# Damage Models in RPGs

## Table of Contents

Approximately 4:49 minutes of reading time.

## 1 Introduction

Although roleplaying games without combat systems exist, for many games a great focus is laid on simulating exchanging blows and taking damage. For this, different approaches exist. This article will summarise some of those and will try to show advantages and disadvantages of the various methods.

## 2 'Flat' Damage Systems

Some roleplaying systems feature armour as a way to prevent getting hit at all (most notably D&D and derivatives). The advantage herein usually lies within ease of play as armour can simply modify the target to roll against when attacking. This is especially useful as it gives skilled attackers a very clear advantage. The biggest flaw on the other hand lies in its lack of realism.

As has been often noted by hobby historians and practitioners of Historical European Martial Arts, the role of armour is not to prevent the opponent from landing a strike, but to stop weaker, lucky strikes of opportunity from doing serious damage. Instead, in real combat, blows are usually parried with one's weapon or shield, with particularly skilled combatants sometimes even parrying with their bare hands (as in Judo). Therefore in a more close approximation to real life, avoiding the enemy's blows does not depend on one's armour, but the skill with which one wields his weapon.

In D&D-like systems, damage is usually determined by a flat roll of a single die, with some special weapons deserving two dice. This damage roll has its high variance as a feature; Low rolls might represent a glancing blow, high rolls hitting a flaw or gap in the armor. Therefore such systems intentionally seperate the real, arithmetic effect and the interpreted, narrative fluff into different aspects of the attack. The attack roll serves to reflect a simplified understanding of armour, while the damage roll is only correctly understood by applying the narrative lens gained from the armour system.

## 3 Towards deterministic Damage Systems

Used by for example GURPS or Mythras, in this system Armor provides the wearer with a certain damage resistance (DR) or an amount of armour points (AP). This threshold is subtracted from any incoming damage. If this subtraction is negative – that is, the defender has more armour than he suffers damage – the armour succeeded in fully protecting its wearer.

This system symbolises wearing a protective layer of some material that is able to disperse some of the impact's energy in a non-harmful manner. Only if a certain amount of damage is reached does some pierce trough – and then only a lessened amount, as the projectile / attack lost some energy on penetrating the armour. In this way it is quite close to what we actually expect of real-life protective gear. Especially for vehicles this system seems reasonable, as usually one can even construct appropriate DRs for materials themselves. These can then be used to determine the DR for armoured vehicles by the thickness of their armour. Determining DR by body / vehicle parts aids realism as certain structural weaknesses can be represented. However, even with this some small but defining weak points may remain irrepresentable.

### 3.1 GURPS

GURPS in particular determines damage by rolling multiple dice, at times as much as half a dozen. The amount is dependent on the energy behind the attack. Particularly strong attacks might – instead of featuring hundreds of dice – also multiply the damage roll result by a constant.

This higher amount of dice leads to a narrower distribution of results. In its basic function, 3d6 is quite similar to 1d20 as it returns a distribution with mean \(10.5\) – both have a one in two chance to succeed at a roll below or above this value. The 3d6 however approximates a bell curve with the standard deviation \(\sigma=3\). With the 1d20, the lowest five possible values have the same probability as any selection of five values, \(\frac{1}{4}\). For the 3d6, the probability of rolling one of five values depend on which values one chooses – the lowest five possible values on the 3d6 have a combined probability of just below \(\frac{1}{6}\).

Of course, many attacks in GURPS use more or less six sided dice. But the general trend of using more dice leading to more predictable random distributions is clear. This is an intended effect of choosing to use more instead of larger dice when rolling for damage. Stronger attacks – by virtue of getting more dice – get more predictable, and part of the reason therefore lies in partially off-loading armor from the attack roll onto the damage roll. As explained in 2, a wider distribution is properly understood by taking 'armour fluff' into account. The narrower damage roll distribution found in GURPS then is best understood as the variation in raw energy the attack may have due to external factors not handled by the system.

### 3.2 Mythras

Mythras actually follows a similar philosophy to damage as GURPS, with the large caveat that few humanly wieldable weapons are deemed massive enough to deserve multiple dice.

## 4 Deterministic Damage Systems

Two kinds of games tend to feature truly deterministic damage systems, though for wildly different reasons.

In tabletop games, we usually find systems of constant damage as a simplification measure. In some narrative-focused roleplaying games damage does not depend on a roll in order to speed up, and 'de-focus' the combative element of the game. In some tabletop strategy games, the success of an attack only depends on the amount of attackers and defenders (e.g. Diplomacy) or on a fixed attribute of the units (e.g. Stratego). These strategy games use deterministic mechanisms to make predicting moves easier, and perhaps in part also due to the perceived increase of skill required. As Philip Sabin elaborates in his 2012 book "Simulating War", this is a misconception common in people unaccustomed to wargames; but in these specific cases the overall flow of the game also profits.

The other type of game which might use a completely deterministic damage model does not do so out of a desire to simplify the damage simulation. In fact, they often try to do the exact opposite. Video games like the military sim Arma, or the hunting sim theHunter try to model the trajectories of bullets accurately enough to determine realistic effects of impacts – with prey in theHunter usually running off – leaving behind a trail of blood – unless you're skilled enough to hit them just right. Although these damage systems – hidden somewhere within the code, unreadable in their binary form – cannot be analysed as easily as rules of a tabletop game, experience with these games and their general focus seem to suggest a negligible effect of random chance.

Although this seems like a natural end-point for conflict simulations, I have yet to come upon a computer-based roleplaying game that foregoes randomized damage completely, and part of the reason might lie with game developers being aware of the misconception Philip Sabin called out in his book. Although chess-like pre-planning of moves does feature in some tactical roleplaying games, both gamers and developers of these games seem to know that dealing with the unexpected, both positive and negative, is a fundamental part of emulating decisions in real conflicts and a simple source of added player engagement.