Nature vs. Nurture: Another Edition Comparison

In researching my previous article regarding the "fun zone" of the D20, I learned much more than I expected about how the various editions of D&D calculated to-hit probability. The two major factors are a PC's natural ability reflected by bonuses from their stats, and a PC's experience reflected by progressively better to-hit charts, THAC0, base attack bonus, or proficiency bonus depending on the edition. What I find fascinating is how much influence each factor (natural ability vs. experience) contributed in each edition. 

Probability of an Ability Score

I've included the probability of a PC attaining a given range of Strength using the most common stat generation method for that edition. For instance, when playing with the Greyhawk supplement, I expect ability scores to be generated by rolling 4d6 for each stat and noting the sum of the best 3 dice. By this method I calculate a 48% probability that a PC would achieve a Strength of at least 7-12, a 43% probability that a PC would attain Strength 13-16, etc. The way the stats are obtained varies by edition and in attempting to replicate the most commonly used method for each I used the following:

 Obviously the option to re-arrange stats significantly improves the probability of obtaining a higher score for a specific ability. In our case I assume the Fighter PC would put their best score in Strength.

Here is the data followed by a brief analysis and my personal preferences.

Natural Ability

In OD&D, natural ability played virtually no role in hit probability - the exception being very low or high Dexterity granting -1 or +1 to ranged attacks. But starting with the OD&D Greyhawk supplement, natural ability bonuses begin to trickle in. The bonus is usually no more than +1 for most PCs, but 5% might attain +2 and less than 1% will achieve the extraordinary bonuses of +3 or +4. AD&D makes adjustments to this already wonky distribution but the probabilities of PCs obtaining the requisite scores to get those bonuses ends up almost exactly the same, even factoring in that AD&D usually allowed PCs to re-arrange their stats. This distribution continues through 2nd Edition AD&D but has a caveat that will disappear in B/X: 

"Strength also aids the fighting man (emphasis mine) in his ability to both score a hit upon an adversary and damage it. This strength must be raw, i.e. not altered by intelligence scores. On the other hand low strength will affect any character’s fighting ability."

B/X normalizes the -3 to +3 range of bonuses, slightly inflating their effect on all abilities, but also applies them equally to the melee attacks of any PC class. Classically, BX generates stats by rolling 3d6 in order so the odds of a bonus or penalty greater than +/-1 is still fairly small (<5%).

3E grants a +1 bonus for every 2 pips an ability score is above 10, thus 16 grants +3 and 18 grants +4, significantly increasing the influence of natural abilities while also making them much more likely to be attained. 93% of PCs will have at least a +2 bonus, 57% a +3, and 9% will obtain a +4 bonus from natural ability alone. Also, 3E allows PCs to put 1 point into an ability score about every 4 levels.

5E is the weird one. The initial stat generation almost exactly mimics 3E, but includes ability score adjustments due to race. Then, 5E allows PCs to put 2 points into ability scores every 4 levels, and Fighters specifically gain this feature two additional times at 6th and 14th level. This means your Strength is only your starting Strength and a Fighter that improves their Strength at every opportunity could gain a +1 bonus to-hit at 4th, 6th, and 8th level until their Strength peaks at 20, just from improving their natural abilities.

Bonuses Due to Level

In OD&D, class level was all that mattered to hit. But as a PC's natural abilities begin to play a larger role, the bonuses from experience must diminish to keep the math reasonable. In a way, what's old becomes new again. The earliest editions make improvements to-hit in a stepped fashion, fighters in steps of 3 levels. Each band or tier of levels grants improvements of 2-3 pips per band, so OD&D and B/X slightly lag behind the linear progression of AD&D and 3E. The 5E designers, perhaps realizing a linear progression is much too fast, return to banded progression with a proficiency bonus improvement of 1 pip every 4 levels while also reducing inflation since PCs are likely to attain natural abilities of 18-20 (+4 to +5).

To me this is a vast overcorrection. I appreciate that 5E maintained the 3E model of ability scores playing a larger role mechanically and differentiating characters statistically. But for a PC's bonuses to stay relatively static I think I disagree with the design decision to make experience play such a small role. Proficiency in 5E starts at +2, or a 10% improvement over non-proficient PCs. But to then only improve by 5% once every four levels is bonkers to me.

Is it reasonable that an untrained (no proficiency, +0) human with super-strength (20,+5) has the same fighting capability in melee that a 5E fighter of average strength (10,+0) will not attain until 6th level (+3 proficiency, +2 from assumed ability score improvements applied to Strength at 4th and 6th level)? Granted, a PC or NPC with Strength 20 is incredibly rare, and a PC with a Strength of 10 is not likely to choose to be a fighter. But the core question remains - at what point should experience and training overtake natural ability?

My Preference

In light of my previous article I firmly believe the most fun at the table is had when target numbers after bonuses are applied generally stay centered on the d20: between 5 and 15. With that in mind I would make a design effort to have very few total bonuses reach, let alone exceed +10 at the top tier of the game. So under that assumption - how much should come from natural ability vs experience? I think experience should overtake natural ability fairly quickly so my preference would be bonuses of up to +2 or +3 from natural ability, and up to +7 to +8 from earned experience.

I also believe a linear progression is much too fast so I would like to see something akin to Greyhawk or B/X ability bonuses, with a stepped progression of bonuses due to experience. Therefore I can get behind 3E or 5E for low level play, but for mid-tier and above I think OD&D+Greyhawk or B/X have the right balance of rewarding progression and maintaining difficulty.

D20: The Fun Zone

What range of probability of success produces the most fun in an RPG? I assume over the course of a single adventure, the difficulty of monsters and encounters should vacillate, but generally trend upward as the climax approaches. Also, as PCs gain experience they generally become more capable. What was once difficult becomes easier and formerly impossible challenges become attainable. But what range of target numbers is ideal and how does that range change as the PCs improve?

To answer this question I analyzed the typical attack bonus of a human fighter and the subsequent d20 rolls needed to strike foes ranging from unarmored to full plate and shield over the various editions of D&D. This is not meant to fuel edition wars. Rather, the product of this analysis should approximate the expected probability of success for common die rolls in that edition - and lend us some insight into how often the designers of that edition thought the PCs should succeed - i.e. what probability of success is the best combination of fun and challenging? Hopefully it will help you determine your own preferences.

Assumptions

I compared levels 1-10 and assumed the fighter has a Strength of 16 at the outset. This may be uncommonly strong in the 3d6-in-order tradition of early editions but pedestrian, if not underpowered, in the 4d6, stack-with-a-racial-bonus, and arrange-to-taste preferences of modern players. But hopefully it's a fair middle point to illuminate trends. For now I also ignored magic weapons and extraordinarily armored foes. I hope to provide a follow-up analysis factoring in the recommended levels at which these are obtained and encountered.

OD&D: The 3 Little Brown Books (LBBs)

In OD&D no character class is granted any bonuses or penalties "to-hit" from Strength. The combat matrix simply specifies what each class must roll to hit each AC at a given band of levels. Fighters improve their "to-hit" by 2 or 3 pips every 3 levels. AC 9 is unarmored while AC 2 is full plate and shield.

Fighter Level	D20 To-Hit AC 9-2
1-3	10-17
4-6	8-15
7-9	5-12
10-12	3-10

OD&D + Greyhawk

With the addition of the Greyhawk supplement we see the first indication of a fighter's Strength improving their likelihood to-hit, with 16 granting a +1 bonus. Thus the d20 rolls required to hit ACs 9-2 are improved by 1.

Fighter Level	D20 To-Hit AC 9-2
1-3	9-16
4-6	7-14
7-9	4-11
10-12	2-9

Basic/Expert D&D

In B/X we see the normalized -3 to +3 distribution of ability bonuses. Here a 16 Strength grants +2 to-hit. Note that at the highest tier this is the first time we see the rule "unmodified attack rolls of 1 always miss". Otherwise the final entry would read [1-8] and a 10th level fighter could never miss when attacking an AC 9 unarmored opponent.

Fighter Level	D20 To-Hit AC 9-2
1-3	8-15
4-6	6-13
7-9	3-10
10-12	2-8

AD&D 1E/2E

Advanced D&D dials back the to-hit bonus from natural abilities. Strength 16 grants +1 damage, but no bonus to-hit short of Strength 17. An unarmored opponent is AC 10 in AD&D while a fully armored foe is still AC 2. However, instead of improving every 3 levels, fighters improve their to-hit (or THAC0 in 2E) linearly by 1 pip per level. Note that a 10th level fighter only need roll a 1 to hit an unarmored foe - effectively they cannot miss.

Fighter Level	D20 To-Hit AC 10-2
1 2 3	10-18 9-17 8-16
4 5 6	7-15 6-14 5-13
7 8	4-12 3-11
9 10	2-10 1-9

3E

3rd Edition has effectively the same progression, granting fighters +1 base attack bonus per fighter level, but also +1 to-hit per 2 points of Strength above 10. Thus Strength 16 grants +3 to-hit and if ability score improvement points at levels 4 and 8 go to Strength, then by 8th level the fighter would have Strength 18 with a bonus of +4. Also note that 3rd edition uses ascending armor class where an unarmored opponent still has a base AC of 10, but a foe in full plate and shield is AC 20. Already at Level 6 we require the same rule as B/X or the fighter becomes unable to miss and at level 10 he will hit AC 20 75% of the time. We quickly see why 3rd Edition and it's descendants are considered plagued by "runaway bonuses" and high level play regularly sees ACs and target numbers well into the 20s to continue challenging the PCs.

Fighter Level	Strength (modifier)	Base attack bonus	D20 To-Hit Ascending AC 10-20
1	16 (+3)	+1	6-16
2	16 (+3)	+2	5-15
3	16 (+3)	+3	4-14
4	17 (+3)	+4	3-13
5	17 (+3)	+5	2-12
6	17 (+3)	+6	2-11
7	17 (+3)	+7	2-10
8	18 (+4)	+8	2-8
9	18 (+4)	+9	2-7
10	18 (+4)	+10	2-6

5E

In 5E, Strength 16 still grants a bonus of +3. But in place of a linear base attack bonus we have a proficiency bonus that starts at +2 and increases by +1 every 4 levels as part of the "bounded accuracy" design. Also, 5E allows for regular ability score improvements as part of normal level progression - even more frequently for fighters - so we raise the fighter's Strength to 18 at 4th and to 20 at 6th level. They would gain even another improvement at 8th level but 20 is the maximum allowed for PCs. 5E seems to do an excellent balancing act, not striking the artificial bottom of the target range until level 9, and yet maintaining the need for double-digit rolls to strike a formidably armored opponent.

Fighter Level	Strength (modifier)	Proficiency bonus	D20 To-Hit Ascending AC 10-20
1-3	16 (+3)	+2	5-15
4	18 (+4)	+2	4-14
5 6-8 9-10	18 (+4) 20 (+5) 20 (+5)	+3 +3 +4	3-13 2-12 2-11

Analysis

There are a few ways we can analyze this data. Averages are difficult given the varying methods of progression but the the shift in target numbers at low levels, the rate of progression from experience, and the overall upper and lower limits tell an interesting tale.

Low Levels (1-3)

Clearly at low levels the game has gotten much easier. Where OD&D and AD&D demanded d20 rolls of 10-18, each subsequent edition chipped away at a fairly consistent rate of about 1 pip each. By 5E a low level fighter need only roll a 5 to hit an unarmored commoner but still needs to roll in the mid-teens to hit a fully-armored opponent. This seems to indicate that it's not particularly fun to fail more frequently than you succeed and that even a low level PC should still be a cut above normal humans. The downside is this leaves less room for improvement before either an automatic hit or automatic miss on a natural 1.

Mid Levels (4-6)

Prior to 3E, mid-level play finds most of its target numbers between 5 and 15, perfectly centered on the D20. 3E and 5E trend slightly easier, only requiring rolls of 2 or 3 to hit unarmored opponents, and again a 6th level fighter in 3E would automatically hit if not for the rule that natural 1 is always an automatic miss.

Upper Levels (7-10)

At the upper end the game appears broken, hence the need for the rule that a natural one is always a miss. Only OD&D (pre-Greyhawk) and 5E still require double digit rolls to hit formidably armored opponents at this tier. Every other edition requires only single digit rolls, with 3E only requiring a 6 to hit a fully-armored, AC 20 foe. It may not be obvious that a 10th level 3E fighter's +14 to-hit is broken, after all 10th level should be formidable, but recall that 3E and 5E are designed to allow for play up to 20th level. Where is there room for improvement?

To be fair, TSR editions also allow for play beyond 10th level - the LBBs suggest a convoluted way to compute requirements and the BX expansion into BECMI adds levels 15-36 and beyond - but PCs beyond "name level" are considered extraordinarily powerful, likely taking many years of play to achieve. Name level - that is Lord for a 9th level Fighter, Wizard for an 11th level Magic User, and Patriarch for an 8th level Cleric - is typically where domain play is introduced. The PC can construct a stronghold, generate income, and attract followers.

All this is to say I think TSR D&D makes some assumptions about a change in the general mode of play around 10th level, where I would argue WotC D&D assumes a PC is still going on adventures, just of a larger magnitude. They're likely saving the world from hellish fiends or the universe from destruction by evil gods - opponents with ACs in the 20s or 30s.

No matter the edition, at this tier PCs succeed far more often than they fail against non-extraordinary opponents which fairly reflects the improvements gained by their experience. The question is, is it still fun? Perhaps - but the game must change in one of two ways to do so: domain-level play or extraordinary threats. Either the game shifts to focus on politics, income, raising armies, and fighting wars, or the ultra-capable, demi-god PCs require other-worldly, mythic, immortal, cosmic-level threats to fight.

Conclusions

The trends seem to show that low level play was too difficult and subsequent editions increased the baseline probabilities of success. Even a low level adventurer is more fun to play if they're a cut above the riffraff. Mid level play generally finds target numbers evenly spread around the midpoint of the D20 and only slightly trends easier against poorly armored opponents. Unarmored commoners have almost no business avoiding the business end of your blade should you set upon them. High level play finds PCs succeeding at nearly every mundane task but doesn't seem to be particularly fun without an extraordinary challenger or world-ending threat.

To me, this seems to support the informal consensus among players and polls done by WotC that mid-tier play is the most fun. If that is true, then our data indicates there could be some encounters that only require very low rolls (2-5), but the majority of target numbers after bonuses are applied should fall in the 5-15 range for a consistently fun challenge. Perhaps this should come as no surprise.

In the end, whatever your d20 game of choice, it will likely be the most fun if you manage to stay within the bounds of the d20. Too high of a probability of success and perhaps you shouldn't even be rolling. Rolling only to avoid a fumble doesn't sound particularly fun. There's little indication of any edition thoroughly exercising the upper bounds of the d20 (perhaps the saving throw charts of TSR editions) but when the target is that high, whether AC or a saving throw, the situation is bound to be interesting. Food for thought...

Other Factors: AC go down. HP go up.

One final note, while we see a trend of the game getting easier in terms of probability of success, the designers clearly recognize the need to maintain the longevity of a fight and give a consistently satisfying encounter experience. How is this addressed? Unfortunately, the answer is Hit Point inflation. Starting with Greyhawk and then B/X, fighters and monsters receive d8 hit points per HD instead of d6. Not a huge deal. But then in 3E and 5E we see even larger HD sizes and when combined with ability bonuses to Constitution, hit point totals start to skyrocket for players and monsters both. A red dragon in B/X has 45 hit points. In 3E and 5E an adult red dragon has over 250... What!?

If hitting the monsters more often is more fun, but we don't want all the monsters to die in a single round, boosting HP is the obvious solution. The unfortunate side effect is dangerous baddies become truckloads of hit points and combat devolves into a slog-fest. Note that typical weapon damage hasn't changed much since Greyhawk. Multiple attacks and bonuses from magic weapons make an effort to keep up, but hardly at the rate HP inflates across editions. Monsters especially don't seem to possess the number of attacks or damage output required to truly threaten a party. I can think of few better ways to deflate the tension in a game than taking turns reliably hitting, but only chipping away at buckets of hit points. To me, the opposite would be far more fun. Only a fool in 3E+ would wade into battle with single digit hit points, even fully armored. In OD&D or B/X though? You'd stand a chance of surviving with a high AC. Huge risk/reward.

Re-rolling Individual Initiative, the Best of Both Worlds?

 This is an idea I can't take credit for, but writing the post on group vs individual initiative has me chewing on it. By traditional methods this appears to only add book keeping - the annoying part about initiative. But perhaps there's a way to keep it simple enough while still introducing the gleefully chaotic tension of re-rolling from round to round. Here's some ideas.

1. Secret countdown.

The situation: The party is sneaking up on a dragon currently asleep on it's hoard of treasure. Rather than steal as much as they can carry (and perhaps due to the righteous paladin and cleric) they've decided to attempt to slay the beast. However, the wizard has just fallen in a pit trap...!

DM: Roll for initiative! Ok counting down: 25, 24, 23...

Rogue: 23! I sneak up on the dragon from my hiding spot and stab him in the ribs!

Resolve mechanics and narrate results.

DM: 22, 21, 20, 19... The dragon wakes from its slumber, bellows in anger, and breathes fire on the intruders!

Resolve and narrate.

DM: 18, 17, 16, 15, 14, 13...

Paladin: 13! But I'm unconscious from the dragon's breath. Here's my death saving throw...

DM: 12, 11...

Wizard: 11! Who knew I'd be glad to be in a pit trap when the dragon woke? Whew! I cast clairvoyance to see what's going on above me...

DM: 10, 9, 8, 7...

Cleric: 7! I'm still conscious after the dragon breath so I climb through the smoking wreckage to heal the paladin...

Get it? Not only will the durations of spells that last for a round or more start to vary a bit (combat and magic should be more chaotic than orderly, no?) but the initiative roll of a paralyzed or unconscious combatant gains tension due to its influence over how the round plays out!

2. Declare Actions

Yet something else that appears to add overhead to the combat round. However, if you allow the players a bit of time to plan before rolling initiative (just like you might in group initiative), declaring actions means all the players at least have a Plan A when their turn comes around. Plus, the fictional value can't be understated. You know how in a movie the hero sees the bad guy going for his gun? Well if they're quick enough they might be able to do something...

The situation: The party has freed the prince from the dungeons beneath the hobgoblin fortress when the jailer stirs awake and shouts for help. Minutes later the chieftain and his retinue stand between the party and the exit.

DM: The chieftain knocks a feathered arrow the size of a small ballista on a bow that may need giant-strength to draw. His priest chants, gathering black magic in blood-smeared hands preparing to cast a spell, and his bodyguards draw razor-edged iron to charge. Discuss and declare actions. You have one minute.

Party discussion happens.

Cleric: Ok, the paladin will charge into melee with the chieftain and attack, the rogue is going to shoot an arrow from the shadows to interrupt the priest, the wizard will conjure a wall of flame to block off the bodyguards, and I will prepare a blessing for whoever needs protection.

DM: Excellent, roll for initiative! Ok counting down: 25, 24, 23, 22, 21, 20, 19... The chieftain draws the heavy bow and looses at the wizard!

Party: Noooooo!

Resolve mechanics and narrate.

DM: Counting down. 18...

Cleric: Whoa 18! I bless the wizard with protection from evil!

DM: 17, 16...

Wizard: 16! Casting the wall of fire is interrupted by the chieftain's arrow. I still try to get the spell off with the cleric's help...

DM: Make a concentration check with advantage - the DC is half the damage taken.

Wizard: Success! Barely. Thank you cleric.

DM: Count 15... The priest casts his blight upon the paladin. Make a save to resist the effect...

DM: 14, 13, 12, 11, 10, 9, 8... The guards roll saves to reduce damage from the wall of fire and check morale to see if they press through or retreat...

DM: Count 7...

Rogue: 7! I fire my arrow at the priest, too late to interrupt his spell.

DM: Paladin, you're left...

Paladin: Dang. I furiously charge the chief and attack with my greatsword!

DM: Great! Next round, discuss. You have one minute...

3. Use a d10

Ok counting from 25 down to 0 is a lot. Also the range of a d20 relative to initiative bonuses might be a bit too random - tough for the casters to know what the state of the battlefield might be when their spell goes off and dexterity should maybe be more reliable of an indicator. How about we roll a d10 instead?

The situation: As above

DM: The chieftain knocks a feathered arrow the size of a small ballista on a bow that may need giant-strength to draw. His priest chants, gathering black magic in blood-smeared hands preparing to cast a spell, and his bodyguards draw razor-edged iron to charge. Discuss and declare actions. You have one minute.

Party discussion happens.

Cleric: Ok, the paladin will charge into melee with the chieftain and attack, the rogue is going to shoot an arrow from the shadows to interrupt the priest, the wizard will conjure a wall of flame to block off the bodyguards, and I will prepare a blessing for whoever needs protection.

DM: Excellent, roll for initiative! Ok counting down: 15, 14, 13, 12, 11...

Rogue: 11! I fire my arrow at the priest... and hit!

DM: The priest rolls to maintain their spell - and fails! The blight spell fizzles!

DM: Count 10... The chieftain draws the heavy bow and... hits the wizard! Roll to maintain your spell...

Wizard: Success! Barely...

DM: Ok, counting down again. 9...

Cleric: 9! I bless the paladin with protection from evil!

DM: 8, 7...

Wizard: 7! Reeling from the chieftain's arrow, I conjure a wall of fire to seal off his guards!

DM: The priest also rolled a 7 and would cast blight simultaneously, but it fizzles due to the rogue's arrow.

DM: 6, 5, 4... The guards roll saves to reduce damage from the wall of fire and check morale to see if they press through or retreat...

DM: Paladin, you're left...

Paladin: Dang. I furiously charge the chief and attack with my greatsword!

DM: Great! Next round, discuss. You have one minute...

4. Held actions

Finally we should recognize the complication of an archer wanting to hold a drawn arrow until an enemy emerges from cover, a healer wanting to hold their spell, or a fighter waiting with axe raised in ambush. I think you could allow players to name a trigger for their action, or allow them to simply hold their turn until they choose to go before the end of the round. I wouldn't attempt to codify it too much. Let the fiction and common sense drive your ruling.