Final Fantasy X (FFX) is when I first became interested in game damage mechanics, wondering how the damage and defense were determined. Modifying games has always entertained me more than the games themselves. I modified a game save of FFX, rebalancing the stat progression to remove grinding while still being relatively difficult. And, the progression rebalance was successful.
Knights of the Old Republic (KotOR) is one of my favorite games, and I put great thought into combat mechanics regarding that game. I entertained the the idea of creating a mod for the game to completely redo the item stats and damage mechanics. That was abandoned as I started college and worked on more worthwhile projects. However, I never lost interest in game damage mechanics, and I periodically ran across YouTube videos discussing damage mechanics.
For some time, I have thought about different ways that I would implement damage mechanics. Would they be different from main implementations? I decided to approach this as stylized art: capture realism, break it into characterizing elements, and capture the essence of the real form using a simple expression leveraging those characterizing elements. So, I will approach damage mechanics by characterizing damage in real life.
Damage Complexity
The discussion of damage mechanics applies not only to video games but also to tabletop games. And, the discussion revolves around balancing realism and simplicity. In the real world, there are types of damage based upon the physics of the transfer of energy, which is too complicated for a casual game. In the case of a tabletop game, the mechanics must be very simple computationally and conceptually. However, in a video game, the mechanics may be computationally complicated. But, the conceptual complexity must be somewhere between simple and strategic while not being overly tedious.
For tabletop games, the computational requirements involve rolling a dice and modifying the roll by adding or subtracting modifiers. The combat mechanics in KotOR use "dice" rolls with similarly simple addition and subtraction of modifiers. In this way, KotOR is computationally simple but somewhat conceptually complicated. The video below discusses the damage mechanics of KotOR. There are many modifiers to keep track of, and the game does not explain nuances of the mechanics, such as damage types. The game manages all the modifiers automatically, so the combat mechanics are accessible to casual players, not through simplicity but by hiding the complexity. However, the complexity exists for more advanced players to utilize.
In the case of Final Fantasy X, the computational requirements of the combat mechanics are high and unintuitive, using multiple polynomials of the third degree. However, although unintuitive, the complexity is hidden behind rather intuitive principles. Higher stats mean more damage or greater damage resistance, and the game clearly explains how the damage types work. While there are many statuses and ailments, the damage types are simple. There is physical damage and elemental magic. This is intuitive. The only unintuitive aspect is how the complex algorithms determine the actual damage done by an attack given the stats of the attacker and the target.
Although they differ in computational complexity, neither FFX nor KotOR have conceptually complex combat mechanics. Neither attempts to present realistic combat mechanics. However, for thoroughness, the authors of combat mechanisms should at least consider more realistic aspects of damage and defense.
Realistic Damage Types
A common consideration is how realistic to make the combat mechanics. In the real world, there are different kinds of damage related to the physics of how the energy is transferred. Below are the main classes of damage that I consider, although most weapons deliver a combination of these damage classes.
Piercing - In piercing damage, a force is applied over a small area of impact, resulting in very high pressure at the point where the weapon impacts the target. Piercing attacks penetrate a target at a point.
Bludgeoning - In bludgeoning, force is applied over a large area of impact. Bludgeoning attacks crush or knock over a target rather than penetrate it.
Slicing - In slicing damage, a sharp edge slides along a surface with a light to moderate force pressing the edge against the surface. Slicing penetrates a target along a line.
Radiation - In radiation damage, ionizing electromagnetic energy or atomic particle emissions bombard a target, causing damage on a cellular level. This affects large surfaces and is not necessarily limited to the directly exposed tissue as it may pass through a target.
Thermal - In thermal damage, a target may become too cold or too hot. This may range from inhibited functionality due to excessive cold or heat to serious injury due to frost bite or severe burns.
Chemical - In chemical damage, a target may be injured in many ways due to inhaling or contacting a reactant. The damage may be instant and obvious. Or, it may be slow and subtle.
Piercing and Bludgeoning Damage
Piercing and bludgeoning damages are very similar in that the only apparent difference is the relative contact area. But, that difference results in very different injuries. There is a gray area where an attack would transition between inflicting primarily piercing damage and inflicting primarily bludgeoning damage, but this is likely not an issue in most cases as the damage type is clear.
Piercing and bludgeoning attacks rely upon the energy behind the stab or swing. Even arrows depend upon the draw weight of the bow, requiring direct physical input from the attacker. Cross bows are less dependent upon strength due to draw mechanisms. And, firearms sidestep this issue by using energy stored in the firearm or bullet to launch the projectile. But, even in the few cases that do not depend upon the attacker's strength directly for the energy behind the attack, the energy dissipated into the target comes from the kinetic energy of the weapon and/or the force exerted by the attacker.
Since piercing and, especially, bludgeoning damage depends upon impact energy, heavier weapons such as halberds and maces have more penetrating and bludgeoning potential. However, heavier weapons take longer to attack, also depending upon the strength of the attacker. Piercing weapons may be lightweight by further reducing the contact area, such as with a rapier. However, this also limits the maximum piercing power of the weapon. Thinner weapons have less structural strength. A stronger weapons such as the European long sword can penetrate stronger target but still is not strong enough to penetrate plates of armor. However, the spike on a halberd is strong enough to penetrate armor, and the weight helps attackers build up energy behind the attack in the form of momentum. So, in short, piercing and bludgeoning attack damages are generally directly dependent upon the momentum of the weapon and strength of the attacker while being limited by the structural strength of the weapon itself.
Note on Ranged Damage
Many games differentiate between ranged and melee damage. But, technically, arrows and bullets merely deal mostly piercing damage. The easy differentiator is asking whether or not the injury is a puncture wound. Going back to bullets, a stab wound is not different from a bullet wound except for two things. First, bullets usually have a larger contact area. Thus, bullets deals a higher percentage of bludgeoning damage, although the piercing damage is dominant. Second, and most significantly, bullets contain far more energy. To stop a bullet, the energy must be dissipated into the target. In short, the piercing damage of a bullet is far greater than the piercing damage of a knife jab.
Slicing Damage
In contrast to piercing and bludgeoning, slicing is unique regarding energy dissipation. Most of the energy in a slicing attack is not transferred into the target. Most of the energy is employed in moving the weapon, and the energy transferred into cutting the target decreases with sharpness. This has some unique properties.
First, slicing damage is significantly less dependent upon the strength of the attacker. Second, since slicing damage is not so limited by energy, lighter weapons may be used for similar amounts of damage. The lighter weapon strains the strength of the attacker less and enables more rapid attacks. In general, an attacker wielding a primarily slicing weapon will have more agility than an attacker with a primarily bludgeoning weapon and, in some cases, more agility than an attacker with a primarily piercing weapon.
Radiation, Thermal, and Chemical Damage
This is a broad range of damage, but they are similar from a conceptual perspective. They may cause damage in a large region, and they may affect a target as a whole rather than just on the surface or in a single limb. They may also linger. A target could avoid a crusher or dodge an arrow. But, a target cannot dodge a cloud of poisonous gas or an area of high radiation. Lastly, these damage types may require no skill or attribute of the attacker when determining damage.
Realistic Damage Resistance
Different personal protective equipment (PPE) protects against different types of damage. Gambeson resists piercing and slashing damage much better than flesh does. And, it pads against some bludgeoning damage, especially when it is underneath plates that more evenly distribute the force of impacts over a larger area. Meanwhile, chainmail blocks all slicing damage, most piercing damage, and negligible bludgeoning damage. Chainmail and other armor is often placed over gambeson to resist more bludgeoning damage. Basically, different materials resist or block the various kinds of damage differently.
Resisting Piercing, Bludgeoning, and Slicing Damage
Structure and surface hardness resist piercing damage. Structure is how strongly the PPE holds its shape. Kevlar, for instance, is very strong. But, a thin, Kevlar cloth will barely resist piercing as the weapon would injure the target through the cloth. Structure effectively distributes the force of an attack over a greater area, transforming piercing damage into bludgeoning damage And, by distributing bludgeoning damage over an even larger area, the energy results in significantly lower pressure on the target. Granted, the energy must still be absorbed. However, if the pressure is low enough, a lot of energy may be converted into kinetic energy of the target without significant damage. In other words, the target would fall over or be pushed away.
So, when a bludgeoning attack strikes PPE, the energy is dissipated in one of three ways. First, damage sustained to the PPE, such as bending a plate, absorbs some damage. Second, if the pressure is relatively high enough, damage will be dealt to the target in the form of crushing. Third, if the pressure is low enough, the damage will be converted to knockback. Simply put, incoming damage = damage to armor + damage to target + knockback to target. A harder armor material decreases damage to armor, resulting in an increase of damage to target and/or knockback. Increased armor structure decreases damage to target and increases knockback. Increased target mass increases damage to target and decreases knockback.
Surface hardness also blocks slicing damage, and structure is irrelevant. Chainmail is a perfect example because it is so hard while having no structure, and it excels at blocking slicing damage. A slicing attack will have some momentum for bludgeoning damage, but the vast majority of the damage would be from slicing.
When PPE blocks piercing, bludgeoning, or slicing damage, the PPE either sustains damage or completely blocks the damage. As PPE sustains damage, its effectiveness may decrease until it offers negligible protection. The more damage the PPE resists, the more damage the PPE sustains. Eventually, the effectiveness will be negligible. This may occur in a single catastrophic failure like gambeson falling off or a chest plate cracking in half. Or, it may be progressive like chainmail getting holes and gaps.
When the target material is harder than the weapon material, slicing damage will be completely blocked. When the materials are similarly hard, slicing damage will be minimal. And, the harder the target material, the more damage the weapon sustains – or the more durability the weapon loses. For softer target materials, the PPE absorbs the damage as a decrease in durability.
Resisting Thermal Damage
For thermal damage, the PPE resists the damage. But, after a certain amount of time (or a after a certain amount of potential damage has been blocked), the target feels more of the thermal attack. The PPE must be removed from the thermal effect to return to ambient temperature. The time it must be removed is proportional to the amount of blocked damage. Moreover, the PPE is not necessarily destroyed by thermal exposure. So, essentially, durability of thermal PPE may be modeled as durability that decreases with exposure and increases in the absence of exposure. And, the actual damage resistance is a function of the durability and maximum damage resistance (resistance at full durability).
For padded PPE like plate armor over gambeson, resistance to cold is inherent. But, natural resistance to heat is reduced. In a moderately warm climate such as a desert, plate armor may result in a target sustaining thermal damage where a target wearing just gambeson would not.
That description is a conceptual simplification. Accurately modeling thermal damage would require thermodynamics. The PPE would absorb a given amount of energy as it increases in temperature. And, the PPE would have a certain thermal conductivity. The body of the target would emit a certain amount of power as heat and have a certain heat capacity per degree change in temperature. Then, when exposed to an elevated ambient temperature, the temperature of the target would increase until it reaches equilibrium, which may or may not be at a damaging temperature.
Resisting Radiation and Chemical Damage
Chemical and radiation damages are rather simple. Chemical damage is usually blocked completely or it isn't. If a PPE is not fully resistant to a chemical, it would likely fail rather quickly as a matter of time rather than as a matter of the extent of exposure. As for blocking radiation, the resistance is usually as a percentage. And, the PPE does not necessarily lose durability as it resists the radiation.
Damage Mechanic Example
Piercing and Bludgeoning
Piercing and bludgeoning are fundamental damage types that most attacks may contain some combination of. And, each piercing and bludgeoning damage would be a function of the strength of an attacker and the weight and strength of a weapon. So, a large broadsword may have a damage profile as follows for three different attacks.
Lunge Attack - (10*STR) Bd + (2*STR) Sd
Jab Attack - (8*STR) Pd + (2*STR) Bd
Swing Attack - (6*STR) Bd + (4*AGL) Sd
STR = Strength Stat
AGL = Agility Stat
Bd = Bludgeoning damage
Sd = Slicing damage
Pd = Piercing damage
Realistically representing this sword involves damage combinations that depend upon the player stats and the type of attack used. This is a reasonable amount of complexity for a few swords, especially if the game centers around swordplay. However, the complexity increases substantially with a dozen different sword items that all have unique damage equations. And, this does not consider the attack speeds, which would be similar equations depending partly upon strength and partly upon agility. And, this neglects the corresponding damage resistances. For a larger game, these mechanics would need simplified.
Alternatively, such a damage mechanic could be hidden behind oversimplified stats and brief descriptions. Then, the weapons deal damage to various armors intuitively. Chainmail would block all slicing damage, block most piercing damage, and not impede bludgeoning at all (although chainmail is usually over gambeson, which absorbs some bludgeoning damage). There is an element of realism to this approach. The numbers above are not empirical; the real world physics involved are far too complicated to definitively quantify.
In reality, the damage of weapons is chaotic. The only conceptual predictions of damage are relative. The damage by bullets are more predictable due to constant variables such as mass and velocity. But, the actual damage still depends upon where the bullet actually strikes a target and what protective gear the target is wearing. So, being realistic actually supports the idea of hiding these computations and exact equipment stats because they are unpredictable in the real world as well.
Damage Variability
Damage varies with each attack based upon chaotic variables. Often, games model this variability with dice rolls or with random numbers within the algorithms. These often use a normal distribution. When rolling a dice, the probability of rolling a 2 is the same as the probability of rolling a 7. However, variability in the real world tends to follow a normal distribution. In a tabletop game, such variability would be computationally prohibitive. But, for a video game such an implementation would be trivial.
The flexibility with a normal distribution is that a skill or weapon stat may reduce the amount of variability of the normal distribution to make the damage more consistent. If the target damage is the 50th percentile, decreasing the variability would reduce the damage of some attacks to maintain the average damage, which is not intuitive. So, the algorithm may be such that the target damage corresponds to a higher percentile, such as the 75th percentile. And, the 25% of damage above that point would be a replacement for critical hits. Then, as accuracy or skill reduces the variability, the average damage also increases. This is essentially just a more intentional method of simply having the average damage increase with skill or accuracy. Because such an approach would not be intuitive, it would need to be hidden as with the damage algorithms in FFX.
Interestingly, the simple mechanics of KotOR loosely model this concept of reduced variability with increased skill. As a player advances, more damage modifiers are added to melee damage. But, the random roll remains the same. Therefore, the random roll accounts for a smaller percentage of the total damage. This is essentially relying on damage inflation to decrease the significance of the random roll. It increases the average damage while decreasing the relative variability, which was the objective of the approach in the previous paragraph. Apart from using a uniform distribution rather than a normal distribution, the simple approach conceptually models the variability reasonably well.
For action games, such variability would not have to replace the skill of the player but rather account for the countless chaotic variables of real combat. However, the more chaotic variables that the player controls, like striking specific areas of a target for more damage, the less variability the damage mechanics should employ. The variability may be thought of as multiplicative damage uncertainty. When a specific uncertainty is offloaded to the player, the player's skill variation accounts for that uncertainty, not the damage mechanics engine.
Multiple Dice Rolls
Although a dice roll follows a uniform distribution, the sum of multiple dice rolls has a distribution more similar a normal distribution with increasingly more rolls. Consider the following probability distributions for a six-sided dice being rolled once, twice, and three times. One roll has a uniform distribution. Two rolls have a triangular distribution. Three rolls have a distribution more similar to a normal distribution.
In one of the videos regarding KotOR, it is suggested that a damage of 4-8 consists of 4x d2 (four rolls of a two-sided dice) rather than d5 +3 (a five-sided dice rolled once with a modifier of plus three). Three or more rolls would result in a normal-like distribution; however, such a system is not practical. The mechanics of KotOR do not sum multiple dice rolls. While the dynamics of such mechanics are interesting, they are not practical for game mechanics. Physical games cannot have two or three sided dice. And, in computer games, a normal distribution function may be used with the actual algorithm implemented being a trivial detail.
Conclusion
This post characterized the nature of realistic damage in a fair amount of depth. There are multiple types of damage, and they are related in complex ways based upon physics. This implementation in a game would be quite complex, too complex for anything outside of a tedious strategy game. But, this was never meant to be implemented into a game. In the next post on this topic, I will explore various options for simplifying this realistic model into something more appropriate for a game.
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