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 sense...in 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.

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.

## 8 comments:

A friend of mine had this comment about your article:

Interesting. It doesn't really change their conclusion but their numbers are wrong and their equations are written incorrectly. Classic mistakes really.Damage would not be multiplied by the chance you take no damage, but rather the chance that you take damage, since your average damage goes down rather than up as your chance of avoiding damage increases.

Also, their average damage calculations for any armor with 2 or 3 damage reduction are off. They fail to take into consideration that you can't do negative damage. The target doesn't heal if you hit them for 1 point but they have 3 armor. So you can't just subtract the armor value from the average roll. You need to average only the positive damage results. Thus the average damage without dodge of 1d6 -3 is not 0.5 but rather 1. So the damage reduction for heavy armor and shield is actually 71.5 rather than 85.7. The tip off comes when they say that applying the chance to avoid damage after subtracting armor is different than doing it before. Since the dodge is all or nothing and you can't take negative damage there is no difference at all.

In addition, they don't properly take into account the change in stats for dodging. Look at the light armor row of the first table where their average damage calculations are correct. The average damage for the highest strength opponent is 3.5 times that of the lowest. The damage reduction from strength 15 to 10 opponent is 35.7%. Better than light armor. Why isn't it 25%? Well the minimum chance of avoiding an attack is 30% not 0% so while the change is 25% of the average damage for just damage- armor you are not comparing it to damage -armor, but rather 70% of that, making it a 42.9% larger effect, or 35.7%. For strength 15 to 5 it is 85.7% the same as heavy armor plus shield.

Whether those statistics are good or not is a matter of preference but they over estimate the effectiveness of armor and underestimate the effectiveness of skill in the system.

Assume 3 damage * Max to hit chance .7

(3 * .7) = 2.1

Light Armor - 1 = 1.1

(3*.7) - 1 = 1.1

Now

Damage Roll - Armor = (3 - 1)= 2

Now apply to hit chance.

(2 * .7) = 1.4

(3 - 1) * .7 = 1.4

That's the difference in average DPR. Where the variables are placed matters to some degree. If he can explain to me the error in the above -- and I am perfectly willing to admit error -- please have him comment here. I'm always willing to learn more and assume no mastery. I'd love to see the variations in the equations to enter into my playtesting spreadsheets.

I believe your friend is correct on the revision of the percentages due to base line 30% chance of 0 damage vs. absolute 0% chance though.

I'll actually be updating this post on Monday. Ah...the quick errors that occur when you go "short hand" and forget to do step by step in statistics.

I actually need to update not just the -3 damage, but the -2 as well. As for the 30% "maximum" to hit chance, that is only true vs. base 10 and for starting characters. There are creatures that have an STR of 20 or higher. The actual maximum to hit chance is 95% -- natural 1s always miss.

That said, it's nice to have someone point out the flaws -- it's what editors are for.

Still, damage reduction systems have greater effects than people think and "armor = miss" systems are also damage reduction systems mechanically.

Good stuff! BTW, I nominated you for the Versatile Blogger Award.

There is one important difference between armor causing misses and armor reducing damage is not accounted for in your stats: the damage happens.

DR means the damage cones a little at a time. It is easy to plan healing. You can do to lower hp without risking death from a critical.

Armor as miss effect is more swingy. Your tank is more of a glass cannon, because he can go from fine to dead very quickly. It just takes a pair of lucky max damage rolls in a row.

I don't mind when a game is designed around AaDR (Armor as Damage Reduction), but trying to convert a game that isn't designed around it usually becomes a bit of a mess.

AaDR also encourages a certain type of play. You end up with a bunch of big, burly guys with heavy armor and heavy weapons. The nimble swashbuckler who wears little or no armor and makes a lot of less damaging attacks isn't very viable in this type of play. Naturally other rules can compensate for this and make the swashbuckler effective, but it's harder with AaDR.

The scale of armor vs damage vs wounding has a big effect. I could see a game where armor usually stops all of the damage of a blow. But PC's don't have many hp. Getting a little damage through causes a wound. In this case HP wouldn't be as abstract as they are in D&D. Taking an HP of damage means you have some sort of wound. In another game I could see armor only stopping a fraction of the damage, but you have a generous amount of HP compared to the damage that gets through.

When you have more than one type of damage, I could also see armor converting some or all of the damage from lethal to bruise/stun/non-lethal (or stopping x amount of bruise/stun/non-lethal damage). This is a good rule for a grittier game where it's harder to heal lethal damage.

But for the specific case of DnDNext, I think we've gotta stick with armor affecting the hit chance. It's too much a part of D&D.

This conversion of DR to "+X to AC" is all well and fine if you assume that all effects that trigger on hitting can be applied to full effect when you hit. Does a high DR mean a better shrugging off of being dazed because you got hit? A poison attack is a prime example. Should a poisoned dart have it's damage reduced to 0 and yet knocks you unconscious because you didn't dodge and thus it hit?

Most RPG's make characters ridiculously durable, at least in comparison to any sort of reality.

There is no one "right" way to handle armor, because different styles of armor work in different ways. Some absorb an impact, spreading it out over a larger area. Others are intended to deflect an impact (a Samurai's laminate armor for one) which is accurately reflected by reducing the probability of a hit.

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