Diceless Pathfinder Combat Mechanic

Question

I have been working on a diceless combat mechanic for Pathfinder (it could be applied to any system in which combat involves a roll to hit and a roll for damage, but Pathfinder will be used for examples) which applies basic concepts of probability theory.

Since every dice roll has an expected value (E[1d6]=3.5, E[1d8]=4.5, etc), every weapon has an expected value for damage. By determining the probability of hitting, we can determine the damage of a given attack by multiplying the probability of a hit by a weapon's expected value.

This leads to a diceless attack mechanic. When an attack is declared, rather than rolling for attack and damage, the attacker would automatically deal damage to the defender based on his expected damage and probability of hitting.

For example, a character wielding a weapon that does 1d8 damage (or 4.5 damage) attacks a goblin. He needs to roll an 11 or higher on a d20 to hit the goblin. Thus when attacking, the character would automatically deal 0.5*4.5=2.25 damage to the goblin (rounding up or down depending on preferences).

I know this would remove critical hits from the game. Perhaps characters could hold critical tokens based on their level, traits, etc which they could spend to attain a critical hit (which could mean double damage, the maximum dice value of damage, weapon's expected damage not multiplied by probability, or something along these lines).

I'm also not sure how this could be applied to saving throws vs death, sleep, etc where there is no expected value of damage, but simply hit or miss.

What other side effects, advantages, or downsides would this averaging method have on gameplay? It's likely some game out there has done similar in the past. Does any one have any experiences playing in a system like this and can report on its effect in play?

Answer 1

The suggested mechanic uses similar maths that optimisers use to build combat-focussed characters. Also White Dwarf magazine presented an optional Monster Mark system of experience built around expected damage to a standardised fighter (I think this may even of made it into a TSR product, but I may be mis-remembering).

In the unmodified game, there are lots of gambling decisions to make, where the results are not guaranteed either way (although usually in favour of the PCs). In essence this is a large part of the combat game, and attempts to mirror risks and unknown factors in fictional combats. It would change almost beyond recognition with dice rolls removed.

There would also be common situations where either the DM or the players could guarantee specific results. For example, if two goblins attack a player character it would reduce the character to 0 hit points. As DM, knowing this, would you play that action or not? Seems you are damned either way - playing it is a decision to take the character out of combat, not playing it is not really trying when the combat tactics to choose are now practically the only part of combat remaining.

Pathfinder battleboard tactics and choices of what actions to take, which spell to cast etc, are not rich enough by themselves to make for a compelling combat game. Without uncertainty due to dice rolls, the game would at best be an exploration to find the end result - not clear until resolved due to free choices of action and position. In my opinion it may well become a joyless, numerical grind with number crunching replacing intuition and certainty replacing risk.

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There are diceless RPG systems (Amber is one I have heard of but not played) - the difference is that have been designed as a game from the ground up without needing dice. Removing dice rolls from a system initially built around them is unlikely to lead to something as playable.

Answer 2

Maybe most importantly, consider the effects on the fun of combat. You mentioned the absence of critical hits; I'll say from experience that finishing the fight against the Big Bad Evil Guy with a critical hit is one of the most satisfying ways to end a battle. On the other hand, the most exciting part of combat shouldn't be "roll a 15 and hit or roll a 14 and miss". IMHO, while being able to react to curve-balls like an unexpected miss, gambling isn't what makes combat fun. Removing the synthetic tension of die rolls would encourage GMs to make more legitimately interesting encounters, and encourages players to find more interesting tactics. Note that removing dice encourages more interesting encounters, but it doesn't make them any easier to create.

Removing dice from combat system would affect damage-dependent mechanics. Consider damage reduction 5/-. An attack rolling 1d8 + 2 would have an expected damage of 6.5 normally (let's assume every attack hits for simplicity). Now you could try to simply subtract 5 from this, but that's no longer statistically accurate. The new average is simple to calculate (3 (0), 4 (0), ... 10 (5))/8 = 1.875.

Now also consider interrupting spells and concentration checks. If I'm a caster with several magical bonuses that boost my AC to 30, technically every character has the chance to hit me with a roll of 20. A system without rolls guarantees that damage will be done and the spell might be interrupted, so long as a roll of 20 is a hit. I'm a lot less likely to cast a spell near combat if I'm certain to be hit for some amount of damage and have to roll to keep the spell.

Other things to consider If you're going with expected values, maybe rounding isn't such a good idea. If you "expect" an average of 4.5 damage per attack, and you're actually getting 4 damage per attack if you round down.

Initiative has its own reasons for rolling. You might be used to the idea that you always hit hard, but plenty of characters have "low" enough initiative that you can't expect to always go first. Leaving initiative in die roll form might mean the +5 initiative bonus character still has to learn how to react to the -2 character.

Answer 3

I believe there would be several unusual side effects from trying to use this sort of averaging system. There are also several circumstances unaffected or unconsidered by this change.

Firstly, any attack that has an unusually high chance of hitting will do a commensurately-higher amount of damage under this system. Any attack that targets touch AC will immediately be much more damaging than an attack that targets normal AC, such as a firearm, or a touch spell. And creatures with unusually high defences are suddenly almost impossible to hurt - if you need a 19 or 20 to hit, you need to have at least an average damage of 10 to even do a single point of damage - if this creature also has any level of DR, you now cannot hurt it at all.

Additionally, this change to the system will actually change the current balance between attack bonus, damage bonus, and damage die type. Right now, taking a d10 weapon over a d8 weapon means a chance of an extra 2 points of damage. Under the proposed system, the average damage will instead increase by a single point, apportioned over the chance to hit. With a 50% chance to hit, that extra point will still round up to a point. Under a 50% chance to hit will effectively negate that extra damage. Bonuses to hit immediately become more important than fixed modifiers to damage - why would anyone use the Power Attack feat under this system? You would trade 5% less damage for an extra +2 damage apportioned over your now-lower chance to hit.

Also, weapons with different damage dice are often balanced by having a different threat range, or a different critical multiplier. How does this system handle this difference? Using the proposed token system, there is immediately no reason to select a long sword over a battle axe, since they will both crit with the same frequency, yet one does more damage on a crit. Perhaps, if you were to use the critical token system, you could expand it to allow a critical token for each point of threat range. This would also allow such things as Keen and Improved Critical to still function in-game.

Lastly, what does this system do with damaging spells? Do they all deal average damage as well? What if they require an attack roll, such as Scorching Ray or Shocking Grasp? What about spells that don't need to roll to hit, like Magic Missile? Save spells, such as Fireball or Lightning Bolt? Depending on how you handle this situation, the Magus is either trivialised or made one of the best classes in combat.

(addendum)Thinking about this again, what now happens to healing spells? Do they also heal average damage, or get rolled? What about trying to hurt objects? Splash weapons?

Answer 4

While I agree with the excellent answers so far, I feel that the complexity of the math has not been addresses quite yet.

For every combination of AC, damage and to Hit, you would have to calculate

Damage = (AC-AttackBonus)/20 * (maxDmg+minDmg)/2

Not taking into account damage reduction (see Envision's answer) Think of a simple fight between 4 PCs and 3 Enemy NPCs, all with different ACs (3 of them) and different weapons, with different Attack Bonuses and Damage Values. Lets just assume 2 per fighter (ranged and melee, for example). That means you do the above calculation 4*3*3*2=72 times.

Now say someone uses power Attack. Recalculate. Someone charges. Redo the calculations for the charger AND everyone attacking him until his next turn.

I know that you have to calculate damage as well when you roll normally, and for every single attack. But the calculations themselves, being just a single addition (d20+Attack Bonus), numerical comparison with AC, and another addition, e.g. 2nd grade math, are much, MUCH simpler than your formula.

Furthermore, how are you going to do combat maneuvers? If you do it based on likelyhood, congratulations, grapple is now an inevitable (slow) death. You absolutely NEED the randomness here.

Answer 5

It sounds like you're trying to reduce randomness in the Pathfinder game.

To be clear, the D&D / Pathfinder system has a lot of randomness baked in. And the system is not just about the averages, but about the range around the averages.

In D&D / PF, the d20 is the most common die and relative to many of the DC numbers in the games, it represents a big range.

Take saving throws for example. A 20th level Fighter (very, very rare) has a base Will save of +6. A 2nd level Adept (common) has a base Will save of +3. So without large amounts of magical enhancement, the d20 is really the deciding factor, the Fighter has only a 15% better chance of surviving a "save or die" spell.

Now of course, the 20th level Fighter likely has a bunch of magical items and other improvements, but the main point is the same, that d20 represents a big range over the expected values.

I think there are a few options here, but they all have their limits.

Option #1: Change the dice

Maybe you can replace the d20 with some other dice (5d4, 2d10?). This reduces the "swing" and emphasizes the base number over the die roll. Your average is still the same but you get more average rolls causing your base number to be more important.

It means critical successes (and failures) are less likely to happen, but that can be adjusted for.

I'm not sure if I love this idea though.

Options #2: Move to a "cards" system

Build / print out a deck of cards with some randomly distributed numbers for each die range. Then you can let players "play out" their rolls strategically. Some players will save their 15s for Saving Throws others will throw them into attacks.

Maybe you give each players a hand of 3 d20 cards and they draw a new one with each played one. They're still going to be forced to play low rolls, but they also get to work the odds at the appropriate time.

Not clear if this is what you really want, but it may be a step in the right direction.