What are the practical limits of d20+mod vs DC?

[Herremann the Wise]

The expected value of d20+X = 10.5 + X.

Therefore, DC - 10.5 is roughly comparable to X. Let's call that value D.

I would say that the game works best when D is within +5 or -5 of X, giving a 25% to 75% chance of success.

So the DC of an action should be between 5.5 and 15.5 points higher than the mod.

I remember Ryan Nock (RangerWickett) mentioning from a study or some such that the common expectation of success is about 65%. This translates to any number 8 or higher on a d20 roll being successful for a common task performed under pressure. I think this is a pretty good base to work from, varying it either way for easier or more difficult tasks.

Best Regards
Herremann the Wise

 

[Crazy Jerome]

Modifiers
The interesting question I have now is looking at two polar uses of the DC skill system. What do you do with a skill that is almost purely about physical or mental capacity (almost completely reliant on the ability modifier) and one that is almost all about training where the ability modifier has a little effect (such as the most esoteric knowledge)? What things go into the modifier of such skills? What things go onto a modifier?

I think the best way of dealing with this, and staying within the system is to break every modifier down into 5 things. I'll use the athletic pursuit of swimming as an example:

- Ability: The ability modifier will always have an effect. Strength would be the main attribute here.
- General Experience and Capacity: This refers to how good the character is athletically in a general sense. Gross motor skills are the order of the day here.
- Specific Experience or Capacity: This refers to whether the character has any particular capacity in swimming versus other athletic pursuits such as climbing or running or jumping.
- Equipment: This refers to objects or things that may assist such as flippers or buoyancy apparel but also to things that may hinder such as armor or bulkier apparel. [For a melee skill, a masterwork sword might provide a +3 bonus where as a dull used sword may provide a -1 penalty or worse.]
All of the above do not stack within themselves (you may remember this CJ from the other thread). A +3 general bonus from one general source and a +2 general bonus from a different source do not stack.

- Special: This is your circumstance bonus, magical bonus, or holy bonus or what have you. All of these "special" bonuses do stack. The trick is that Special bonuses are usually derived from transitory rather than permanent effects. This is the best way to have variety, while keeping things balanced and having the capacity to strictly enforce modifier caps on each of these five modifier sources.

Interesting. I can't award XP to you right now.

So if I am reading this correctly in relation to your whole post, a "master" will only be able to get the necessary +20 mod (or part of it not covered by "special") via that specific experience, most of the time, because the other stuff won't be that high, and won't stack. A godlike character might have the correct attribute. A real master of a wide-spread area, like athletics, might achieve it that way. And I guess a legendary artifact could do this in the equipment category. Most characters won't be any of these things, and thus mastery will only come with specific skills. Is that right?

BTW, I'm not looking for a particular way to apply this to my own system. I'm more interested in everyones' general view on what works here and what doesn't, so as to delve into the ideas behind those views. Your post was still very helpful, though.

 

[Janx]

That tracks pretty consistently with what I have observed in Hero System and GURPS. Using the 3d6 versus a DC, the mods can rarely exceed -3 to +3. In Hero, this is even baked into some of the standard numbers, where 11 is considered the baseline, and 8 and 14 are the standard outer edges, representing success chances of 25%, 65%, and 90%.

I do like my baseline somewhere closer to the 2/3 success mark, though I understand people have argued for 50% to 75% or so.

GShamster has some interesting math.

I would have surmized, that for a d20, bonuses ranging from +1 to +10 seem like they're OK. Which is basically half the die size.

Once you get over +10, you eliminate the significance of the the lowest roll vs. the easiest DC

So easy DC of 10, when you got +10 is an auto-success (ignoring 1 as auto-fail).

the problem gets worse as the + goes up. Because the + dominates the value of the total, as it contributes to the die roll.

To sum up, when the modifer is worth more that the die roll, the glitch in the mechanic is revealed.

 

[prosfilaes]

Once you get over +10, you eliminate the significance of the the lowest roll vs. the easiest DC

So easy DC of 10, when you got +10 is an auto-success (ignoring 1 as auto-fail).

the problem gets worse as the + goes up. Because the + dominates the value of the total, as it contributes to the die roll.

To sum up, when the modifer is worth more that the die roll, the glitch in the mechanic is revealed.

I find it interesting you think that a problem. In real life, there's a number of skills I have where I would have no problem on any problem that a novice might have a chance at. Math and computer science, mainly. On the other hand, my sister can scramble up cliffs with no problem, whereas if you asked me to climb the same cliff with the standard collection of whatever they use (nutcrackers? bottle-openers?) I'd have no chance. And she's an amateur; there are people who routinely do climbs that would be nigh impossible for her.

 

[Janx]

I find it interesting you think that a problem. In real life, there's a number of skills I have where I would have no problem on any problem that a novice might have a chance at. Math and computer science, mainly. On the other hand, my sister can scramble up cliffs with no problem, whereas if you asked me to climb the same cliff with the standard collection of whatever they use (nutcrackers? bottle-openers?) I'd have no chance. And she's an amateur; there are people who routinely do climbs that would be nigh impossible for her.

Thats a fair point. But it might also be impacted by time and pressure. Given a reasonable chunk of time, I can figure out anything on a computer that a novice may struggle with (which may in fact be why they called me).

That's kind of like taking 10.

Wheras climbing a wall has a bit more riding on it. Falling hurts.

My theory is just a guesstimate, but for DCs 10-30 and a cap of +10 leaves room for auto-success and really hard.

it also allow the d20 itself to contribute meaningfully to any bonus or DC combination in that range.

Once the + gets over 10 is where stuff starts getting silly. As the OP noted, +30 or so is definitely silly.

 

[Dannager]

The size of the die is not the issue. At all.

The issue is the compound effect that character options (like feats, for instance) have on specialization. A 1st-level character's ability to specialize is very limited, while a 20th-level character's ability to specialize is very large. If those characters choose to act on that ability to specialize, the DC system will break down at about the same point no matter what your die size is.

To illustrate, if at 1st level the difference between no specialization (no character options invested in that particular skill) and full specialization (every character option possible invested in that particular skill) is five points, then you might decide to use a d10 for your core mechanic because it handles the influence of random chance for your range fairly well. But if your characters then reach level 20 and the difference between no specialization and full specialization is 30, your d10 no longer serves you well if you want to keep chances of success/failure fairly static (note: this isn't necessarily desirable!). But you can't change it to a d50 (or whatever), because if you did then your 1st level characters' choices in terms of skill investment would matter very little.

The only impact die size has is on how much of a given check's success depends on chance. The larger the die size relative to the median and spread of the DCs (not the size of the DCs), the bigger the role that chance will play.

Again, size of die type doesn't really matter, in terms of when the system will break down. Size of bonuses doesn't really matter, in terms of when the system will break down. The gradual increase in the specialization gap that is the result of an accumulation of character options as level increases is what's important.

And, really, none of this is inherently a bad thing. Continued investment of character options in specialization should be rewarded. The only danger lies in allowing a specialized character to perpetually "pick his battles" in such a way that he is only ever faced with challenges that play to the strengths of his specializations.

 

[FireLance]

Mind you, there are other ways to play with d20+mod vs DC instead of simply increasing the modifier and the DC.

What 4E has called "brutal" dice (with respect to rolling for weapon damage), i.e. allowing for a re-roll if the result is below a specified number, is another possible way to tinker with the probabilities. Let's say that skill allows you to re-roll results that are below your "skill level"; if you have a skill level of 5, say, than a roll of 1-4 on a d20 is always disregarded. Effectively, you will always get a result of between 5 and 20, and are rolling 1d16+4.

Assuming no other modifiers (and a DC cap of 20), this means that success is never impossible even for an unskilled character, but highly skilled characters will succeed more often, possibly even automatically.

An unskilled character would succeed on a DC 10 check about 55% of the time. A skill 5 character, would succeed about 75% of the time (12/16) and success would be automatic for a skill 10 character.

EDIT: Past a certain point, it becomes more efficient to simply change the die type instead of re-rolling the d20. At skill 9, you might as well be rolling 1d12+8, for example.

 

[Herremann the Wise]

Interesting. I can't award XP to you right now.

So if I am reading this correctly in relation to your whole post, a "master" will only be able to get the necessary +20 mod (or part of it not covered by "special") via that specific experience, most of the time, because the other stuff won't be that high, and won't stack. A godlike character might have the correct attribute. A real master of a wide-spread area, like athletics, might achieve it that way. And I guess a legendary artifact could do this in the equipment category. Most characters won't be any of these things, and thus mastery will only come with specific skills. Is that right?

Just to expand further to frame my concepts.

I would break skills into two levels, the general and the specific. At this point, I would have the general skills as follows:

Base Source Orientated Skills
- Martial [Melee]
- Martial [Ranged]
- Divinity
- Casting
- Spirituality

Base Personal Skills
- Agility
- Adventuring
- Athletics
- Communication
- Deftness
- General Knowledge
- Lore
- Perception

The chance of accruing mastery in any of these 13 categories is highly unlikely. To achieve a +20 modifier in any of these without including the benefit of the "specific" bonus mentioned upthread would seem beyond the realm of mortals and into that of Legends. It is only in a specific pursuit of one of these general skills that would include the specific bonus such as for example the previous "swimming" in athletics as against the other specific skills in athletics: climbing, jumping, running etc. The character might still have a +14 Athletics (which flows through to each of these specific climbing, jumping and running skills), but the +6 specific bonus on swimming takes the total to +20 and the mastery level previously mentioned.

An interesting further application is in a highly populated and diverse general skill such as Martial [Melee]. Garnering a high level of proficiency/mastery in using axes might get you a +4 Specific Axe Bonus as well as a +6 Specific Greataxe bonus. If the character's Melee [Martial] modifier is +14, they have a +14 bonus when using a mace, +20 when using a Greataxe [Mastery] but a +18 when using different sorts of axes.

A further application is for skills highly reliant on ability such as jumping, agility based specific skills and so on. These skills can (by acquiring a certain feat or ability) replace their usual specific bonus with a further ability modifier (usually through spending some sort of additional resource such as action points or a more generic version of "surges"). This modifier might be a repeating of the base ability (str for jumping) or if suitably flavoured, it might involve a different ability (dex for jumping). In this way, you can have adrenalized "moments" of mastery for skills heavily ability modifier reliant.

As such, there are a few options for characters but typically, it comes down to the slow accrual of different and sometimes synergistic skills.

BTW, I'm not looking for a particular way to apply this to my own system. I'm more interested in everyones' general view on what works here and what doesn't, so as to delve into the ideas behind those views. Your post was still very helpful, though.

Cool.
I still like to think that the statement "A master can automatically do what the novice finds impossible" and ones like it the best guides as to what numbers make sense and what numbers do not. For example, you could then define Godhood as automatically doing what the master finds unachievable. In this case, this "epic" sphere of DCs between 41 and 60 might have some level of meaning. Achieving what the gods find impossible? Well who knows what type of entity we are talking about then and what relation they have to a game is beyond my faculties.

I suppose the scale in terms of each of these spheres or "tiers" is hard-coded by the use of a d20.

Best Regards
Herremann the Wise

 

[Herremann the Wise]

The gradual increase in the specialization gap that is the result of an accumulation of character options as level increases is what's important.

For a relative system, I agree that it is the "gap" that has the greatest effect on play and the greatest determination of whether something "feels wonky" at the table during play.

For an absolute system, what breaks or "wonkifies" it would seem to be something slightly different. I'd say the biggest culprit here is the 3e Fort/Reflex/Will save system. Through a highly irregular modifier system that when multi-classing can simultaneously supercharge some saves while completely unaffecting others, the modifiers never seem to correctly relate the character's level and experience to their capacity for saving against certain effects. The half-level system of 4e while being an efficient sledgehammer that would straighten out the irregularities if applied to 3e's save system, perhaps does not have the finesse some (such as myself) are looking for. My point being that the mechanics for creating total modifiers had issues, rather than the scope and spectrum of the raw DC/core mechanic of 3e/4e.

Another 3e culprit was synergy bonuses. I think most of us met the 2nd level diplomacy monster in some form. Again I think this was a case of neat idea but poor execution. PF "fixed" this by stripping synergy bonuses completely from the system using more refined mechanics through feats to weigh such bonuses at more appropriate points in a character's development.

And just on another point, I think the following is still one of the great ideas when talking about DCs.

Table: Difficulty Class Examples
Difficulty (DC) Example (Skill Used)
Very easy (0): Notice something large in plain sight (Spot)
Easy (5): Climb a knotted rope (Climb)
Average (10): Hear an approaching guard (Listen)
Tough (15): Rig a wagon wheel to fall off (Disable Device)
Challenging (20): Swim in stormy water (Swim)
Formidable (25): Open an average lock (Open Lock)
Heroic (30): Leap across a 30-foot chasm (Jump)
Nearly impossible (40): Track a squad of orcs across hard ground after 24 hours of rainfall (Survival)

The 3e DMG was much better (p31) but the SRD approximates it.

My favourite is still the final entry of p31:

DC: 43
Description: Track a goblin that passed over hard rocks a week ago, and it snowed yesterday.
Key Ability: Survival (Wis)
Who could do it: A 20th-level ranger who has maxed out his survival skill and has been fighting goblinoids as his favored enemy since 1st level.

Pure Awesome Sauce!!!

The overall idea is brilliant. The breakdown in my opinion as I highlight above came from the mechanics not universally following the guidelines.

Best Regards
Herremann the Wise

 

[pemerton]

Interesting topic.

I don't think I've got a lot to add on the maths front, but I do have some views on how modifiers contribute to play.

From experience, I think that fiddly modifiers arising from manipulating the fiction don't necessarily add a great deal directly to the play experience. For example, when a player declares that his/her PC is going to walk a tightrope, I'm not sure that it adds a great deal to play to have the player announce "I change out of my boots into my special slippers" in order to get a +2 bonus (or eliminate a -2 penalty) or whatever. (Of course, these fiddly adjustments can matter to the maths, but I'd probably rather get those mathematical elements from somewhere else.)

On the other hand, I find in 4e that daily utilities that grant significant modifiers (eg the paladin's Wrath of the Gods (? I think that's it) utility that grants everyone +CHA to damage) are interesting, because (unlike changing your footwear, or pulling out your special piton hammer) they have a resource management dimension to them (in the case of Wrath of the Gods, for example, it is a daily, and it affects only allies in a limited area, and used during a combat that suddenly turns out to be harder than anyone thought it woudl be, it sucks a minor action).

What I have found, in running 4e, is that multiple checks embedded in the fictional situation go a long way to making play engaging, and smoothing out issues of big bonuses vs small bonuses. For example, if winning a social skill challenge requires 4 successes on Diplomacy, then even the PC whose Diplomacy bonus is (or is close to) an autosuccess still has to engage with the fiction 4 times in order to win, and that creates the possibility for interesting things to happen (eg in order to motivate the second or third check, perhaps the PC offers a concession).

I find that fictional positioning of this sort can also be more fun than fiddly modifiers for dealing with things like slippers and pitons. Instead of encouraging scrounging for bonuses, which can quickly become tedious, use the fiction to help shape the unfolding consequences of failure and success. This means that climbing barehanded rather than with rope and line doesn't necessarily become more likely to fail, but has different (but not necessarily worse, in some absolute sense) consequences for failure.

Does any of that make sense?