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.
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