DPS Multiplier
1.3×
+30% effective DPS vs no crit
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The Critical Hit Chance Calculator determines how critical strike probability affects average damage output across games and builds. Critical hits (crits) deal bonus damage when triggered — the bonus ranges from 25% in some mobile games to 200% in games like League of Legends (which doubles damage on a crit). Understanding the mathematical relationship between crit chance, crit damage multiplier, and average DPS is essential for optimizing offensive builds across all RPG, MOBA, and action game genres. The fundamental formula for average damage from critical hits is: Average Damage = (1 - Crit Chance) x Normal Damage + Crit Chance x Crit Damage, which simplifies to: Average Damage = Normal Damage x (1 + Crit Chance x Crit Bonus). The Crit Bonus is the additional damage percentage above normal (for example, 100% bonus crit damage means crits deal 2x normal). This formula reveals the linear relationship: each percentage point of crit chance adds exactly Crit Bonus% of Normal Damage to average output. At 100% crit chance, average damage equals Crit Damage (the maximum possible from crits). The DPS uplift from crit can also be expressed as a multiplier: DPS Multiplier = 1 + (Crit Chance x Crit Bonus). For Path of Exile with 200% crit multiplier at 40% crit chance: multiplier = 1 + (0.40 x 2.0) = 1.80x DPS. This 80% DPS increase from crit alone demonstrates why crit builds are so powerful. The relationship between crit chance and crit damage scaling means these two stats multiply each other's effectiveness — stacking both simultaneously produces superlinear gains, making 'crit builds' dramatically more efficient than builds that invest in only one of the two stats.
Average Damage = Base Damage x (1 + Crit Chance x Crit Bonus%) DPS Multiplier from Crit = 1 + (Crit% x Crit Bonus) Optimal Crit Ratio = Crit% / Crit Damage% = 1:2 (for games where both scale from 0)
- 1Step 1: Note your base damage per hit and current crit chance and crit damage multiplier.
- 2Step 2: Calculate crit bonus: crit multiplier minus 1 (e.g., 2.5x crit = 150% bonus).
- 3Step 3: Compute DPS multiplier: 1 + (crit chance x crit bonus).
- 4Step 4: Multiply base DPS by the DPS multiplier to get crit-adjusted DPS.
- 5Step 5: Compare the value of adding more crit chance vs. more crit damage for the next investment.
- 6Step 6: Check if capping crit chance at 100% is achievable and what multiplier would be needed at cap.
In League of Legends, base crit damage is 175% (1.75x), with Infinity Edge adding +35% to make it 210% (2.1x) at 60% crit. Calculating without IE: DPS multiplier = 1 + (0.60 x 0.75) = 1.45x. With IE (requiring 60% crit to activate): 1 + (0.60 x 1.10) = 1.66x. The difference shows why Infinity Edge is the highest-priority item after reaching the 60% crit threshold — it dramatically amplifies existing crit chance.
PoE crit builds can reach extraordinary multipliers. At 70% crit chance and 400% crit multiplier (300% bonus), the DPS multiplier is 3.1x — meaning crit alone triples average damage output compared to zero crit. Adding more crit chance (from 70% to 80%) adds 0.10 x 3.0 = 0.30 to the multiplier, going from 3.1x to 3.4x (+9.7% DPS). Adding more crit damage (from 400% to 450%) adds 0.70 x 0.50 = 0.35, going from 3.1x to 3.45x (+11.3% DPS) — similar value at this ratio.
In Genshin, crit rate provides a probability of triggering the crit damage bonus. At 60% rate and 180% CRIT DMG, average damage is 2.08x base. The optimal 1:2 ratio (CR%:CD%) is satisfied here (60%:180% = 1:3 — CD is weighted higher than optimal, suggesting more CR% investment would improve DPS). Adding 10% more Crit Rate: 1 + (0.70 x 1.80) = 2.26x (+8.7%), better than adding the equivalent in CD.
At 100% crit chance, average damage equals crit damage — every attack is a critical hit. The DPS multiplier equals the crit multiplier exactly (2.0x in this case). Further increasing crit chance above 100% has no value. At this point, all stat investment should shift to increasing the crit damage multiplier, as each additional 10% crit damage adds 0.10 to the DPS multiplier linearly.
Comparing crit-focused vs non-crit builds in damage output. This application is commonly used by professionals who need precise quantitative analysis to support decision-making, budgeting, and strategic planning in their respective fields
Determining optimal crit rate to crit damage ratio for character builds. Industry practitioners rely on this calculation to benchmark performance, compare alternatives, and ensure compliance with established standards and regulatory requirements
Calculating DPS impact of crit-boosting items or passives. Academic researchers and students use this computation to validate theoretical models, complete coursework assignments, and develop deeper understanding of the underlying mathematical principles
Researchers use crit chance calc computations to process experimental data, validate theoretical models, and generate quantitative results for publication in peer-reviewed studies, supporting data-driven evaluation processes where numerical precision is essential for compliance, reporting, and optimization objectives
Guaranteed Crit on First Hit
{'title': 'Guaranteed Crit on First Hit', 'body': "Some abilities or items guarantee a crit on the next hit (like Praxis Jab in WoW, or Garen's Q in LoL). These effectively set crit chance to 100% for that specific hit, guaranteeing maximum damage. Optimizing around guaranteed crits often means stacking crit damage rather than crit chance, since chance is irrelevant for the triggered hit."}
Negative Crit Chance
{'title': 'Negative Crit Chance', 'body': "Some games implement 'crit reduction' as a defensive stat that reduces the enemy's effective crit chance against you. A player with 20% crit reduction against an enemy with 40% crit chance effectively faces only 20% crit chance. In PoE, evade and fortify mechanics partially mitigate crit contribution by either avoiding hits entirely or reducing damage regardless of crit."}
Negative input values may or may not be valid for crit chance calc depending on the domain context.
Some formulas accept negative numbers (e.g., temperatures, rates of change), while others require strictly positive inputs. Users should check whether their specific scenario permits negative values before relying on the output. Professionals working with crit chance calc should be especially attentive to this scenario because it can lead to misleading results if not handled properly. Always verify boundary conditions and cross-check with independent methods when this case arises in practice.
| Crit Chance | 50% Crit Bonus | 100% Crit Bonus | 200% Crit Bonus |
|---|---|---|---|
| 10% | 1.05x | 1.10x | 1.20x |
| 25% | 1.125x | 1.25x | 1.50x |
| 50% | 1.25x | 1.50x | 2.00x |
| 75% | 1.375x | 1.75x | 2.50x |
| 100% | 1.50x | 2.00x | 3.00x |
Should I prioritize crit chance or crit damage?
The optimal balance depends on your current ratio. The marginal value of adding 1% crit chance equals (Crit Damage Bonus) x base DPS, while adding 1% crit damage equals (Crit Chance) x base DPS. When crit chance equals 1/(crit damage bonus) — for a 200% bonus, this is 50% crit rate — both stats provide equal value. Below this threshold, crit chance is more valuable; above it, crit damage is more valuable. For most games, the optimal ratio works out to approximately 1 Crit Rate to 2 Crit Damage.
What is the soft cap for crit chance?
Most games cap crit chance at 100%, though some (Valorant headshots are not really a crit system, Dark Souls has no crit cap) differ. In games like Genshin Impact, there is a hard 100% crit rate cap. In Path of Exile, the crit chance cap is 95%, with a mandatory 5% chance to not crit. In League of Legends, crit chance is capped at 100% but diminishing returns apply through item count scaling rather than a mathematical cap.
How does crit variance affect gameplay?
Crit builds have high damage variance — against the same enemy, you might deal 5,000 or 15,000 damage depending on whether crits trigger. This variance is exciting but also means kill-timing is less predictable than constant-damage builds. In PvP games, high variance can be advantageous (you can 'spike' enemies unexpectedly) or disadvantageous (you might not burst them when needed). In PvE, variance generally doesn't matter long-term since average damage determines boss kill time.
Do attacks need to hit to crit?
In most games, a critical hit first requires a successful hit — missed attacks cannot crit. This makes accuracy/hit chance a prerequisite for crit builds to function. In Path of Exile, accuracy determines hit chance (separate from the dodge/evade of the enemy), and low accuracy dramatically reduces effective crit contribution. Always verify your hit chance meets a minimum threshold (typically 90%+) before investing heavily in crit scaling.
What is Lucky Critical Strikes (Genshin/Diamond Flask)?
Lucky Critical Strikes (used in Genshin Impact's Resonance or Path of Exile's Diamond Flask) means each hit rolls the crit check twice and takes the higher result, effectively squaring the probability of NOT critting. P(no crit with Lucky) = (1 - CR%)^2. For 30% crit rate: normal P(crit) = 30%; lucky P(crit) = 1 - 0.70^2 = 1 - 0.49 = 51%. Lucky nearly doubles effective crit rate at 30% CR. At 80% CR: lucky = 1 - 0.20^2 = 1 - 0.04 = 96% — almost guaranteed crits.
How do crits interact with damage over time effects?
This varies by game. In Path of Exile, critical hits can cause ailments (ignite, bleed) based on the hit damage — so a crit that deals 3x damage triggers an ignite worth 3x the hit. In Diablo IV, some DoT effects separately benefit from crit chance but calculate damage independently. In Genshin Impact, transformative reactions (Overloaded, Vaporize) are not directly multiplied by crits but scale from elemental mastery and level. Always check your specific game's crit-DoT interaction rules.
Can crit chance exceed 100% and is it useful?
In most games, crit chance above 100% provides no benefit — it is capped. However, some games convert excess crit chance into crit damage, bonus effects, or apply it to secondary mechanics. In a few systems, having more than 100% crit chance acts as a buffer against effects that reduce crit chance (debuffs, curses). Check your specific game to determine the behavior of over-capped crit chance before investing in excess.
プロのヒント
Calculate your current 'effective DPS multiplier' from crit: 1 + (your crit% x your crit bonus%). Then estimate whether adding 1% crit chance vs 1% crit damage yields more DPS gain. Invest in whichever is currently lower relative to the optimal ratio.
ご存知でしたか？
The concept of 'critical hits' in video games traces back to Dungeons and Dragons table-top gameplay in the 1970s. The first confirmed video game critical hit system appeared in the original Dungeons and Dragons computer game in 1974. Modern games have evolved this system into deeply mathematical stat interactions that would be unrecognizable to early RPG players.