Friday, March 16, 2012

DnDNext: What's Wrong with Having Armor "Reduce Damage" in RPGs?

Last year, I posted about the various rpg mechanics for representing the effects of armor in combat.  I often hear from some corners of the gaming community that armor "reduces damage" and it shouldn't "reduce your ability to hit." 

On the surface, this argument makes sense.  Armor prevents the impact of a blow that did in fact come into contact with you from doing damage, and it doesn't make opponent's "whiff."

The problems with the argument only really come to the fore when one looks at armor from a strictly mechanical presentation.  As my prior article mentioned, all armor effects are part of a linear equation -- at least in systems with a "to hit" mechanic.  The to-hit roll represents one variable, the damage roll another, etc.

Damage = (Probability of an attack hitting)*[average weapon damage + damage bonus] - Damage Reduction

Pretty much all role playing games have some variation of this basic equation.  Hero games, d20, Chaosium's systems...they all have some variation of the basic linear equation above.  What this means in mechanical terms is that whether you use damage reduction or you use "increased chance to miss" armor always mechanically reduces damage.  If it only reduces the probability of an attack "hitting," then it reduces the average damage of an attack by that percentage.  In d20 based systems, this means that armor reduces damage by approximately 5% per point of armor class.  One could arguably represent armor as a percentage damage reduction without ever altering any mechanics in D&D by doing exactly this.

There are many "reduce damage" systems on the market, Tunnels and Trolls and Hero come to mind quite readily.  Some of these systems understand the linear equation and thus their mechanics reflect a certain threshold of effectiveness that armor/defenses should apply to attacks.  T&T doesn't have "to-hit" rolls in the traditional sense at all, so having armor reduce damage is a direct effect of that system.  Hero's mechanics are heavily playtested and balanced applications that are quite mechanically robust, and I won't bore you with the details of point cost to damage effectiveness.  Just let me say that the system is remarkably predictable in this an amazing way.

While there are very sophisticated, or simple, damage reduction systems that work, I think that a large number of these systems don't work at all.  Those that don't work tend not to work because they fail to understand that the mechanical equation is always a linear equation and they end up with armor reductions that are out of order with the basic percentages to-hit.  By having a to-hit roll, which as I mentioned is a percentage of damage reduction system in its nature, with an added static damage reduction system armor there is the potential to create everlasting combats.  This is because the armor reduction values often end up as making the effective Damage Per Round of attacks zero.

To illustrate this, I'd like to look at Christopher McDowall's new quick to play game Into the Odd.  The game is open for playtesting under the Creative Commons, and I recommend taking a look.  It has some very good ideas.  I like that the system is based on an underlying ability "Save" system that has quick and easy determination of attribute bonuses that reflect a nice bell curve.

Attributes range from 5 to 15 and bonuses range from -5 to +5.  The bonuses are applied to rolls against an opponent's attribute.  Roll d20 and add your bonus, if it equals or exceeds the opponent's attribute (or the difficulty of a non character task) then you are successful.  Quick and elegant.  I really like it.

That said, Into the Odd includes a "dodge" system and an armor damage reduction system.  Armor doesn't increase the chance to dodge, it reduces damage directly, but players have a chance to dodge and suffer no damage.  The basic combat system is as follows:

  • Attacker rolls damage -- the assumption is that if an attack isn't actively dodged then it hits.  I like that.
  • Damage bonuses (from size of weapon, magic, or circumstances) are applied.
  • Subtract Armor Reduction.
  • Target rolls to avoid attack.
In the linear equation, this would look as follows:

Damage = [Damage Rolled + Damage Bonuses-Armor Defense] * Chance to Avoid Damage

The average damage per round for a light weapon (which does 1d6 damage) would be:

Avg. DPR = [3.5+0-Armor]*Chance to Avoid Damage

By having the reduction effect applied before the chance to avoid, McDowall allows for some interesting effects and makes the damage reduction effect less exaggerated than it would be if armor's bonus was applied after the chance to dodge was resolved.  But armor still has an amazing effect on the game's combat system.  Let's look at the average damage of a light weapon versus the armor types based on an opponent's attribute. 

You can see by looking at the picture that even light armor provides a pretty significant defense against a light weapon.  The average damage of a light weapon is 3.5, but depending on your opponent's STR you might take as little as 0.5 points of damage on average per round.  The above chart includes the chance to dodge factored into the damage equation.  If you have a 10 in a stat and you are trying to dodge someone with a 15, you have only a 30% chance of success (15+ on the roll). 

But let's look at the Armor reduction from a different perspective.  Let's remove the effect of the dodge roll completely.  Into the Odd doesn't give Armor defensive reduction values that look in any way extreme.  Light armor subtracts one point, heavy two, and a shield adds one additional point.  That seems pretty moderate...until you look at how big a percentage of damage this is for an average light weapon.

Light Armor's 1 point of reduction is 28.57% of the average damage (3.5) of a Light Weapon, and heavy armor and shield reduce the average damage amount by 85.71%.  This is before any chance to dodge has been applied.  You see similar, though not as drastic effects, against the "maximum" damage a light weapon can do.  The protection of Light Armor, against a Light Weapon's average damage, is a greater percentage than would be gained by having a +5 bonus from a statistic.  Wearing Light Armor is a better benefit than being among the 2.78% most physically capable people in the world.

Here you can see that even when applied to the maximum amount of damage possible from a Light Weapon, Light Armor reduces the damage by 16.67%.  This is the equivalent reduction of having a +3 bonus in a statistic.  The amount of protection provided makes equipment more important than statistics in Into the Odd.  

This seems odd to me.  Should Light Armor be a better defense than being epically agile?  I don't think so, but that is what is reflected in this system.  If weapons did more damage, then this effect would be muted.  If attribute bonuses were added to the damage dealt, this is not clear in the rules as written, the effect of attributes would be increased.  My personal recommendation for this system is to step up the weapons a die, or to use something other than a d20 for the dodge roll.  The d20 has linear probability of 5% for any value, and thus each +1 bonus equals a 5% shift.  If a 2d6+bonus system vs attribute were used, this would radically change things and make attributes matter more.  

As you can see, even when an armor "reduction" value is low, it might end up being the most significant combat effect.  Is this the effect you want in your game?  If it is, then this is what you want.  If you want the game to be attribute -- or even skill driven -- then you might want to consider some alternatives.  I like the "armor penetration" roll system where each armor has a penetration value that must be equaled or exceeded to hit the target underneath and where different weapons roll different armor penetration dice.  This is the system used by the classic game Dragon Warriors.  You can also create an "armor save" where armor protects from damage on a specific roll.  Say a 6 or better.  Light Armor could roll a d6, Medium a d8, Heavy a d10 and a shield could provide a die bump to the next better die.

Remember that damage when converted to a mechanic always creates an equation.  Look at how big a factor armor ends up being in that equation and ask if that is what you want.  In D&D attributes and Armor are equal in what a +1 difference means.  A +1 to hit increases damage by 5% and an increase in Armor Class reduces damage by 5%.  The fact that attributes also add to damage -- post to-hit determination -- means that attributes have a greater impact than armor.

There's a lot you can do in game systems, but don't let "common sense" be the only tool you use to analyze games.  Break them down to the mechanics.  In D&D Armor does "mechanically" reduce damage even though it seems like it reduces chances to hit.  It's all a matter of perspective.  I hope D&D Next sticks to the classic AC system.  It's more balanced and robust than you might initially think.
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