem rather simple and efficient. Oh well. All that math gone to waste. :P
If you want to make falling dangerous I'd simply say that if you fail a save you become bloodied and if you fail be 10 you are unconscious. Add one to the save for every half level and minus one per 10 feet. A first level person has a 1 in 20 chance of going unconscious from a 10 foot fall which sounds about right if you aren't talking about a controlled jump.