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== Calculation == === Total modifier === Bonuses and slows are combined under separate rules: positive bonuses are additive, while slows are multiplicative. :<math>\text{Total Modifier} = (\text{Sum of Bonuses}) - \left(1 - \text{Total Slows}\right)</math> Where: * '''Sum of Bonuses''' = all positive bonuses added together (e.g., {{#tag:math|{{#expr: {{DataProp|Ricochet|BonusFireRate}}/100 }} + {{#expr: {{DataProp|Swift Striker|BonusFireRate}}/100 }} }}) * '''Total Slows''' = the result of multiplying the remaining values of each slow: <math>(1 - \text{Slow}_1) \times (1 - \text{Slow}_2) \times \dots</math> Any total modifier lower than '''-50%''' is capped at that value. === Applying the modifier === The total modifier is not applied the same way in both directions. Its effect depends on its sign: * If the total modifier is '''positive''', it increases Fire Rate directly: :<math>\text{Final Fire Rate} = \text{Base Fire Rate} \times (1 + \text{Total Modifier})</math> * If the total modifier is '''negative''', it instead increases the gun cycle time, the interval between shots: :<math>\text{Final Fire Rate} = \frac{\text{Base Fire Rate}}{1 + |\text{Total Modifier}|}</math> Because a negative modifier lengthens the interval rather than shortening the rate, it reduces the number of bullets fired per second by less than its stated value: * A '''-10%''' modifier leaves '''{{#expr: 100 / 1.1 round 1}}%''' of base Fire Rate. * A '''-25%''' modifier leaves '''{{#expr: 100 / 1.25 round 1}}%''' of base Fire Rate. * A '''-50%''' modifier, the maximum, leaves '''{{#expr: 100 / 1.5 round 1}}%''' of base Fire Rate, a reduction of only {{#expr: 100 - 100 / 1.5 round 1}}% in bullets per second. Positive modifiers have no equivalent discrepancy: a +50% modifier grants a full 50% more bullets per second. The in-game UI reports the total modifier itself, not the resulting change in bullets per second. === Examples === ==== Combined bonuses and slows ==== For an example with multiple sources: * '''+{{DataProp|Ricochet|BonusFireRate}}%''' Fire Rate from {{ItemIcon|Ricochet}} * '''+{{DataProp|Swift Striker|BonusFireRate}}%''' Fire Rate from {{ItemIcon|Swift Striker}} * '''-{{DataProp|Vexing Bolt|Upgrades.1.FireRateSlow}}%''' Fire Rate Slow from {{HeroIcon|Sinclair}}'s {{AbilityIcon|Vexing Bolt}} * '''-{{DataProp|Suppressor|FireRateSlow}}%''' Fire Rate Slow from an enemy's {{ItemIcon|Suppressor}} First, the groups are calculated separately: * '''Bonuses:''' {{#tag:math|{{#expr: {{DataProp|Ricochet|BonusFireRate}}/100 }} + {{#expr: {{DataProp|Swift Striker|BonusFireRate}}/100 }} {{=}} {{#expr: ({{DataProp|Ricochet|BonusFireRate}} + {{DataProp|Swift Striker|BonusFireRate}})/100 }} }} * '''Slows:''' {{#tag:math|(1 - {{#expr: {{DataProp|Vexing Bolt|Upgrades.1.FireRateSlow}}/100 }}) \times (1 - {{#expr: {{DataProp|Suppressor|FireRateSlow}}/100 }}) {{=}} {{#expr: 1 - {{DataProp|Vexing Bolt|Upgrades.1.FireRateSlow}}/100 }} \times {{#expr: 1 - {{DataProp|Suppressor|FireRateSlow}}/100 }} {{=}} {{#expr: (1 - {{DataProp|Vexing Bolt|Upgrades.1.FireRateSlow}}/100) * (1 - {{DataProp|Suppressor|FireRateSlow}}/100) }} }} They are then combined into the total modifier: :{{#tag:math|\text{Total Modifier} {{=}} {{#expr: ({{DataProp|Ricochet|BonusFireRate}} + {{DataProp|Swift Striker|BonusFireRate}})/100 }} - (1 - {{#expr: (1 - {{DataProp|Vexing Bolt|Upgrades.1.FireRateSlow}}/100) * (1 - {{DataProp|Suppressor|FireRateSlow}}/100) }}) {{=}} {{#expr: ({{DataProp|Ricochet|BonusFireRate}} + {{DataProp|Swift Striker|BonusFireRate}})/100 }} - {{#expr: 1 - (1 - {{DataProp|Vexing Bolt|Upgrades.1.FireRateSlow}}/100) * (1 - {{DataProp|Suppressor|FireRateSlow}}/100) }} {{=}} {{#expr: (({{DataProp|Ricochet|BonusFireRate}} + {{DataProp|Swift Striker|BonusFireRate}})/100 - (1 - (1 - {{DataProp|Vexing Bolt|Upgrades.1.FireRateSlow}}/100) * (1 - {{DataProp|Suppressor|FireRateSlow}}/100))) round 4 }} }} Because the total modifier is negative, it is applied to the gun cycle time: :{{#tag:math|\text{Final Fire Rate} {{=}} \frac{\text{Base Fire Rate} }{1 + {{#expr: abs(({{DataProp|Ricochet|BonusFireRate}} + {{DataProp|Swift Striker|BonusFireRate}})/100 - (1 - (1 - {{DataProp|Vexing Bolt|Upgrades.1.FireRateSlow}}/100) * (1 - {{DataProp|Suppressor|FireRateSlow}}/100))) round 4 }} } {{=}} {{#expr: (1 / (1 + abs(({{DataProp|Ricochet|BonusFireRate}} + {{DataProp|Swift Striker|BonusFireRate}})/100 - (1 - (1 - {{DataProp|Vexing Bolt|Upgrades.1.FireRateSlow}}/100) * (1 - {{DataProp|Suppressor|FireRateSlow}}/100))))) round 3 }} \times \text{Base Fire Rate} }} The hero therefore fires '''{{#expr: ((1 - 1 / (1 + abs(({{DataProp|Ricochet|BonusFireRate}} + {{DataProp|Swift Striker|BonusFireRate}})/100 - (1 - (1 - {{DataProp|Vexing Bolt|Upgrades.1.FireRateSlow}}/100) * (1 - {{DataProp|Suppressor|FireRateSlow}}/100))))) * 100) round 1 }}%''' fewer bullets per second, while the in-game UI displays the total modifier of '''{{#expr: (({{DataProp|Ricochet|BonusFireRate}} + {{DataProp|Swift Striker|BonusFireRate}})/100 - (1 - (1 - {{DataProp|Vexing Bolt|Upgrades.1.FireRateSlow}}/100) * (1 - {{DataProp|Suppressor|FireRateSlow}}/100))) * 100 round 0 }}%''', rounded to the nearest whole number. ==== Maximum slow reduction ==== For an example with only slows applied: * No positive Fire Rate bonuses (0) * '''-{{DataProp|Vexing Bolt|Upgrades.1.FireRateSlow}}%''' Fire Rate Slow from {{HeroIcon|Sinclair}}'s {{AbilityIcon|Vexing Bolt}} * '''-{{DataProp|Suppressor|FireRateSlow}}%''' Fire Rate Slow from an enemy's {{ItemIcon|Suppressor}} * '''-{{DataProp|Rusted Barrel|FireRateSlow}}%''' Fire Rate Slow from an enemy's {{ItemIcon|Rusted Barrel}} The calculation is: :{{#tag:math|0 - (1 - ({{#expr: 1 - {{DataProp|Vexing Bolt|Upgrades.1.FireRateSlow}}/100 }} \times {{#expr: 1 - {{DataProp|Suppressor|FireRateSlow}}/100 }} \times {{#expr: 1 - {{DataProp|Rusted Barrel|FireRateSlow}}/100 }}))}} :{{#tag:math|0 - (1 - {{#expr: (1 - {{DataProp|Vexing Bolt|Upgrades.1.FireRateSlow}}/100) * (1 - {{DataProp|Suppressor|FireRateSlow}}/100) * (1 - {{DataProp|Rusted Barrel|FireRateSlow}}/100) }}) {{=}} {{#expr: (0 - (1 - (1 - {{DataProp|Vexing Bolt|Upgrades.1.FireRateSlow}}/100) * (1 - {{DataProp|Suppressor|FireRateSlow}}/100) * (1 - {{DataProp|Rusted Barrel|FireRateSlow}}/100))) round 4 }} }} This results in a calculated modifier of '''{{#expr: (0 - (1 - (1 - {{DataProp|Vexing Bolt|Upgrades.1.FireRateSlow}}/100) * (1 - {{DataProp|Suppressor|FireRateSlow}}/100) * (1 - {{DataProp|Rusted Barrel|FireRateSlow}}/100))) * 100 round 2 }}%'''. Due to the cap, the value is raised to the maximum of '''-50%''', which is then applied to the gun cycle time: :{{#tag:math|\text{Final Fire Rate} {{=}} \frac{\text{Base Fire Rate} }{1 + 0.5} {{=}} {{#expr: 1 / 1.5 round 3 }} \times \text{Base Fire Rate} }} Even under the maximum possible slow, the hero still fires two thirds of the bullets per second of an unslowed hero.
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