Does "critical chance" have any reason to exist?

Question

How do you make critical attacks not useless in video games?

In most games, critical attacks are just a random chance to deal extra damage—but why would players choose random chance rather than extra damage if the end result is the same?

Whether you increase your raw power or your critical chance, the result is always more damage, so players will always pick either what sounds cooler or what is mathematically more efficient in the game.

Answer 1

Critical hits are a form of variable ratio reward.

• "ratio" means the player has to do an action some number of times to get the reward (it doesn't just arrive on a timer - you have to attack to get a critical hit)

• "variable" means that the player can't predict how many times they need to do the action before the next reward comes. Any attack could be the one to land a critical, but you don't know until you try.

Behavioural psychology experiments have found that this type of reward is one of the stickiest and most habit-forming, which is why they're so commonly used in games, like random loot drops. They're so effective that we've fielded questions here before wondering why games would even bother with any other reward schedule. (This is also reason to use them with caution and professional responsibility, as this can easily cross the line from giving the player a compelling and enjoyable experience to a compulsive/addictive one)

In the case of critical hits, the reward is a spike of excitement when something goes better than expected, and added anticipation leading up to the attack hitting. (Brain scanning experiments with slot machine players find the thrill ramps up while the wheels are still spinning - the unknown dials up the mental engagement even for the attempts that don't pay off)

This is especially true in JRPG-style games where you select an attack from a menu and then the characters animate to act it out. If the damage was already pre-determined, this is just dead time - the player already knows the outcome of the attack from the moment they select the move, and the animation is just an enforced delay to sit through. But if the attack can miss or hit better or worse, then the player stays engaged throughout to see the outcome of their move and adjust tactics for their next play accordingly.

This can give the player stories to tell - events that make one encounter with a generic monster different from the next. "Oh, you should've seen it, I landed three crits in a row and basically melted the enemy into goo before it could act!" Whether or not these rise to the level of salience you actually tell someone about, they add texture that reduces the repetitive grind.

The possibility of more-than-expected damage also gives you something else important: hope. In a game with no randomness, the player can already predict the outcome several steps ahead. And if they're losing, this is deeply demoralizing. Let's say you know the enemy has 50 HP left and your sword only does 30 damage per hit. That means it's going to take 2 more attacks to kill it. If it's readying a one-hit kill or a nasty status effect, there's no way you'll kill it before it gets the move off. You see your defeat coming and the mechanics drag you through the mud waiting for it to unfold. But if there's some possibility you could score a critical and end the monster before it gets its attack off, now you have hope. Now you're still engaged in the fight and striving for a good outcome, and if it pans out, you'll have a story to tell about snatching victory from the jaws of defeat - something you just can't get with deterministic damage.

See the Prototype that was Banned from Halfbrick for more on the psychological impacts of fully-deterministic combat versus systems with some non-deterministic relief valves built-in.

Critical hits also form a new building block from which designers can build more complex dynamics. As other answers note, critical hits can proc other special effects, bypass defenses or debuffs, or even influence loot drops.

One example I want to add is in Team Fortress 2, the critical hit chance ramps up from 2% to 12% (ranged) or 15% to 60% (melee) depending on the amount of damage the player has done in the last 20 seconds. This creates a positive feedback loop where getting crits leads to getting more crits, contributing to an exhilarating rush and feeling of being "on a roll". It also encourages aggressive play and pressing the advantage rather than slow and methodical defensive play. That's not to say that this style of play is always "better", but in this case the choice to include critical hits and ramp their chance like this helps support the style of play and emotional experiences Valve's designers wanted TF2 to deliver.

Answer 2

(Almost) no mechanic is bad

It's very difficult for a single mechanic to be bad. Unless it causes harm to a player's health or well-being, pretty much every mechanic could potentially be part of a good game.

There are two big objections to crit chance stats which I often see from players: "Crit is just another flavor of damage" and "Random crits diminish the effect of skill." I'll address both.

Crit as a calculation

I've sometimes heard crit jokingly called "Yellow attack power" (in a multiplayer game where crits show up in yellow text and normal attacks show up in red). This is because of the perception from players that because only the long-term expected value of damage matters (which was true for that game), crit and attack power could be thought of us just two different flavors of the same stat.

Such jokes aside, I'd contend that having yellow attack power isn't a bad thing.

Simple calculations aren't bad

If you have a game with attack power and crit chance, and the expected value of damage over time is a simple multiplication of the two, and the player can freely assign points between the two, and there is a trivial calculation that the player can do. Even if all of those things are true, that's still not worse than only having an attack power stat that grows quadratically.

Some players enjoy calculations. Calculating the most optimal stat build engages players' senses of accomplishment and mastery, even if the puzzle is easy enough to be solved by elementary schoolers. In fact, if you're making an RPG that's designed to appeal to elementary schoolers, you might consider including a lot of simple calculations like that so that they can have optimization puzzles to solve that are on their own level.

Most calculations aren't simple

In modern games, you very rarely have a binary choice between x points of "attack power" and the same points of "crit chance." The most common way is that players pick items as complete packages. Players can't pick and choose individual points - they can take the gloves with +60 crit and +20 damage to pair with the chestplate of +100 damage and +40 crit. Finding the exact combination of items which gets them closest to the optimal ratio of crit to damage is an NP Complete problem - though often presented at a small enough scale that players can solve it (or look up the answer in a guide).

Sometimes, it's not a calculation at all

Sometimes, the difference between a sword that gives more crit and a sword that gives more damage is so complicated that it can't fully be solved, even by the best players or modern AIs.

Consider a roguelite game, where players are frequently resetting their build from scratch, but where they must replay the early levels of their build in order to do so.

Suppose that the player starts with has 20 damage and no crit chance, and crits deal double damage. Early on, they are presented with a choice of either +20 damage or +25 crit chance. This might seem like a no-brainer - a choice between either +100% DPS or +25% DPS - but if damage grows by +10/level while critical chance has no automatic scaling, then the two choices become incomparable.

The +damage option would serve weaker players who are struggling with the early stages of the game, while the +crit option would serve more experienced players who are confident that they can reach the stage of the game where the crit will pay off.

This sort of trade-off can increase both the replayability and the approachability of the game overall (both important considerations for a roguelite!): beginners who choose the +damage option will progress further into the game than if only the +crit option were offered, which makes the game seem more approachable to them, while players who choose the +crit option will be effectively playing the early levels of the game on a higher difficulty level, commensurate with their greater skill and make it take longer for them to get bored of it.

The role of randomness

Critical hits being a random element that inhibits skill is another common objection. After all, in a good game, the best player should win every time, right?

No, the best player shouldn't necessarily win every time, actually

For a competitive game to succeed, it needs to be fun to lose as well as to win. Games which are only fun if you're already winning, it will have a hard time retaining new players, who lack the skill to win consistently.

One of the easiest ways to make losing fun is to make losing feel like winning: If games are played best-3-of-5, with enough randomness in the game that a rookie can hope to win at least one round, then the impact of their overall defeat is blunted because they got to experience victory while losing.

This is (I think) why Magic: the Gathering requires that players build 60-card decks even though in most games, they will only see about 20 cards from them - but also treats best-of-three as its premier competitive format. They could make the game more consistent by allowing 40-card decks (outside of limited) and then not need as many games to decide winners, but doing so would make losing less fun.

If it averages out, chunkiness is exciting

Even if the game is best-of-one and competitive, there's still sometimes some merit to including some RNG in combat.

A critical hit is a moment in the game, which can be emphasized in the game's sensation - such as by screen shake, popping out larger damage text, playing a more impactful sound for that attack, and sometimes even having a more dramatic attack animation entirely. These sorts of things can create break up the monotony and make combat feel more engaging, well in excess of the actual mechanical impact of critical hits on the numbers.

Crits aren't for every game

There are situations where the cons outweigh the benefits and neither of the arguments above apply. For a highly competitive game where fights are often determined by thin margins and where the predictability of the game is an important part of its skill (like fighting games), crits would do more harm than good. A competitive game with long match-times which are played best-of-one might suffer from including them. Even if crits average out enough that over the course of a long match, the winner is still almost always the player who played better, crits can make the match feel less legitimate.

Also, not every game needs or wants the effects that crits have on combat pacing. Games where skill already creates variance even in the resolution of an attack (like headshots in first-person shooters), wouldn't benefit from adding crits. Games where individual attacks are so common that emphasizing crits would be meaningless noise to the player (like Starcraft and other RTS games) can't use them to create pacing. Indie game which can't afford the level of sensory polish needed to take advantage of crits would not benefit from including them.

In the end, crits, and crit chance/"yellow attack power" is just another tool in the designer's kit for building different experiences. Sometimes it will be the right tool, and sometimes it won't.

Answer 3

Critical hits are much more than just flat additional damage. If the game supports different careers, some of them might offer additional traits that interact with critical hits (e.g. your critical hits now add burn damage, you heal X% on dealing critical damage, ...), opening the door to all new kinds of strategies.
Some games also have an opponent type, that is simply immune to critical hits. So you could be a crit monster obliterating everything, but still struggle against those opponents, which encourages you not to put all your skill points on one lane.

Answer 4

Some game design goals you can fulfill by adding critical chances are:

• Breaking situation where the game stalls. You might have a situation where two combatants fight each other who both have high defense and low damage. So they can't cause serious damage to each other. Such a combat can take forever. But a "Critical hit" mechanic might allow those combatants to occasionally overcome each others defense, allowing such a combat to resolve before the player becomes bored.
• Using the skinner box effect to generate positive emotions in the player when their character causes critical hits. Psychological research has shown that a randomly occuring positive event has a stronger reward effect than a reliably occuring one. A rarely occurring critical hit generates an "ooh, nice!" emotional response in the player that increases the enjoyment of the game.
• Generating interesting situations when the enemies land critical hits. A random critical hit might turn an otherwise boring combat encounter into an exciting one. When the combat system is relatively predictable, then the player will in most cases know whether they will win or lose a combat encounter. That isn't a lot of fun. But a random critical hit by an enemy might suddenly put the player into a situation that is far more perilous than they expected from that encounter and generate a moment of excitement. But this is a double-edged sword, because when you apply this mechanic carelessly, then it can just as well turn a combat encounter that is already challenging into an unfair or even impossible one. Which can be a really frustrating experience for the player ("I just lost because the random number god hates me!").

Answer 5

I wanted to offer some things critical hits may not do inherently, but games can and do use critical hits as a vehicle to do, which they are inherently fairly well-suited for. Crits may not be the only ways to do these, but they work (and have precedent, I guess).

Case Study 1: Pokemon

In pokemon, a crit does 1.5x damage--but it also ignores debuffs to your own attack and buffs to the enemy's defence.
The general idea here is likely to reduce the benefits of stall tactics.
If you super-debuff your enemies' attack, and super-buff your own defence, you haven't won yet, because there's still a risk they will get crits, which can chip away at and potentially kill you. You've only half-won, and you still need a good offensive plan to pair with this, which I think is what Nintendo wants to be the case.
(There are also moves that are guaranteed or more likely to crit, which thereby serve as counters to defensive buffing.)
This mechanic doesn't have to be implemented as a random chance, but implementing it as a random chance has some nice features:

• The alternative would be nerfing defensive buffs directly, which might be tricky or disadvantageous to do, or might feel bad, or might hurt non-stall-based defensive tactics.
• The randomness means that e.g. a combination of defensive buffs and healing will not be fully reliable--both the enemy pokemon getting a crit on the same turn might 100->0 one of your pokemon. This lack of reliability reduces the viability of stall as a go-to strategy--you can choose a tactic that benefits from defensive buffs, but not something that relies on them.

Case Study 2: League of Legends

In League of Legends, there are a bunch of stats, and you can buy items to buff those stats.
Let's compare an AD (attack damage) caster, and an autoattacker. We'll assume an item increases your damage by 100%, and you have 4 item slots.
(This is all massively oversimplified, and the math is fudged.)

• AD caster: buys 4 +AD items, does +4*100% damage = 5x damage.
• Autoattacker: Buys a +AD item, a +attack speed item, a +crit chance item, and a +crit damage item. Does 2x damage * 2x speed * 2x crit chance * 2x crit damage = 16x damage.

(Basically, critical-based damage increases provide more things that boost attack that multiply with each other, which can be useful as a balancing lever. It's not easy to describe "oh, this item increases your attack damage by 100%, which is multiplicative with other percent-attack-damage-boosting items, as long as you have four or fewer total.")
(Side note: also, the multiplicative effect goes both ways--+crit chance and +crit damage are much less useful alone then together. Choosing to go for a crit-based build (a) locks you into this path, and (b) makes you weaker earlier and stronger later. In LoL, I think this is intended, and is part of what term "AD carry" is generally understood to imply as a role.)

Answer 6

It's only useless if you design it that way.

A critical strike mechanic gives you (the developer) additional knobs to use to tune the combat experience. Lets say you have two characters with different gear/builds. One focuses on crits and the other on base damage. Even when their overall stats generate the same average damage per second, you can give those two players very different gameplay experiences. Throw in an enemy type that is resistant or immune to crits, and the base damage build has an advantage. Or, use an enemy type whose armor reduces incoming damage by a flat amount (not a percent) to give the crit damage build an advantage. Game mechanics that reflect damage can turn crit-heavy builds into a high risk/high reward playstyle option. You sometimes end fights so fast that you don't take any damage at all, but sometimes those crits get reflected back at you and leave you in an extremely vulnerable position. When enemies can crit, players get those same knobs as well. Choosing the wrong armor or defensive abilities for an encounter becomes a lot more punishing.

Depending on the type of game you're making, critical hits can be (at least partially) a reward for skill or strategy. Perhaps a critical hit can only occur when striking an enemy's vulnerable spot, when attacking with the right timing, when successfully executing combos, etc. New players would get more benefit from a more-forgiving flat damage build, and experienced players would be better able to take advantage of critical hits. You can even limit critical hits to certain weapon type + monster type combinations, giving the player an advantage only if they bring the right gear to an encounter. Another option is to use critical hits to encourage teamwork by making them the result of two players using complementary abilities.

At a higher level, saying that increased crit chance is the same as increased base damage is only true in the statistical sense. That is, the overall damage per second numbers would be the same if you averaged them out over a long period of time. In most games, battles don't last anywhere near long enough for the two trend lines to converge like that. Defeating an enemy in 4 turns with a crit vs. 6 turns without a crit makes the battle feel completely different and far less predictable. Fighting against a group exaggerates this difference even more. Let's say I'm fighting against two enemies. The base damage build takes 5 turns to kill each enemy, and the crit build takes one enemy down in 2 turns with a crit but then takes 8 to whittle down the other one. Both builds took 10 turns to do the same amount of damage. The base damage build was attacked 15 times in the process, while the crit build was attacked only 12 times (or possibly 18 times, depending on which enemy was killed first). Those are all the same on average, but the fights are short enough that they don't feel remotely the same. The base damage build is more predictable, provided I can withstand the additional attacks. The crit damage build enables me to quickly take out enemies that are beyond what I could normally survive, but I have to be prepared to flee if the dice aren't falling in my favor. Two completely different experiences and playstyles, even though the high-level math looks the same.

Answer 7

This answer is in addition to the psychology (crits feel good) and meta-game (crit as a stat is an additional lever to play with when determining the optimal build) aspects that are covered by other answers.

When a game includes the ability to heal, in addition to just dealing damage, the timing of when damage arrives, along with the size of that damage, has an impact on how survivable the damage is.

Generally, big spikes of damage are harder to heal through, so even if over time the damage is mathematically equivalent, having X DPS and Y crit chance will make it easier to kill the opponent than simply having X * (1 + Y) DPS and no crit chance.

As an extreme example, consider an attacker who deals exactly 10 damage with every attack, attacking once per second, and a defender who has 20 health and is able to heal 10 health every second. The attacker will never make any progress, and the defender will never die. Now, consider an attacker who deals 9 damage with every attack, but has a 10% chance to do 18 damage, attacking the same defender. While the defender will slowly heal back up after a crit, getting hit with a second crit within 8 seconds (which isn't particularly unlikely) would leave the defender dead.

When the game incorporates other mechanics related to timing like healing abilities with different cast times, this can add additional layers beyond just allowing crit strings to affect/determine who wins. For example, if the healer's target gets hit with a big crit while the healer is in the process of using a heal with a long cast time, the healer needs to decide whether to continue with the existing cast, or abandon it to cast a heal that will take effect sooner instead. This can have a positive impact on healing-centric game play, by making healing a more dynamic experience where choices matter. A similar situation arises for a single player who, after losing a big chunk of health to a crit must decide between continuing to attack, or switching to healing.

Answer 8

The nature of critical hits as an occasional multiplier on damage has been covered by other answers.

But critical hits do not need to be that, or just that. You can add additional mechanics to them, such as "crits set enemy on fire", or perhaps different weapons having different critical strike rates or multipliers for each body part.

In this generalised form, form they are often called "lucky hits" or something to that effect, and on games with lots of opportunities for build combinations, they can become cornerstones of builds that count on indirect effects to succeed.

Answer 9

but why would players choose random chance rather than extra damage if the end result is the same?

Let me demonstrate the answer to you with Math. Imagine you have 40m of fence, and you want to maximize the area it surrounds. It must be a rectangle btw.

side lengths | area
1,1,19,19    | 1m * 19m = 19m²
3,3,17,17    | 3m * 17m = 51m²
5,5,15,15    | 5m * 15m = 75m²
8,8,12,12    | 8m * 12m = 96m²
10,10,10,10  | 10m * 10m = 100m²

So the quadratic multiplication yields the best result. If you have 'n' factors that influence the outcome, it's always best to increase all of them, but in a way where there is some kind of exponential equilibrium.

In games where you have 'n' stats that increase damage (attack speed, critical strike chance, outright bonus damage), it's best to increase all of them (taking weighting into regard). Critical strike is just one of multiple factors that need to be increased for optimization.

So players are basically forced to go for critical strike, simply because it's one factor of many.

How do you make critical attacks not useless in video games?

This is an excellent question, because in many games critical strikes are just another fancy way of increasing the damage/heal output of players (as you said). If the critical strike chance is 10%, and the damage multiplier is 200%, it means you make 10% more overall damage. Some games add some special effect, like gaining some buff if dealing a critical strike. Said games often have a high ratio of attack rates and critical strike chances though, meaning its occurrence is part of the basic attack rotation. Some games give you even 80%+ critical strike chance at some point, rendering its concept into absurdity.

So what would be a good way to implement critical strikes:

1. Make them not chance based, but situation based. Both parties should affect its occurrence. An easy example is flanking - aka striking an enemy from behind or the side. Or in shooter games, hitting the head or the back.
2. Stealth attacks, and maybe skills that manually cause a critical strike. Or as Fallout 4 did, having critical strikes being manually triggered, whereas the "critical meter" fills up by just attacking.
3. If it's supposed to be a random chance, it should occur rarely enough, so that it is significant. That means maybe 1 occurrence every ~20-40 seconds. I made a formula in which "critical strike" is an attribute that influences both, the chance and modifier at once. First it raises the chance quickly from 0% to 5%, then it smoothly converges to 10%, while the modifier is first increased very little, and then more rapidly. This ends up in the total extra output being linear, meaning 10% of critical gives 10% bonus damage, 50% gives 50% bonus damage. And it will make critical strikes more impactful as that stat increases. Otherwise you have the problem that it's up to the player to do the x*y Math (that's the case for most games).
4. Make critical strikes occur rarely, but it causes bonus flat damage, meaning the attack is independent, and the occurrence can be based on time (like procs per minute).

By the very nature of what critical strikes are supposed to be, they should be rare and something a player would notice when it occurs.