Hitting the to-hit sweet spot

(This post continues a discussion I started in “What does D&D have to do with ironclad ships?”)

Through the evolution of Dungeons & Dragons, the game uses two mechanics to determine an attack’s damage output: to-hit rolls and damage rolls.

In D&D, hitting is fun, while missing feels like a bummer, particularly if you waited a while for your turn. Why not remove misses from the game?  Once characters gain enough hit points to survive a few attacks, D&D could drop to-hit rolls and─with a few adjustments─still work.

Skipping damage rolls

Back in the third-edition era, Jonathan Tweet advised dungeon masters to speed high-level fights by substituting average damage for rolled damage. In fourth edition, first-level characters have enough hit points to make this approach possible at any level. In a The Dungeon Master Experience post, Chris Perkins explains how he uses nearly average damage plus 1d6, added for a bit of flavor.

The Chivalry & Sorcery game (1977) skipped damage rolls, assuming “that the damage inflicted by a particular weapon in the hands of given character will be more or less constant.”

The notion of dropping to-hit rolls may seem strange but here’s the crux: Against high hit points, to-hit rolls just turn into another damage-reduction mechanic. In fourth edition, everyone but minions has fairly high hit points and everyone hits about 60% of the time. The damage dealt in combat would work out about the same if we just assumed everyone always hits and multiplied everyone’s hit points by 1.67.

Of course, your to-hit percentage varies from a set percentage, because armor can make hitting more difficult. How can a system without to hit rolls account for armor class? In my post, “The brilliance of unrealistic hit points,” I explained how hit points in D&D function as an ingenious damage-reduction mechanic. Virtually every tabletop role-playing game that aimed for realism made armor reduce damage. In our hypothetical rules variant, why not use D&D’s damage-reduction mechanic to represent protective armor? Suppose different types of armor multiplied your hit points. Suppose high dexterity increased hit points, giving more ability to “turn deadly strikes into glancing blows,” just like the game says.

Does abandoning to-hit rolls seem crazy? It has been done.

Tunnels & TrollsTunnels and Trolls (1975) stands as the one early system that defied RPG hobby’s early mania for realism. Ken St Andre, T&T’s designer, aimed for greater simplicity. T&T drops the to-hit roll entirely. Combatants simply weigh damage rolls against each other. Like Tunnels & Trolls, most RPG-inspired video games seem to drop anything equivalent to a to-hit roll. The damage simply rises as you click away at your enemy.

Drawbacks of always hitting

While undeniably simpler, and probably about as realistic as D&D, the you-always-hit approach suffers three problems:

  • Especially with ranged attacks, rolling to hit fits real-world experience much closer than assuming a hit and skipping straight to damage. Technically speaking, skipping the to-hit roll feels bogus.
  • The two possible outcomes of a to-hit roll offer more drama than the mostly-average damage roll.
  • The to-hit roll provides intermittent, positive reinforcement to the process of making an attack.

You know all about positive reinforcement. It makes you stay up late chasing one more level when you should be in bed. Reinforcement that randomly rewards a behavior is more powerful than reinforcement that occurs every time. In a casino, the best bet comes from the change machines, which pay 1-for-1 every single time. Intermittent, positive reinforcement drives people to the slot machines. As the Id DM might say, “The variable ratio schedule produces both the highest rate of responding and the greatest resistance to extinction.” In short, hitting on some attacks is more fun than hitting on every attack.

Although D&D uses a d20 roll to hit, the game plays best when the odds of hitting stand closer to a coin flip. At the extremes, the math gets strange. For combatants who almost always hit, bonuses and penalties become insignificant. For combatants looking for a lucky roll, small bonuses can double or triple their chance to hit. Also, the game plays better when your chance of hitting sits around 60%. When your nears 95%, the roll becomes a formality. When your chance dwindles toward 5%, then the to-hit the roll feels like a waste of time, especially because beating the long odds probably still earns minimal damage.

When the chance of hitting stays between, say, 30% and 70%, the game reaps play benefits:

  • The to-hit roll provides intermittent, positive reinforcement to the process of making an attack.
  • Many attacks can hit and inflict damage, providing constant, positive feedback to players while everyone contributes to the fight.

So D&D designers face the challenge of arranging to-hit bonuses and armor classes so to-hit rolls require a result between a 6 and 14, a precious small sweet spot for all the levels, magic, and armor classes encompassed by the game. In practice, designers like to push your chance to hit toward the top of the 30-70% range, because while missing remains part of the game, it’s no fun.

The Palladium Role-Playing Game (1983) recognized the play value of the to-hit roll, but it avoided D&D’s problem of finessing to-hit bonuses and armor classes to reach a sweet spot. The game simply declares that “any [d20] roll above four (5 to 20) hits doing damage to the opponent.” Armor in the game takes damage, effectively serving as an additional pool of hit points.

In upcoming posts, I’ll discuss the very different steps the D&D Next and 4E designers took to find the to-hit sweet spot.

Next: Riding the power curve

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One Response to Hitting the to-hit sweet spot

  1. Matt Miller says:

    This talk of a ‘sweet spot’ does make me wonder about the abandonment of 2d6 in Chainmail (or replacing 1d20 with 2d10). It fell by popular acclaim. Yet 2d6* provides a very nice ‘sweet spot’**. Hitting on a 5+ would give you about 70%, and hitting on a 9+ would give you 30%. It also has the nice property that the relative value of a +1 bonus is variable: It’s more valuable to the weaker character than to the stronger. Adding an additional +1 to your +2 does less for your chances than adding a +1 to your -2. It’s one of the things I really like about FATE–the closer the scores are, the more a +1 bonus matters.

    **Rolling opposed d6’s would have the same effect, assuming +1 bonus to the defender).

    *For 2d6:
    2 or 12: 1 in 36
    3 or 11: 2 in 36
    4 or 10: 3 in 36
    5 or 9: 4 in 36
    6 or 8: 5 in 36
    7 or 7: 6 in 36.

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