Quote from: Baron Opal;970915Where does it say that? I've never heard of that before.

Its also in AD&D to a degree. But Im not sure if its in 2e. PC level modifying EXP from monsters and treasure earned. But it was on a case by case basis.

Quote from: finarvyn;967753The basic problem is that most actions are resolved using a d20, so either (1) you have to limit how fast a character can get bonuses, or (2) the system will break somewhat at high levels. This isn't just a function of D&D, but is a byproduct of the mathematics. I remember tinkering with Decipher's Lord of the Rings RPG, which I thought was cool until I realized how fast a 2d6 dice rolling range gets "broken" and that kind of took the fun out of it for me. Games based on a d20 die roll have the same philosophical issue, but it doesn't come into play quite as quickly because the number range is larger.

I think that 5E has done a nice job of limiting the bonuses, but I have to confess that I've only played a couple of sessions at levels 10+.

I'd love to hear more about the mathematical aspect. So far, I don't understand why the size of the die is related to the size of the bonuses. It seems to me that the numbers would get higher, yes, but would still operate over the same range, since bonuses are flat and not, say, percentages of the roll. I'm sure my understanding is naive ... can anyone break this down further?

A d20's probabilities are flat (not curved like 2d6), so that each number-face on the die has an equal 5% chance of being rolled. If your target number is 11 you have a 50% chance of rolling 11 or better (results 11-20 * 5%). In 3E target numbers and bonus got a bit crazy (DC 30 on a d20?!?!) meaning you HAD to have bonuses to even have a decent % chance of making the roll. But if you have a +15 to your whatever skill, that suddenly becomes more important than the result of the roll (you will roll 20+ 75% of the time). As the bonuses grow, they "overwhelm" the result of the dice, making the die roll actually the least important part of the skill-check.


This is one of the big reasons I prefer the Earthdawn system. There is a unified dice mechanic that does not suffer this problem, as all dice can "explode", going up a rank gives you a new dicepool with better odds, and all character and monster abilities (saves, etc) run on the same "Step" scale.

Step..Action Dice
1......d4-2
2......d4-1
3......d4
4......d6
5......d8
6......d10
7......d12
8......2d6
9......d8+d6
10.....2d8
11.....d10+d8
12.....2d10
13.....d12+d10
14.....2d12
15.....d12+2d6
16.....d12+d8+d6
17.....d12+2d8
18.....d12+d10+d8
19.....d20+2d6
20.....d20+d8+d6
21.....d20+2d8
22.....d20+d10+d8
23.....d20+2d10
24.....d20+d12+d10
25.....d20+2d12
26.....d20+d12+2d6
27.....d20+d12+d8+d6
28.....d20+d12+2d8
29.....d20+d12+d10+d8
30.....2d20+2d6

I can't speak for finarvyn, but what I think he's saying matches something I've observed, so I'll talk about my own observation.

All game mechanics, no matter what sort of funky dicing mechanism the designer pulls out of his ass, follow an "S" curve probabilisticly. Let me explain.

Do we roll dice for every last thing? Eating? Walking? Breathing? Generally, no. Some things happen with certainty. 100%. Do we also roll dice for an ordinary human, unaided, to flap his arms and begin flying? No. 0%. If you chart this, with the horizontal axis representing skill at a certain thing (left being lower, right being higher), the vertical axis representing probability of that thing happening, because of the bounds of probability any skill higher than the point at which the graph touches the 100% bound will also yield a probability of 100%. Likewise for lower skills and the 0% bound.

Some RPGs for most uncertain actions (combat, etc) may include rolls that are "auto success" or "auto failure". This just means the graph goes horizontal at those probabilities instead. For instance, if you use a d20 system, then yes, the middle 90% of all results fall upon a linear slope. If '20' is auto success, then no matter how low the skill is, the probability is 5%. At the 5% bound, the graph is no longer sloping. It turns horizontal. Likewise on the other end. So the d20 mechanic as such is NOT truly linear. It still follows the 'S' curve, even if in a low-res, angular sort of way.

A lot of RPGs are designed to side-step this 'S' curve by placing severe limits on how high or low skill can be. 5E, for example, does not "cure" the problem of these bounds. The range of play in 5E, from level 1 to 20, is a proficiency bonus of 2 to 6, and the equivalent of AD&D's levels 3 to 7 in terms of, say, Fighter THAC0. On the other hand, 5E's hit points (again, in AD&D terms) range from level 1 to 29 (or higher for the likely case of above-average constitution).

I'm not sure this solves the problem. I guess it depends what you think the problem is. I first got on usenet in 1995, and the vast majority of the gripes I've heard about D&D in general (non-denominational) is that high level combat takes forever. High level characters are invincible to the point of killing suspension of disbelief. A high level character is better off diving head first from orbit than face a slightly superior foe. Each of these problems are only exacerbated by a system which nerfs skill while ramping up hit points. The "S" curve inherent in approaching or hitting the upper and lower bounds of probability, however, I've never had a problem with. I've heard very few complaints about this. And near as I can tell, it never actually causes a problem in play. Only in theory.

Quote from: Telarus;971185In 3E target numbers and bonus got a bit crazy (DC 30 on a d20?!?!) meaning you HAD to have bonuses to even have a decent % chance of making the roll.

It seems to me this solves the problem being discussed entirely. Some tasks just may not be possible at low levels with no bonuses. And some tasks that are chancy at low levels should be near rote at high levels -- which is what that +15 represents. Is the objection here aesthetic? Because high numbers are ugly?

Quote from: Telarus;971185But if you have a +15 to your whatever skill, that suddenly becomes more important than the result of the roll (you will roll 20+ 75% of the time). As the bonuses grow, they "overwhelm" the result of the dice, making the die roll actually the least important part of the skill-check.

That's true if the highest possible result is bound by the size of the dice, but again, I'm not sure I understand why that bound is necessary beyond the aesthetics issue.

Quote from: Lunamancer;971195Do we roll dice for every last thing? Eating? Walking? Breathing? Generally, no. Some things happen with certainty. 100%. Do we also roll dice for an ordinary human, unaided, to flap his arms and begin flying? No. 0%. If you chart this, with the horizontal axis representing skill at a certain thing (left being lower, right being higher), the vertical axis representing probability of that thing happening, because of the bounds of probability any skill higher than the point at which the graph touches the 100% bound will also yield a probability of 100%. Likewise for lower skills and the 0% bound.

Hm, I'm not sure we're charting all conceivable action, just all possible and uncertain action. If something isn't possible, or is perfectly certain, then maybe it's not part of this chart.

Quote from: Lunamancer;971195Some RPGs for most uncertain actions (combat, etc) may include rolls that are "auto success" or "auto failure". This just means the graph goes horizontal at those probabilities instead. For instance, if you use a d20 system, then yes, the middle 90% of all results fall upon a linear slope. If '20' is auto success, then no matter how low the skill is, the probability is 5%. At the 5% bound, the graph is no longer sloping. It turns horizontal. Likewise on the other end. So the d20 mechanic as such is NOT truly linear. It still follows the 'S' curve, even if in a low-res, angular sort of way.

If I understand correctly, even this slight curve is based on 20 being automatic success and 1 being automatic failure. Without that rule, the probability is flat again -- is that right?

Quote from: Lunamancer;971195I first got on usenet in 1995, and the vast majority of the gripes I've heard about D&D in general (non-denominational) is that high level combat takes forever. High level characters are invincible to the point of killing suspension of disbelief. A high level character is better off diving head first from orbit than face a slightly superior foe. Each of these problems are only exacerbated by a system which nerfs skill while ramping up hit points.

I can certainly understand where it would make sense to for defensive abilities to scale with offensive ones, and I've run into similar issues at high level. Surviving swimming across lava and such, using nothing more than sheer hit point totals.

Quote from: Zalman;971262Hm, I'm not sure we're charting all conceivable action, just all possible and uncertain action. If something isn't possible, or is perfectly certain, then maybe it's not part of this chart.

It's stating the obvious to head off the argument that games who deny the S-curve by truncating the extremes by pointing out, no, there are things even in such games which hit the 100% and 0% extremes. No amount of clever design can avoid this. Consider it a throw-away line if you need no convincing at absurd extremes.

QuoteIf I understand correctly, even this slight curve is based on 20 being automatic success and 1 being automatic failure. Without that rule, the probability is flat again -- is that right?

Without auto-success, the curve still changes from sloped to horizontal. Only it does so at 0% rather than 5%. Likewise on the other end. Without autofail, instead of going horizontal at 95%, it goes horizontal at 100%. AD&D 1st Ed gets a little fancier with the six repeating 20's in the hit tables. The slope goes horizontal at 5% for a very short time, then drops to 0% and goes horizontal again. It approximates asymptotic behavior at the zero bound more closely than either of the other options. So to answer your question, no, the changing of the slope, which technically makes d20 not a linear mechanic, is not dependent upon the particular rules of the RPG. It's a feature inherent with the bounds of probability.

I think the mistake in typical probability analysis in RPGs comes from the fixation on the raw numbers produced by the dice or stats rather than their practical effects on actual play. If I'm attacking AC 10 and I have THAC0 11, and we're playing with no auto-success, no auto-failure, my odds of a successful hit are 100%. It's tempting to think of THAC0 7 as being 4 points, or 20% better, and in many cases it is, but against the same defender with the same AC 10, the odds of success are the same 100%. Whereas the value of a +4 modifier when you're near the 50% mark really is worth 20%, beyond the 80% mark, the worth of the same modifier diminishes. Advocates of "curved" or multi-dice mechanics claim the so-called "linear" single die d20 mechanic lacks this feature. We see here that's not so.

QuoteI can certainly understand where it would make sense to for defensive abilities to scale with offensive ones, and I've run into similar issues at high level. Surviving swimming across lava and such, using nothing more than sheer hit point totals.

Well, let's take a look at scaling then.

Here are three ways to look at it. You'll have to take my word that this example is totally off the top of my head and not engineered to produce any particular conclusion, and I think the reasonableness of my assumptions on stats and magic items help lend credibility. So a level 3 fighter an 18/50 strength (+1 to hit, +3 damage) and a +2 longsword attacks a clone of himself who has AC 1 (+2 chainmail, shield, and -1 dex bonus) and 24 hit points (average hp per level assuming a 16 CON). Three average hits result in a kill. Odds of a hit are 35% each attack. So in terms of expected numbers, this is 9 rounds of combat. Store that in memory. 3 hits. 9 attacks, 9 rounds.

Fast forward. This same fighter is now 17th level, has acquired gauntlets of ogre power (raising his strength bonuses to +3 to hit, +6 damage), and he's upgraded to a +5 longsword. His clone also has upgraded gear, +5 chainmail and a +3 shield, giving him AC -5. He now has 2 attacks per round, dealing an average damage of 15.5 per hit, and a hit probability of 70%.

Question: If you wish to retain the 3-hit kill as your measure for scaling, how many hit points should he have?
Answer: Definitely more than 31 so that two average hits will fail to kill him. But definitely less than 47 so three average hits will suffice.
Question: How many hit points does 1st Ed actually give him on average?
Answer: 92 (128 in 5E). Double-to-Triple what scales. It's already high in terms of scaling hit counts. You don't want to make it higher.

Question: What if you want the 9 rounds to be your measure for scaling instead, then how many hit points should he have?
Answer: Somewhere between 174 to 195. About double what 1E gives him.
Question: And what if you want the 9 attacks to be your standard for measure (this is the measure that will probably most closely approximate how much table time this combat will take)?
Answer: Between 87 and 97.

Three measures. Wildly varying answers. But I think there's a really strong case here that AD&D nailed it perfectly. 5E would have been more like 6 attacks to kill at level 3, 28 attacks (equivalent hit prob would only be like 20%) to kill at level 17. No wonder why the battles are taking so long!

Might be worth noting that if 5E gave the fighter about 35 hit points without ever increasing the total, the combat would be about 9 attacks long both at level 3 and level 17. Also worth noting, that in 1E, the number of rounds the battle lasts tends to diminishes as power levels scale up. The number of blows exchanged doesn't change, the number of dice flying around the table doesn't change, but do you know what does change? The number of opportunities to cast spells.

Quote from: Lunamancer;971293Might be worth noting that if 5E gave the fighter about 35 hit points without ever increasing the total, the combat would be about 9 attacks long both at level 3 and level 17. Also worth noting, that in 1E, the number of rounds the battle lasts tends to diminishes as power levels scale up. The number of blows exchanged doesn't change, the number of dice flying around the table doesn't change, but do you know what does change? The number of opportunities to cast spells.

Wow, this is really zen. Never thought of it that way before! :eek:

I feel Enlightened in the Way of Gygax. :cool:

I think the "big sack of HP's" is meant to carry the Fighter through multiple battles without recovery, though (isn't it?).

Yes. And represent more and more skill at just not getting hit, and the gradual fatigue accumulating as they wear down.

Quote from: cranebump;971384I think the "big sack of HP's" is meant to carry the Fighter through multiple battles without recovery, though (isn't it?).

I interpret HP in AD&D1e as abstracting parries, too. As the fighter becomes more skilled and experienced (level goes up), they become better at hitting things (to-hit numbers change) and better at parrying (part of HP).

For comparison, in classic Traveller you only had so many melee attacks before fatigue set in and you had a malus to your rolls. Occasionally someone will write a system where fighting fatigues you, but there's usually some separate number to track, so it gets tedious and kind of takes you out of things; abstracting parries into another number works better in that regard. If you abstract it into armour then parries are infinite like attacks, if you abstract it into hit points then they're finite.

This is where someone pops up and says "yeah but you can't parry a fireball" and where we answer, as the DMG did at one point, that in the end it's a system for fantasy adventures, if we have fireballs and dragons and bullettes and so on, we can't really question it too much.

Quote from: cranebump;971384I think the "big sack of HP's" is meant to carry the Fighter through multiple battles without recovery, though (isn't it?).

I was answering a specific question of scaling. To apply that to what you're asking, it's harder to come up with a non-contentious example. I mean, an orc has hit dice equal to one-third of the 3rd level fighter's level. Should I find a monster with one third the hit dice of the 17th level fighter (so 5 and two-thirds hit dice) to do a comparison? Say, a wereboar perhaps?

HD 5+2, THAC0 15, AC 4. Avg hit points 25. It will have only a 5% chance of hitting the 17th level fighter. The 17th level fighter will have a 95% chance of hitting the wereboar. The only way the wereboar suvives two hits from the fighter is if both damage rolls are absolute minimal (only 1 in 144 chance of that). There's an 89.6% chance the wereboar is toast in round 1. The fighter automatically gets his first attack on round 2 before the wereboar goes, so it's less than 1% likely the wereboar will even get a second attack. If this fighter were walking down the road, fighting one wereboar after another one at a time, he'd probably survive 260 wereboars. But he'd probably contract lycanthrope by the 28th wereboar or so.

There's no way the 3rd level fighter will get through nearly as many orcs. So wereboar isn't a fair comparison. In order to find something that is, I'd have to figure out how many orcs the 3rd level fighter can get through, and then figure out which monster or group of monsters provide an equal challenge to determine what would be fairly "scaled up" from the orc. But if I did that, then we automatically know that, of course the fighter's hit points will have scaled up to last as many scaled up encounters.

Though one point this example does illustrate--instead of taking 260 wereboars to kill the character, it only takes 28 to kill his humanity. So you can see how these effects that don't have to deplete hit points really 10x the challenge pittily monsters pose to high level characters. With those odds, even a group of 3-5 wereboars is more than I'd like to risk a 17th level character on. Even a reasonable number of wereboars provides an obstacle, even if only as a deterrent.

Quote from: Lunamancer;971293Might be worth noting that if 5E gave the fighter about 35 hit points without ever increasing the total, the combat would be about 9 attacks long both at level 3 and level 17. Also worth noting, that in 1E, the number of rounds the battle lasts tends to diminishes as power levels scale up. The number of blows exchanged doesn't change, the number of dice flying around the table doesn't change, but do you know what does change? The number of opportunities to cast spells.

~MIND BLOWN~

However, I don't think your math is quite right on 5e.

I'll spare you the details, but I'm getting 3.77 DPA for third-level champion fighters. At level 17, if we mirror your assumption and the clone gets +3 armor while the original gets a +3 sword, it goes up to 9.15 DPA.

Level 3 fighter (14 CON) has 28 hp, down in 7.4 attacks. With Action Surge, that's ~6-7 rounds.
Level 17 fighter (16 CON) has 157 hp, down in 17.5 attacks. With Action Surge 2x, that's ~4 rounds.

So the number of rounds is down, but I guess not as much as in 1e. I know, I know, 5e is low magic, but who doesn't have any magic gear by level 17?

Edit: Details: http://anydice.com/program/c1de

Quote from: fearsomepirate;971710However, I don't think your math is quite right on 5e.

I'll spare you the details, but I'm getting 3.77 DPA for third-level champion fighters. At level 17, if we mirror your assumption and the clone gets +3 armor while the original gets a +3 sword, it goes up to 9.15 DPA.

That could be. I don't know 5E rules nearly as well as 1E. I think you forgot about the shield, though. I had the 17th level guy with a +3 shield. That was one of the things I observed. In any edition, defensive plusses stack more readily than offensive ones. As I recall, my numbers (which may be incorrect) had the 1E guy going from 35% hit prob, to 70% hit prob. Which I'm thinking that may have been a mistake as well. The hit prob in 1E probably should have gone to 95%, making combat go a bit quicker. And since I don't know 5E so well, I assumed beginning with a similar probability (not necessarily the same specifics in terms of ability scores and magic items--Strength and its bonuses work so very different in the 2 editions it wasn't worth trying to imitate that way). When I scaled up to level 17, I knew the 1E guy would gain 14 points worth in THAC0 while the 5E guy would gain only 4 points in proficiency bonus (at best--I don't have the exact levels in which the prof bonus changes memorized). The error of going 70% in 1E rather than 95% thus carried over since I just deducted 50 percentage points to account for the 10 point gap in attack skill between the two editions. If I were to redo it with the assumptions I had in mind, the 5E guy would have gone from 35% to hit up to 45% to hit while the 1E guy went from 35% to 95%.

QuoteLevel 3 fighter (14 CON) has 28 hp, down in 7.4 attacks. With Action Surge, that's ~6-7 rounds.
Level 17 fighter (16 CON) has 157 hp, down in 17.5 attacks. With Action Surge 2x, that's ~4 rounds.

This is where it gets dicey. I'm definitely not familiar with the little special abilities 5E characters get along the way (I considered it to be one of the major things that put me off to 5E). But that led me to leaving out something that I think really hammers my point home. Don't 5E fighters at a certain level start to regenerate 10 hit points per round whenever they are down by 50% or more of their hit points? If your 9.15 DPA is accurate, that's like ignoring a full attack and then some each round. I'm sure there are other offensive abilities as well that make doing the math on this a little trickier.

Quote from: Lunamancer;971721That could be. I don't know 5E rules nearly as well as 1E. I think you forgot about the shield, though. I had the 17th level guy with a +3 shield. That was one of the things I observed. In any edition, defensive plusses stack more readily than offensive ones.

5e does work somewhat differently. +3 armor and +3 shield is the highest you could get, and +3 armor is a "legendary" item (500,000 GP to make, and therefore 20,000 days of crafting by 17th level characters); +3 shield and +3 weapon are "only" very rare, at one tenth the cost. An attacker equipped with the best possible (for attack) legendary and very rare item would probably have a belt of storm giant strength (29 strength, so +9 to hit, +9 to damage) and a +3 sword (+3 to both). So, a 3rd level fighter is likely (point buy ability scores) to be +5 to hit (16 STR, +2 proficiency), and likely to defend with AC 18 to 21 (the latter if they take defensive fighting style and have plate armor and shield which is probably too expensive for a 3rd level character). The well equipped very high level fighter could have AC 27 (+3 plate, +3 shield, +1 defensive fighting style, from plate AC 18 and any shield giving +2) but would be +18 to hit (+6 proficiency, +9 from storm giant strength, +3 for the sword). So hitting on 13 to 16 in the first case and 9 in the second. In fairness the character could add three more +1 AC items like ring of protection but those seem to all require attunement so three is the limit (and the belt of giant strength also requires attunement). (A belt of storm giant strength is probably way more legendary than +3 plate armor, but a "merely" very rare belt of fire giant strength would drop the strength bonus by 2 to +7.) There are probably some other items that might modify this that I haven't thought of, and I'm ignoring potential advantage/disadvantage.

So defensive bonuses from items are potentially more common, but that's offset in that, meager as the increase in proficiency is from +2 at first level to +6 at 17th level, it is still an increase. And the fighter at 17th level has also gotten 6 ability score increases (or feats) by 17th level, so there's additional opportunity to increase beyond just proficiency but without adding a magic item, through strength increases; less so for defense because dexterity doesn't help with heavy armor and is bounded at +2 for medium armor.

Of course it's up to the DM whether the various items can be made (unlikely just from the time required, but that could be moved downward) or found.

QuoteThis is where it gets dicey. I'm definitely not familiar with the little special abilities 5E characters get along the way (I considered it to be one of the major things that put me off to 5E). But that led me to leaving out something that I think really hammers my point home. Don't 5E fighters at a certain level start to regenerate 10 hit points per round whenever they are down by 50% or more of their hit points? If your 9.15 DPA is accurate, that's like ignoring a full attack and then some each round. I'm sure there are other offensive abilities as well that make doing the math on this a little trickier.

An 18th level champion gets Survivor, which adds 5+CON bonus to hit points at the start of their turn if they have greater than 0 HP but no more than half their hit points. The fighter also gets Second Wind at 1st level, which adds d10+level HP as a bonus action once per short or long rest. At 15th level, the champion gets critical hits (doubling damage dice but not other bonuses) on 18 to 20. Extra attacks are added at 5th and 11th level (and again at 20th level). Action surge at 2nd level (for another action in a round), and a second at 17th level but can't use both in the same round.

With the very well equipped characters above, hitting on a 12 with maximum defensive items in use but +12 damage to a one handed weapon doing d8, I see average damage per attack as 45% of 16.5, so 7.425, multiplied by three per round for the extra attacks not counting the extra critical hits which would add 4.5 points on 15% of hits, so 8.1 per attack on average and 24.3 per round. So 4.36 rounds to chew through the defensive character's base hit points of 10+16*6=106, and another 3.5 to 4.9 rounds to chew through the likely CON bonus (20 CON and possibly the Tough feat for +2 HP per level, so 85 to 119 HP), and finally 0.88 rounds to chew through the average of 21.5 hit points from second wind. Two uses of action surge reduce this by one round each by repeating the three attacks in two separate rounds; total of 6.74 to 8.14 rounds.

For the 3rd level champions, critical hit on 19 to 20; one action surge, no extra attack, second wind of d10+3; taking +5 to hit and AC of 19 (defensive fighting style but only the starting equipment of chain mail). Hitting for d8+3 damage with 35% chance once per round, plus an extra 4.5 in 10% for the criticals, gives 3.075 damage per round; likely HP are 22 for 3rd level (10+6+6) and 6 more for 16 CON over three levels, and 7.5 for second wind: with one use of action surge to reduce the time by one round, that gives 10.54 rounds.

A hill dwarf defender would get an extra HP per level, and a half-orc attacker would get an extra die of damage on critical hits, but obviously the only possible race for both of these champions is spherical cow. What are we trying to demonstrate again? Yes, slightly shorter fight so fewer chances at high level to throw as many spells, but the 3rd level caster allies don't have ten plus spells, and the 17th level caster allies have some spells that would slow down the fight (e.g., heal for 70 points to extend the fight by almost three rounds) but mostly spells that would end things more quickly -- the rate of combat damage probably doesn't determine the length of the fight at 17th level, unless spell slots are really running low.

Note: And I neglected to consider the attacker's possible fighting styles like dueling for +2 damage per hit (or reducing defense to get more damage using a two handed weapon or two weapon fighting - giving up a +3 shield for additional damage seems a mistake, though), or feats like Defensive Duelist or Savage Attacker. Correcting for these (and finding my errors) is an exercise left to the one person other than me in the entire world who cares, if that person exists.

I'd probably give the representative 5e Fighter-18 a +2 weapon, +1 armour, +1 shield. +1 ring of protection - those are all Rare items - never seen giant strength girdle yet so I'd keep STR at 20. IME 5e PCs tend to go through most of their career with just bits & bobs of +1 stuff unless there's a specific quest for powerful items. NPCs don't routinely carry any gear since there are no magic items on the Individual Treasure rolls, and Hoard rolls rarely turn up what you want. If items are commissioned from NPCs or crafted by PCs, following the rules (DMG pg 129) only up to Rare stuff is at all practical - at 5000gp, 25gp of crafting per day, that's 200 man-days to craft, which can be reduced by multiple workers (level 6 casters). Very Rare such as +3 weapons and +2 armour needs 2000 days and spellcasters of 11th+ level, so you generally can't get groups working on them.