D&D without To-Hit Rolls

I feel like whenever I preface a post with, “I don’t expect this to be a long one,” it ends up being a long one. I’m going to avoid jinxing myself and get to the point. Here is a simple method to remove to-hit rolls from your dungeony dragony game, but perhaps coming from a different angle than other articles or rulebooks have suggested.

1. Roll a monster’s hit dice, each 1-6, and multiply by two [1].
2. Damage rolls are from 1-6 minus armor class, which can be anywhere from 0 to 4.

• Alternatively, owing to Ty of Mindstorm: Armor classes are descending from 6 to 2, and damage rolls must be less than or equal to armor to deal damage indicated.

Knock on wood!

Motivation

I wanted to look into this because I’ve been working, yet again, on a ruleset for my white whale project The Brimstone Gospel. There are three ability scores, and the average of all three is equal to the character’s level. This allows me to roll hit dice to find a character’s level (e.g. for a monster) and directly find their stats, with some extra randomization if desired by the referee.

I wanted to define # HP as the sum of two ability scores, bios and psyche. If an ability score is equivalent to rolling hit dice, that would mean that (on average) a character’s # HP is double what it would be in any other ruleset. Is it feasible? Having done the analysis below, I think so! There are other things I want to experiment with, like having constant damage rather than random damage, or using square roots of a character’s ability score as their bonus to damage and other things. That’s all outside the scope of this, though, so I won’t get into it. Instead, I’m assuming usage for more typical D&D fare.

There are, of course, other games that don’t have to-hit rolls. Into The Odd popularized the move away from to-hit rolls, and even uses subtractive armor like I suggest here. However, the monsters it gives have preset HP values, and this makes them difficult to use with existing bestiaries etc. that list HD instead. Errant also has only damage rolls, but monsters converted from D&D materials have increased HP to represent their AC, and player characters wear armor to reduce damage rolls by die size (e.g. 1-6 to 1-4) rather than by subtracting integers. Both rulesets simply require overhead math prior to a game to convert materials, or else require effort on the referee's part.

What I suggest here is totally compatible with existing D&D materials without even having to convert anything, save for a different scale of AC which wouldn’t be unfamiliar to anyone who’s poured over pre-D&D character rulesets before. The goal is just to be quick about it.

The Math

I’ve discussed the math for to-hit rolls at length before [2] [3]. For most D&D-like rulesets that have to-hit rolls, the base chance to hit an opponent is 55% (e.g. rolling d20 ≥ 10). This means that for every 1 HD ≈ 3.5, a character with the base AC has a virtual HP of 3.5 / 0.55 = 6.36, where virtual HP represents how many damage rolls a character can take before dying while accounting for damage rolls that “equal” zero due to failing the to-hit roll. Virtual HP increases exponentially as AC improves and the corresponding to-hit chance decreases.

Multiplying a monster’s hit dice roll by two accounts for the effect of the base to-hit chance on a character’s longevity expressed as virtual HP. A goblin of HD 0.5 can have an HP of {2, 4, 6}, or an average of 4 HP. An orc of HD 1 can have an HP of {2, 4, 6, 8, 10, 12}, or an average of 7 HP [4]. An large gold dragon of HD 12 will have on average 84 HP. You can see that judging by these possible HP scores, they basically account for the ~50% chance to hit by having double the typical HP.

Subtractive Armor

You can account for armor without fussing with HP scores. Instead, with armor that subtracts from damage rolls made against the character, you reintroduce the prospect of virtual HP except in one roll. Let’s suppose possible armor classes from 0 to 4, with zero being no armor (*alternatively, 6 to 2 as mentioned above*).

1. Leather Armor OR Shield
2. Chainmail Armor OR Leather Armor AND Shield
3. Plate Armor OR Chainmail Armor AND Shield
4. Plate Armor AND Shield

For a damage roll of 1-6, 1 HD at 0 AC has a 25% of being depleted for its possible scores {2, 4, 6, 8, 10, 12}. For different values of AC, each subtracting from 1-6 down to nil, it has lower chances of getting depleted. Look at how nice the fractions turn out!

1. 16.67% (1/6)
2. 11.11% (1/9)
3. 5.56% (1/18)
4. 2.78% (1/36)

I am representing this differently than with virtual HP because I can’t fathom how to represent it that same way (rather than percentages, we’re replacing options on a die roll with zero). Still, you can tell that as AC increases, an individual HD’s longevity also does.

Comparison with Usual AC

Here are equivalent percentages for to-hit rolls where hit dice are simply 1-6 as are damage rolls, and thus any damage roll has a 58.33% chance of depleting a single hit die at a 100% chance “to-hit”. I have attached the equivalent descending and ascending AC values for a character without any bonuses.

• 55% TH (AC 9 [10]) → 32%
• 50% TH (AC 8 [11]) → 29%
• 45% TH (AC 6 [12]) → 26%
• 40% TH (AC 5 [13]) → 23%
• 35% TH (AC 5 [14]) → 20%
• 30% TH (AC 4 [15]) → 18%
• 25% TH (AC 3 [16]) → 15%
• 20% TH (AC 2 [17]) → 12%

It seems that the method I suggest is somewhat more punishing on a per-HD basis. This, to me, is totally fine and to be expected. Still, being worried, I compared my results to the later convention of rolling 1-8 for HD instead of 1-6, against which a damage roll 1-6 has only a 43.75% chance of depleting.

• 55% TH (AC 9 [10]) → 24%
• 50% TH (AC 8 [11]) → 22%
• 45% TH (AC 6 [12]) → 20%
• 40% TH (AC 5 [13]) → 18%
• 35% TH (AC 5 [14]) → 15%
• 30% TH (AC 4 [15]) → 13%
• 25% TH (AC 3 [16]) → 11%
• 20% TH (AC 2 [17]) → 9%

Looking at this, I don’t think my method is unusually punishing towards characters or overpowering of armor! In fact, I sort of like that a character of HD 1 and leather armor has a 1-in-6 chance of getting defeated on the first hit. Besides, I think when it comes to characters who do not yet have fighty bonuses, it encourages thinking outside of combat mechanics, but it doesn’t feel as hopeless as a missed to-hit roll does either.

Damage Bonuses

Monsters could have +1 for every three HD. This way, a monster of HD 12 has a bonus of +4.

If you want progression by character level: fighters gain +1 every three levels up to +4; clerics +1 every four levels up to +3; mages every five levels up to +2.

A net +1 against an opponent has a 72% chance of depleting their hit die. For +2, 83%. For +3, 92%. For +4, 97%.

Damage bonuses thus have very obvious effects, more so than to-hit bonuses are thought to have [5].

Generic Monster Writing

Since this method is, except for the AC scale, compatible with all sorts of D&D materials, I wanted to take some time to develop a vocabulary to write monsters for adventures and bestiaries et cetera without being constrained to the mathematical interface of any one ruleset. All these materials really work with the same fictional ideas, so let’s just call them what they are in the world of the game.

• Humanpower: Usually called HD; the measure of how many human beings a creature is as powerful as. Two goblins are as powerful as one human being. One orc is as powerful as one human being. One dragon is as powerful as ten human beings. Et cetera.
• Defense: In medieval fantasy, there are 4-5 degrees of armor or equivalent protection: like skin, like leather, like chainmail, like plate mail, or stronger. Using a scale of eight different AC values obfuscates the comparison being made between a suit of armor and a dragon’s scales. If a monster has something like a shield, say so.

Those two things are the only numbers that really matter, and there’s no reason those numbers should be specific to any one ruleset. What they really represent is a base level of power (i.e. HD) and a relative degree of protection (i.e. per HD), respectively.

Everything else, the important stuff, is up to description. This isn't to suggest that game materials can be wholly 'agnostic' with respect to the play they imply by their content or structure, but we can make them a great deal more flexible by using descriptive language rather than definitions with respect to any one ruleset.

 

[1] Alternatively, let each HD give 6 HP; this is just below the average of 2 × {1, 2, 3, 4, 5, 6}.

[2] https://chiquitafajita.blogspot.com/2021/08/comparisons-of-combat-rules-in-tabletop.html

[3] https://chiquitafajita.blogspot.com/2021/11/effects-of-armor-class-on-character.html

[4] Of course, if HD rolls are simply doubled and HD are not instead rolled twice, a result of 7 HP is impossible and so that average is only theoretical.

[5] I have argued before that to-hit bonuses are indeed impactful, especially since they tend to be given in +2 or +3 when leveling. See the above posts [2] [3].