Falling off the RNG

‘Falls off the RNG’ is an expression many designers use to describe designs that cause two characters of comparable power to have large enough differences that they exceed the size of the random number generator (RNG, usually dice in a tabletop RPG).  At this point it is impossible for the lower-score character to defeat the higher-score character on the relevant check.  It can be impossible to find a challenge that one will find interesting (i.e. some chance of success and some of failure) that the other either will not fail automatically or succeed automatically.

Many people consider this a bad design.  I am no longer convinced.

Comparing Existing Editions

I will start with a summary comparison of three editions of Dungeons & Dragons.  I am not so familiar with D&D 4e so I had help from Nik (thanks Nik!), D&D 3.x I’m quite familiar with but stuck mostly to core, AD&D 2e I have not played in somewhat over a decade but do still have the books handy.

The details behind the values described below (‘showing the work’) can be seen in Falling off the RNG (Heavy Lifting).

Measure D&D 4e D&D 3.x AD&D 2e
Attack Bonus, different classes Within a few points for standard attack; slightly lower for attacks targeting defenses other than AC At high levels, varies greatly (+36 vs. +14) At high levels, varies greatly (+29 vs. +10)
Attack Bonus, different levels Changes over time, slowly (between +1/2 levels and +1/level) Changes over time, will be more than +1/level for full martial classes Changes over time, a little more than +1/level for full martial classes
Armor Class, different classes Within a few points, usually At high levels, varies somewhat (about 10 points for ‘obvious efficient’ builds) At high levels, varies somewhat (about 10 points for archetypal builds)
Armor Class, different levels Changes over time, slowly (between +1/2 levels and +1/level) Changes over time, a little more than +1/level Changes over time, about 1/2 levels (mostly from magic)
‘Save Defenses’, different classes Usually within a few points, hard to get big differences.  Usually a few points lower than Armor Class N/A N/A
‘Save Defenses’, different levels Changes over time, slowly (similar rate as Attack Bonus).  Usually a few points lower than Armor Class N/A N/A
Save Bonuses, different classes
N/A At high levels, varies greatly (+26 vs. +13 for ‘decent, obvious’ build) At high levels, varies moderately (11 vs. 4 is biggest difference between classes)
Save Bonuses, different levels
N/A Changes over time, a little more than +1/level for optimized defense, about half that for optimized but poor defense Changes over time, about 1/2 levels
Skill bonuses, different classes Trained characters average several points higher, always, than untrained, and can do a little bit more with them. At high levels, huge differences (30+ points between skill ranks and ability score differences), even before magic or Skill Focus Nonweapon proficiencies are modified ability score checks, so trained can make checks and untrained usually cannot, or do so at a penalty.  Differences not very huge.
Skill bonuses, different levels Changes over time, slowly (similar rate as Attack Bonus) Changes over time, a little more than +1/level for optimized, about half that for crossclass development, not at all for untrained. Little change over time (spending an additional NWP slot gives +1 with the check).
Save DCs, different classes N/A At high levels, can vary somewhat.  Highest-level abilities are usually 10+level/2+ability modifier (spells may generally be around DC 28). At high levels don’t usually vary much.  Most are a flat save DC determined by target class and level
Save DCs, different levels N/A For your ‘good powers’ they climb a little more than +1/2 levels. Higher-level effects may apply penalties to saves (effectively increasing DCs) but these are usually fairly small.


  • What were ‘saving throws’ in previous editions are now defenses in D&D 4e.  Attacker must overcome them with an attack check, and there is no ‘save DC’.  What are now called ‘saving throws’ (duration-ending checks) have a fixed DC.
  • AD&D 2e has generally quite small ability score modifiers (+1 or +2  at scores of 17 or 18) and it is uncommon to permanently improve ability scores, so I am basically ignoring their effect.

What This Means

Dungeons & Dragons 4e

As far as I can see, in D&D 4e you can expect at-will powers to be fairly consistent across all classes at any given level.  Each class has about the same bonus relative to the targeted defense (fighter is weapon attack vs. armor, wizard might be a magic attack vs. Reflex), and damage for these attacks is usually a function of weapon (or 1d8 for magic — which is standard weapon damage) plus ability score modifier.  In other words, everybody hits about as often and about as hard, when they use their good powers.

Encounter and daily powers can be somewhat better than the at-will powers, and in different ways.  However, I will assume for now that they are roughly equivalent in value between classes and that the summary of the math above still holds (a power that targets Reflex will have a slightly lower attack bonus than one that targets Armor Class).  Given that each class gains encounter and daily powers at the same time, I’m going to consider this a wash.

I think this is about as mechanically balanced as I think you can get.  You can expect that efficient play (in an obvious manner, too) will result in much the same result regardless of class, and that this happens at all levels.

Advanced Dungeons & Dragons 2e

This is the second-simplest case.  The relatively low impact of ability score differences compared to D&D 3.x and the relative lack of magic bonuses limits how big the differences get.  The only thing that solidly falls off the RNG is attack bonus — at high levels the Fighter can hit things the Wizard cannot.

On the other hand, the high-level Wizard should not be trying to hit these things.  The Fighter has three places he shines: the ability to hit things, the ability to avoid damage (good AC and saves), and the ability to soak damage when he can’t avoid it.  The Wizard, on the other hand, can target weaker defenses (things requiring saving throws, with partial effect even on a save), can avoid damage by not being there (fly to get out of range, dimension door or teleport to be somewhere else altogether, invisibility to not be seen and targeted, and so on).  Oh, and warp reality (using wish is an obvious way).

AD&D 2e does not really try for mechanical balance, but instead develops characters with stronger archetypes that should approach situations in different ways.

Dungeons & Dragons 3.x

I saved this one for last because I think it is the most complex of the three to summarize.

On the face of it, at high levels D&D 3.x is perhaps the most mechanically imbalanced of the three games.

  • Attack bonuses?  Fall off the RNG.
  • Armor Class?  Not really close, but still on the RNG (you can expect about ten points difference).
  • Saving throws?  Can fall off the RNG (I assume Darwin the Merciless collects those who allow that to happen), but I think most people end up investing in a standard kit (ability score buffs and the best cloak of resistance they can find) in order to prevent it.  However, while +26 vs. +13 is still technically on the RNG, it isn’t by very much.
  • Skill checks?  Trained vs. untrained isn’t even close.  At 20th level you can expect some 30 points of difference between someone optimized for a skill (really good ability score modifier, Skill Focus, 23 ranks can easily push the check over +30 even without a magic item) and someone not (net modifier of -1 for a substandard ability score, no ranks, no Skill Focus).
  • Save DCs?  Actually not often so large in differences because people who have abilities that have save DCs tend to have high DCs, and everyone else doesn’t even have the ability to require saving throws (Wizards have lots, Fighters basically have none whatsoever).

I can understand why many people didn’t like this and moved away from it.

Why Falling off the RNG is not Necessarily Bad

And now to the meat of the post.

In some of the cases above, falling off the RNG is, I think, actually somewhat desirable.  Consider the differences above.

Differences by Level

This was a bit of a trick and was included mostly to show differences in the power curves.  As far as I’m concerned difference by level — regardless of the curve — is something I want to see.  If my players’ high-level characters are scared by bog-standard orcs, I think something isn’t right.  They should be concerned about armies of orcs or that dragon demanding tribute of the barony (not from the barony, of the barony) after it let them live last time.  High-level characters are more capable and imposing than low-level characters?  Good.

Differences by Class

In most areas described above (attack bonus, Armor Class, saving throws) I have become fairly comfortable with the differences.  It did take some adjustment to my thinking, though.

Let’s take saving throws, since I have talked about saving throws in detail before.  Recalibrating saving throws so the ‘poor’ saves become the baseline works pretty well, I think.  ‘Normal’ characters of that level are less likely to die because of it (and thus might not need to optimize as much — DC 19 for a spell when you have +7 to your save isn’t laughably hard, though you might want a bigger bonus).  The moderately optimized character with +21 to his save (Cleric Will save, Rogue Reflex save, Barbarian Fortitude save) can only fail on a 1 (and honestly, I’d probably ditch this rule), and at this point I am completely comfortable with it.  This is one of the benefits of the build.

Armor Class, there are too many ways to get around it (touch attacks and saving throw-based powers), and honestly I’d like to see them toned down (for instance, losing touch attacks altogether and let casters with ranged touch attacks add the spell level to their attack roll — with similar mechanisms for other creatures with touch attacks).  The cost of maximizing Armor Class (four +5 items, Dexterity 16+, and limited movement) is immense, it should be worth something.

Attack bonus can span more than twenty points and falls off the RNG, but honestly I don’t think this is truly a problem.  Let it — and calibrate most opposing Armor Classes to be somewhere in the middle, such as an Armor Class at 20th level of between 30 and 36.  The Cleric will hit about half the time, the Rogue a little more, and the Fighter almost certainly… which gives the opportunity to spend attack bonus on other things.  Power Attack.  Combat Expertise.  Iterative attacks (he can certainly hit once, probably hit the second time, has a decent chance the third, and might on the fourth).  The Rogue doesn’t have the almost certain hit but has the remaining three (and does a little better with them if he can flank).  The Cleric is not as effective at hitting as the Rogue, but is still a threat.  The Wizard is unlikely (needs a high roll) but has so many other offensive options that it is hardly worth worrying about.


Through much of the D&D 3.x era I have been told that being a skill monkey sucks.  While at the same time the skills system falls off the RNG, hard.  These sound to me like they should solve each other — let skills fall off the RNG.  A twentieth-level character can have more than +30 on his strong skills.  He literally cannot fail DC 30 checks.

According to Wikipedia, the world record long jump is 8.95m — 29.36 feet.  If the character above were optimized for Jump, he would exceed this Taking 0… and would generally do about ten feet more, and could do up to twenty feet more on a good day.  At the same time, at the peak of his arc he would be (7.5/10/12.5 feet) off the ground — most of the time, he will also exceed the world record high jump.  He doesn’t really threaten the world record pole vault, that’s a little over twenty feet.

Unlike attack bonuses, Armor Class, and saving throws, skills are close to being binary abilities at high level.  You can either do them, or you cannot.  There are places where you cannot expect to compete between worst and last (you are almost two RNGs apart).  I do not see a way to reconcile this within the D&D 3.x model (which is a large part of why I don’t try to in Echelon d20).  I have seen an analysis at Hack & Slash (the ‘Skill Deconstruction’ series with regard to D&D 3.x) that suggests that most skills as written could either be rewritten or dropped.  Given the difficulties I see here I would be tempted to park the entire skill system and overhaul it.

Closing Comments

All in all I think the problem with spanning the RNG is not that you can fall off it or be able to adequately challenge characters who are at one end or the other of the range.  I think the problem lies in too much being calibrated to challenge the people at the high end, who paid for the ability to be good at the ability in question.

  • Targets that require Fighter-calibre combat training in order to hit will freeze out those lower down (who still have options that let them be quite effective), while leaving nothing extra for the Fighter to work with.  Realigning target Armor Classes so they are moderately challenging to the moderately-capable gives the Fighter to meaningfully use extras (such as iterative attacks, Power Attack, and so on) to improve his lot.
  • Armor Class differences are not as great as attack bonus, but do fall outside the range just described.  I might be tempted to trim them down (four different magic bonuses that stack — armor, shield, natural, and deflection — is a bit much).  I don’t mind this so much because the differences in practice aren’t generally even this big because of the extreme cost (monetary and opportunity) in developing them.  That kind of investment should have some kind of payoff.
  • Saving throws calibrated so the ‘poor saves’ are the baseline mean that having good saves is a nice thing, instead of a necessity.
  • Skills… you fall off the RNG, but I think they work better as binary abilities anyway.  I would be prepared to live with it for now, until I could review and replace the subsystem.  The problem here does not, I think, lie with the range of skill check bonus.

I am no longer comfortable saying that the spread over the RNG and falling off the RNG is truly a problem.  Placing too much emphasis on the high end shuts out less-capable characters and reduces the amount of awesome available.  Placing emphasis in the middle can let the characters who are supposed to be good at the activity actually be good at it (such as the Fighter who can expect to hit his opponents almost always) while characters not so good at it may find it difficult or even hard enough that other options should be found.  Placing emphasis at the bottom end (as with saving throws) means you can have most characters be ‘good enough’ a lot of the time, while those who are really good really are that good (the Barbarian who can safely drink most mundane poisons or handle pestilent materials without concern because he is that robust).

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1 Comment to "Falling off the RNG"

  1. tussock's Gravatar tussock
    January 28, 2012 - 7:43 pm | Permalink

    Yeh, the epic fighter that can’t miss and almost can’t be hurt just seems right (given what the Wizards are doing), like the high level AD&D Thief with 99%+ to all his skills who just does it all (even if the Wizard can too, at least a few times).

    To some extent, it’s about what purpose is still being served by any failure chance for those high level characters who might fall off the good end. Even with opposed checks, is there really any point to stopping the Fighter disarming a Wizard? Is there a need for that same Fighter to stop the Rogue being a successful sneak once shadow-walking is in play?

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