### Armor Algorithms: Reduction vs. Resistance

Was thinking about two similar methods of single-roll attacks with damage points built into the outcome. The first is subtracting a value from the (random) damage dealt, to a minimum of zero. The second also uses random damage, but the damage is only dealt if it meets or exceeds a certain value (and it is not itself modified). These are called reduction and resistance. I did some quick math to compare the two, using 1d6 as the damage roll. The average of 1d6 is, of course, 3.5, so that’s my baseline to compare.

Below is the table for damage reduction, down to an average of 1 point of damage per attack. For example, a target with reduction 3 would take 0 damage on a roll of 1, and 3 damage on a roll of 6.

Reduction | Average | % Max | Δ |
---|---|---|---|

0 | 3.50 | 100% | — |

1 | 2.50 | 71% | 29% |

2 | 1.67 | 48% | 23% |

3 | 1.00 | 29% | 19% |

Below is the same for damage resistance. The value is what the damage die must meet or exceed in order for the resulting pips to be dealt as damage points. For example, a target with resistance 6 would take 0 damage on a roll of 1 (or any roll from 1 to 5), and 6 damage on a roll of 6.

Resistance | Average | % Max | Δ |
---|---|---|---|

1 | 3.50 | 100% | — |

2 | 3.33 | 95% | 5% |

3 | 3.00 | 86% | 9% |

4 | 2.50 | 71% | 15% |

5 | 1.83 | 52% | 19% |

6 | 1.00 | 29% | 23% |

In order to attain an average roll of 1, you need to either have reduction of 3 or resistance of 6. The effect is that resistance has more granularity but results in more misses (non-damaging attacks), while reduction has less granularity but results in lower numbers of damage. Another pattern is that damage resistance is more effective as the value increases relative to previous values, while damage reduction has diminishing returns.

I think that, of the two, damage reduction seems the less frustrating. Even if damage dealt per hit is decreased, characters miss less often so it feels more productive still. Besides, I don’t think the granularity of the other approach is necessarily appealing in itself. Just four values from 0 to 3 is fine. Plus, too, resistance values 2 to 3 are so similar to a resistance value of 1 that they are trivial, while resistance values of 4 or greater result in misses half the time or even more often than that.

By the way, my friend Ty from *Mindstorm* came up with a cool alternate representation of the reduction algorithm: instead of the armor value being subtracted from damage, treat it as the maximum possible damage that can be dealt. If you roll equal to or less than the armor value, you deal that amount of damage; otherwise, you deal no damage. This means that a value of 6 is like a reduction of 0, a value of 5 is like a reduction of 1, a value of 4 is like a reduction of 2, and a value of 3 is like a reduction of 3. This only works if the only damage die used is d6, so the range of values is from 6 to 3.

Hello, interesting analysis! If you have some spare time and you are curious enough, I have written a new game where I tried to avoid this problem by using a single mechanic to resolve both "to hit" and "to damage" concepts! Should you not be interested, my apologies in advance! Have a great weekend!

ReplyDeletehi aia, sorry i'm only now able to respond but thank you for reaching out to me via discord and i'm really excited to see your solution!

DeleteThank you. I agree with your preference, and use something like it for my house-ruled D&D games. It was interested to see the damage resistance option written up. I don't believe I've ever seen it used in a published RPG. Are you aware of any games that use it?

ReplyDeleteSome people report using the equivalent of 'advantage' (roll 2 dice, keep highest) and 'disadvantage' (roll 2 dice, keep lowest) on damage rolls to represent respectively 'big' and 'small' attacks. So something to watch out for in those cases is the interaction between those two factors.

Well, I honestly do not remember any specific rpg... however there have been so many that I am nearly sure you can find one with a damage resistance feature. I have too many of them to remember every mechanics... (I do collect FRPGs).

DeleteRe to the game mechanics I used in my game, there is a kind of resistance concept: it is not exactly as you defined it... it applies when a difference in size exists between two opponents: let's consider a fight between an average creature (i.e. a human) and a large one (i.e. a bear): there is a modifier of -2 per each step in size difference (each part gets a modifier of 1, the human +1 and the bear -1) in the determination of the "to hit" result and a x2 or /2 in the "to damage" calculation per step (considering the same example: the human applies a damage/2 in case of attack). In the other way round, the bear would get an overall -2 modifier on the "to hit" and a damagex2. This reflects the idea a small creature is harder to be hit but in case it does, the damage is larger than the "average". The reduction/amplification in this case is applied by means of multipliers on the "to damage" roll. Did you even considered this as a reduction?

That is interesting. From your description, I think the bear takes -2 to hit the human, but does double damage; the human gains +2 to hit the bear, but does half damage. Is that right?

DeleteI think this is an interesting approach. It seems to play off the -X AC (i.e. improved by X) unsystematically awarded to small demi-human characters against large monsters in early editions.

My concern would be cases where the bear's unmodified to hit chance is already small. In this situation, the -2 to hit modifier can reduce the expected damage to the point where the human is expected to defeat the bear. Of course, you might regard that as a positive feature of the system. Or your method of determining base to hit chances might ensure that this case doesn't arise in normal play.

hi kenco, thank you as well! :) i actually have not seen damage resistance in a rulebook, only in some people's house rules that they mentioned off the cuff. i did however see another person's rule, where the armor value represents only a single die roll that can be negated---such as if someone has an armor value of 5, then rolls from 1-4 or 6 will deal damage but a roll of 5 deals none. like damage resistance, it is very granular with little benefit, i think.

Delete"From your description... Is that right?" Yes, it is.

ReplyDelete"It seems to play off the -X AC..." well it is broader than that: it works also in the opposite sense; a small-size creature has +2 to hit and damage halved. The underlying logic is: large -> easy to be hit but low damage suffered vs small -> hard to be hit but high damage suffered. I know it seems difficult but I find it a natural reasoning.

"My concern would be..." if the starting point is already a small chance to hit, a neg modifier doesn't help but at the same time this rule should work. In any case, by means of the underling idea I mentioned in here above that can happen: this rule allows any creature to have the same stats base! In other words, if you have to think to the strength of a bear on a 1-10 scale, an average strength is still 6 because of the application of the modifiers of the size (i.e. you don't need to think since the bear is a large size creature then the strength should be higher than the average strength of a human character). Do you get the advantage of such a rule?

Hope you won't be offended but tonight I quoted this post in the last update of my page... (my page has definitely a limited nr of readers though!).

Yes, I can see that your method is generalising the concept, and I certainly appreciate some of the possible benefits of a scale-based approach to attribute scores. It sounds as though your game is quite different than standard D&D in some ways. That's great.

DeleteThanks! I have written the core rules at the moment... the book it's free of charge (in the digital version) or at cost (in the POD version). I'd be happy if you have a look at the rules and ideally your opinion! If you want instead have only a glance at the game, you can reach me at my substack page where I wrote some posts with selected insights of the game! The name of the game is VI·VIII·X KUP RPG. Thanks in any case and best

ReplyDelete