Procs Per Minute: Difference between revisions

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(intro: rephrase because some procs always fire and don't use PPM, rephrase to clarify recharge buffs and enhancements are different for PPM)
(→‎Single Target: table: removed 5.5 and 6.5 PPM (no such procs in game), added 7 PPM (superior brute ATO proc))
 
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'''Procs Per Minute''' (PPM) is the "average" number of times per minute an enhancement's special effect will attempt to fire. This mechanic is used by all enhancements with a chance to proc or not.
'''Procs Per Minute''' (PPM) is the "average" number of times per minute an enhancement's special effect will attempt to fire. This mechanic is used by all enhancements with a chance to proc or not.


Procs Per Minute are adjusted for the ''enhanced recharge + activation time'' of a power, not its final buffed number. So, making a power recharge faster with recharge enhancements usually leaves its PPM unchanged. Making a power recharge faster with recharge bonuses or buffs usually increases its PPM.
Procs Per Minute are adjusted for the ''enhanced recharge + activation time'' of a power, not its final buffed number. So, recharge enhancements usually leave PPM unchanged from the proc's description. Recharge bonuses and buffs usually increase effective PPM above the proc's description.


== Calculating Chance to Proc ==
== Calculating Chance to Proc ==
The current formulae used by the game:
The current formulae used by the game:


If power is a click: PPM * ((Enhanced Recharge Time + Time To Activate) / (60 * Area Factor))
If power is a click: PPM × ((Enhanced Recharge Time + Time To Activate) / (60 × Area Factor))


If power is not a click: PPM * ((Activate Period) / (60 * Area Factor))
If power is not a click: PPM × ((Activate Period) / (60 × Area Factor))


Note: For this calculation, "Enhanced Recharge Time" includes reductions from enhancements and Alpha slotting, but not from Luck of the Gambler bonuses, other enhancement set bonuses, Hasten, or other recharge buffs. The calculation uses activation time, not [[Arcanatime]].
Note: For this calculation, "Enhanced Recharge Time" includes reductions from enhancements and Alpha slotting, but not from Luck of the Gambler bonuses, other enhancement set bonuses, Hasten, or other recharge buffs. The calculation uses activation time, not [[Arcanatime]].
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* Single Target Area Factor = 1
* Single Target Area Factor = 1
* Sphere Area Factor = [1+(0.15*Radius)] * 0.75 + 0.25
* Sphere Area Factor = [1 + (0.15×Radius)] × 0.75 + 0.25
* Cone Area Factor = [1+(0.15*Radius)-(0.011*Radius*(360-Arc)/30)] * 0.75 + 0.25
* Cone Area Factor = [1 + (0.15×Radius) − (0.011×Radius×(360−Arc)/30)] × 0.75 + 0.25


Area Factor applies regardless of how many you ''actually'' hit. When using AoE and cones on single targets, proc performance will be significantly lower than with comparable single target powers.
Area Factor applies regardless of how many you ''actually'' hit. When using AoE and cones on single targets, proc performance will be significantly lower than with comparable single target powers.


The final chance to proc is clamped between a minimum and a maximum.
The final chance to proc is clamped between a minimum and a maximum.
* The minimum chance to proc is (PPM * 1.5%) + 5%.
* The minimum chance to proc is (PPM × 1.5%) + 5%.
** For example, a typical damage proc, with 3.5 PPM, has a minimum chance to proc of 10.25%. It will have at least a 10.25% chance to proc per target, even if the power has a large radius and short recharge.
** For example, a typical damage proc, with 3.5 PPM, has a minimum chance to proc of 10.25%. It will have at least a 10.25% chance to proc per target, even if the power has a large radius and short recharge.
* The maximum chance to proc is 90%.
* The maximum chance to proc is 90%.
** Procs that always happen, such as Kismet's to hit buff and Miracle's recovery buff, ignore this maximum, and proc 100% of the time.
** Procs that always happen, such as Kismet's to hit buff and Miracle's recovery buff, ignore this maximum, and proc 100% of the time.


== Guaranteed Proc ==
== Maximum Proc Chance ==
=== Single Target ===
=== Single Target ===
The formula for calculating the required ''enhanced recharge + activation time'' to achieve a 90% proc chance in a click power is ''54/PPM''.
The formula for calculating the required ''enhanced recharge + activation time'' to achieve a 90% proc chance in a click power is ''54/PPM''.
* Example 1: For Decimation or Gaussian's build up proc with 1 PPM, 54/1=54 seconds. A single-target click power with an ''enhanced recharge + activation time'' of at least 54 seconds will have the maximum proc chance of 90%, even if the power's ''actual recharge'' is faster due to Hasten, set bonuses, etc.
* Example 1: For Decimation or Gaussian's build up proc with 1 PPM, 54/1=54 seconds. A single-target click power with an ''enhanced recharge + activation time'' of at least 54 seconds will have the maximum proc chance of 90%, even if the power's ''actual recharge'' is faster due to Hasten, set bonuses, etc.
* Example 2: For a typical damage proc with 3.5 PPM, 54/3.5≈15.43 seconds. A single-target click power with an ''enhanced recharge + activation time'' of at least 15.44 seconds will have the maximum proc chance of 90%.
* Example 2: For a typical damage proc with 3.5 PPM, 54/3.5≈15.43 seconds. A single-target click power with an ''enhanced recharge + activation time'' of at least 15.43 seconds will have the maximum proc chance of 90%.


Note that non-click powers cannot change their "activate period", so their chance to fire will always be the same, even if the power can be slotted or buffed with recharge.
Note that non-click powers cannot change their "activate period", so their chance to fire will always be the same, even if the power can be slotted or buffed with recharge.


{| width=35% class="wikitable"
{| class="wikitable" style="width: 30em;"
|-
|-
! 1PPM
! 1PPM
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! 2.5PPM
! 2.5PPM
| 21.6 seconds
| 21.6 seconds
! 5.5PPM
! 6PPM
| 9.82 seconds
| 9 seconds
|-
|-
! 3PPM
! 3PPM
| 18 seconds
| 18 seconds
! 6PPM
! 7PPM
| 9 seconds
| 7.71 seconds
|-
|-
! 3.5PPM
! 3.5PPM
| 15.43 seconds
| 15.43 seconds
! 6.5PPM
| 8.31 seconds
|}
|}


=== Cone/Area of Effect ===
=== Cone/Area of Effect ===
The formula for calculating the required ''recharge + activation time'' to achieve a 90% proc chance is ''(54 * Area Factor)/PPM'', where Area Factor is ''[1+(0.15*Radius)-(0.011*Radius*(360-Arc)/30)] * 0.75 + 0.25''.[http://web.archive.org/web/20120906120413/http://boards.cityofheroes.com/showpost.php?p=4215577&postcount=301] Note that when Arc is 360 degrees (which is true for any non-Cone AoE) the Area Factor simplifies to ''1+(0.15*Radius)''.
The formula for calculating the required ''recharge + activation time'' to achieve a 90% proc chance is ''(54 × Area Factor)/PPM'', where Area Factor is ''[1 + (0.15×Radius) − (0.011×Radius×(360−Arc)/30)] × 0.75 + 0.25''.[http://web.archive.org/web/20120906120413/http://boards.cityofheroes.com/showpost.php?p=4215577&postcount=301] Note that when Arc is 360 degrees (which is true for any non-Cone AoE) the Area Factor simplifies to ''[1 + (0.15×Radius)] × 0.75 + 0.25''.


A refactored equation for the Area Factor which converts the decimal fractions into long-form with a single linear order of operations and no decimals is ''(((((Arc-360)*11)+4500)/40000)*Radius)+1''.
A refactored equation for the Area Factor which converts the decimal fractions into long-form with a single linear order of operations and no decimals is ''((((Arc×11)+540)/40000)×Radius)+1''. When Arc is 360 degrees, this equation simplifies to ''Radius×9/80+1''.


== Developer Comments ==
== Developer Comments ==
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It's base recharge time. If you have a single target attack slotted with a 2 ppm IO, the power would need to have a 30 second recharge to have a 100% proc chance. You could then IO it to ~100% recharge and combine that with 100% global recharge bonus to get the power's recharge down to 10 seconds, and it would still have that 100% proc chance. This is how all of the store-bought IO set procs work, as well as the ATO procs that are not global bonuses. This changes the math on "optimal proccing" significantly from the traditional "flat rate" approach, and causes the performance delta of optimal and non-optimal to be much smaller, so you can really slot these in any power you use and you will see them be effective.}}
It's base recharge time. If you have a single target attack slotted with a 2 ppm IO, the power would need to have a 30 second recharge to have a 100% proc chance. You could then IO it to ~100% recharge and combine that with 100% global recharge bonus to get the power's recharge down to 10 seconds, and it would still have that 100% proc chance. This is how all of the store-bought IO set procs work, as well as the ATO procs that are not global bonuses. This changes the math on "optimal proccing" significantly from the traditional "flat rate" approach, and causes the performance delta of optimal and non-optimal to be much smaller, so you can really slot these in any power you use and you will see them be effective.}}
== Historical ==
{{historical|type=section}}
[[Issue 24]] introduced a 0.75 adjustment into the area factor equation. Prior to [[Issue 24]], area factors on AoE powers were larger, so AoE proc chances were lower. The pre-Issue 24 area factor formulas were:
* Sphere Area Factor = 1 + (0.15×Radius)
* Cone Area Factor = 1 + (0.15×Radius) − (0.011×Radius×(360×Arc)/30)
[[Category:Gameplay]]
[[Category:Gameplay]]

Latest revision as of 20:29, 8 November 2023

Overview

Procs Per Minute (PPM) is the "average" number of times per minute an enhancement's special effect will attempt to fire. This mechanic is used by all enhancements with a chance to proc or not.

Procs Per Minute are adjusted for the enhanced recharge + activation time of a power, not its final buffed number. So, recharge enhancements usually leave PPM unchanged from the proc's description. Recharge bonuses and buffs usually increase effective PPM above the proc's description.

Calculating Chance to Proc

The current formulae used by the game:

If power is a click: PPM × ((Enhanced Recharge Time + Time To Activate) / (60 × Area Factor))

If power is not a click: PPM × ((Activate Period) / (60 × Area Factor))

Note: For this calculation, "Enhanced Recharge Time" includes reductions from enhancements and Alpha slotting, but not from Luck of the Gambler bonuses, other enhancement set bonuses, Hasten, or other recharge buffs. The calculation uses activation time, not Arcanatime.

When accounting for powers that potentially can effect multiple targets and the proc potentially hitting off each target, the game discounts the probability of proc-ing off any one target by an Area Factor. The current way to calculate this number:

  • Single Target Area Factor = 1
  • Sphere Area Factor = [1 + (0.15×Radius)] × 0.75 + 0.25
  • Cone Area Factor = [1 + (0.15×Radius) − (0.011×Radius×(360−Arc)/30)] × 0.75 + 0.25

Area Factor applies regardless of how many you actually hit. When using AoE and cones on single targets, proc performance will be significantly lower than with comparable single target powers.

The final chance to proc is clamped between a minimum and a maximum.

  • The minimum chance to proc is (PPM × 1.5%) + 5%.
    • For example, a typical damage proc, with 3.5 PPM, has a minimum chance to proc of 10.25%. It will have at least a 10.25% chance to proc per target, even if the power has a large radius and short recharge.
  • The maximum chance to proc is 90%.
    • Procs that always happen, such as Kismet's to hit buff and Miracle's recovery buff, ignore this maximum, and proc 100% of the time.

Maximum Proc Chance

Single Target

The formula for calculating the required enhanced recharge + activation time to achieve a 90% proc chance in a click power is 54/PPM.

  • Example 1: For Decimation or Gaussian's build up proc with 1 PPM, 54/1=54 seconds. A single-target click power with an enhanced recharge + activation time of at least 54 seconds will have the maximum proc chance of 90%, even if the power's actual recharge is faster due to Hasten, set bonuses, etc.
  • Example 2: For a typical damage proc with 3.5 PPM, 54/3.5≈15.43 seconds. A single-target click power with an enhanced recharge + activation time of at least 15.43 seconds will have the maximum proc chance of 90%.

Note that non-click powers cannot change their "activate period", so their chance to fire will always be the same, even if the power can be slotted or buffed with recharge.

1PPM 54 seconds 4PPM 13.5 seconds
1.5PPM 36 seconds 4.5PPM 12 seconds
2PPM 27 seconds 5PPM 10.8 seconds
2.5PPM 21.6 seconds 6PPM 9 seconds
3PPM 18 seconds 7PPM 7.71 seconds
3.5PPM 15.43 seconds

Cone/Area of Effect

The formula for calculating the required recharge + activation time to achieve a 90% proc chance is (54 × Area Factor)/PPM, where Area Factor is [1 + (0.15×Radius) − (0.011×Radius×(360−Arc)/30)] × 0.75 + 0.25.[1] Note that when Arc is 360 degrees (which is true for any non-Cone AoE) the Area Factor simplifies to [1 + (0.15×Radius)] × 0.75 + 0.25.

A refactored equation for the Area Factor which converts the decimal fractions into long-form with a single linear order of operations and no decimals is ((((Arc×11)+540)/40000)×Radius)+1. When Arc is 360 degrees, this equation simplifies to Radius×9/80+1.

Developer Comments

Arbiter Hawk explained it in several posts on the official forums regarding the PPM system:

Arbiter Hawk (From several posts on the Official Forums)

This is a bit of a trick question - these procs that you mention function like store-bought IO procs, so their chance to proc with any given power activation fluctuates with the power's recharge time and some other factors. The long and short of it is that you should put the proc in a power you like to use, but this Proc-per-minute functionality does not advantage, say, Neutrino Bolt over X-Ray Eyes, if you like using X-Ray more. Slot the procs into attacks that you use, and you'll see them go off fairly regularly.

It is not limited to its displayed number of procs per minutes - that is representative of the average number of times it will proc over a minute if you use a single-target power every time it comes off recharge. You can still "get lucky", roll high numbers on the under-the-hood dice, and get many more than 4 procs in a minute. Its just that instead of a flat 20% chance to proc (which gives higher proc uptime per minute to a power that can be used more times per minute), the chance of proc'ing is now variable with the recharge (and other special factors) of the power that you're enhancing.

It's base recharge time. If you have a single target attack slotted with a 2 ppm IO, the power would need to have a 30 second recharge to have a 100% proc chance. You could then IO it to ~100% recharge and combine that with 100% global recharge bonus to get the power's recharge down to 10 seconds, and it would still have that 100% proc chance. This is how all of the store-bought IO set procs work, as well as the ATO procs that are not global bonuses. This changes the math on "optimal proccing" significantly from the traditional "flat rate" approach, and causes the performance delta of optimal and non-optimal to be much smaller, so you can really slot these in any power you use and you will see them be effective.

Historical

This section contains information that no longer applies to the current version of City of Heroes/Villains. It is provided for historical purposes.

Issue 24 introduced a 0.75 adjustment into the area factor equation. Prior to Issue 24, area factors on AoE powers were larger, so AoE proc chances were lower. The pre-Issue 24 area factor formulas were:

  • Sphere Area Factor = 1 + (0.15×Radius)
  • Cone Area Factor = 1 + (0.15×Radius) − (0.011×Radius×(360×Arc)/30)