ppm Procs Per Minute (PPM) Information Guide

[Bopper]

Procs Per Minute (PPM) Information Guide
by Bopper

Written: 9 August 2019

Last updated: 16 August 2019
(Information that might help new players in understanding the PPM game mechanics)

 

Update (9 August 2019)

This thread has adapted quite a bit since I first put the call out for Testers to determine how the PPM mechanics actually work and to clear up the confusion from outdated resources (love you Paragon Wiki, but you're i23, and we've moved on). Since then a lot of good information was discovered and plenty of mechanics have been confirmed. Now that I have a good understanding of most of the important pieces, I wanted to change the format of this post. I will still keep the Formulas that have been vetted at the top, that way people can see the important stuff right away. As for the rest of the post, I will slowly build it up to look more like a Guide (since the Mods moved my post to the Guide Section, might as well try to do them proud). 

 

As for building up a guide, that will take time, but I will clean it up and make it nice. For now, I'll try to keep adding sections periodically.

 

PPM Formulas

 

Breakdown of Formulas

Quote

For Click Type Powers:

Probability to Proc = PPM * (MRT+ CastTime) / (60 * AreaMod)

 

For all other Powers (Toggles, Auto, Pseudopets?):

Probability to Proc = PPM * ActivatePeriod / (60 * AreaMod)     

*Note* This is not the ActivatePeriod of the power, it is the ActivatePeriod of the Proc Enhancement which seems to always be 10 seconds. 

 

Modified Recharge Time:    

MRT = BaseRecharge / ( 1 + RechargeBoost_from_Enhancements_and_Alpha / 100 )

*Note* The MRT is not affected by outside global recharge boosts, such as Hasten, Set IO bonuses, team buffs, etc

 

Area Modifier:     

AreaMod = 0.25 + 0.75 * AF

*Note* This is a dampening effect Phil "Synapse" incorporated for i24. He felt the game's Area Factor punished procs too much

 

Area Factor:

Single Target:     AF = 1

 

Sphere (PBAoE or Target AoE):     AF = 1 + 0.15 * Radius

 

Cone:     AF = 1 + 0.15 * Radius - 0.011 * Radius x (360 - Arc) / 30

*Note* The original Range of a Cone Attack is considered the Radius. Enhancing the Range will not change the Radius, thus will not affect the proc probability.

 

Chain:     AF = 1 + 0.75 * MaxTargetsHit

*Note* I have yet to find a power in the game that is tagged as a kEffectArea_Chain that would use this Area Factor. FYI, Refractor Beam is tagged as kEffectArea_Sphere

 

One Formula to Rule them All (Except Chain):     AF = 1 + Radius x (11 * Arc + 540) / 30,000 

*Note* For Single Target use Radius = 0. 

*Note* For Sphere use Arc = 360.   

 

Maximum Probability to Proc:

MaxProb = 0.90     

*Note* Max probability is 90%

 

Minimum Probability to Proc:

MinProb = 0.05 + 0.015 * PPM

*Note* Min probability is 5% + PPM x 1.5%

 

List of PPM values for Procs:

The PPM for each Proc can be found HERE although this information has not yet been vetted for Homecoming servers as of yet. (Credit: @macskull)

 

 

 

Single Formulas (for Copy/Paste)

Spoiler

Here are single formulas you can Copy/Paste to perform the entire Proc Probability calculations (including some minor simplification). In the preceding quoted section, I broke down these formulas piece by piece.

Notes:

1.  I do not include a Chain formula here. I will when I can confirm which powers truly use it. What's listed below is all you need...for now.

2.  For Single Target use Radius = 0

3.  For Sphere (i.e. non-cone AoE) use Arc = 360

4.  For Cone use the original Range (non-boosted) as the Radius

5.  The ActivatePeriod is the activation period of the enhancement, which is always 10 seconds. Feel free to replace the ActivatePeriod with 10 in the Toggles formula.

 

Click Powers:

Probability to Proc = PPM * ( CastTime + BaseRecharge / (1 + RechargeBoost_from_Enhancements_and_Alpha / 100) ) / ( 60 * (1 + Radius * (11*Arc + 540) / 40000) )

 

Toggle, Auto (and Pseudopets?):

Probability to Proc = PPM * ActivatePeriod / ( 60 * (1 + Radius * (11*Arc + 540) / 40000) )

 

Scope

The purpose of this guide is to clear up the PPM mechanics that are used in i25+, which incorporated changes made in i24 Beta but never made it to Live. Most of the information in this guide comes from reviewing the original forum posts discussing this topic (Phil “Synapse, circa April of 2012), extensive testing used to confirm the proposals made in the forum discussion, and reviewing source code by the SCoRE team which further confirmed these formulas. The formulas are provided at the top of this guide for easy viewing, and I will update the formulas and this guide when new information is revealed.

 

Background

A “Proc” is a procedure that has a chance of happening. Every time you hit a target (self, ally or enemy) with a power slotted with a Proc enhancement, the effect of the Proc has a chance to trigger. For more information on Procs, check out the ParagonWiki article.

 

History (possibly a Drunken History)

Honestly, I don’t know the whole history, so I apologize if some of this is wrong. Basically, prior to i21 almost all Proc enhancements worked as a fixed percentage. This allowed for many exploits such as slotting AoE powers with a high tick rate to “buzzsaw” enemies. Then sometime in the i21 timeframe, the game introduced Archetype Origin enhancements (ATOs) which introduced the new Procs Per Minute (PPM) mechanic, which used base recharge, area factor, and cast time to calculate the probability of a proc triggering its effect. Finally, in i23, the original Proc enhancements had their fixed percentage mechanics replaced with PPM.

 

Due to exploits that could be achieved with the PPM mechanics (100% Proc probabilities, increased Proc rates using extremely high recharge builds, etc.), the devs decided to retune the PPM mechanic such that it used global recharge instead of base recharge and cap the probability to Proc at 90% (which was an attempt to preserve the spirit of a Proc always being a random occurrence). There was an obvious outcry as this unfairly punished players who built high-recharge characters and there was no way to predictably control your proc performance when teaming with players who could buff your recharge…which effectively debuffs your Proc performance. After much discussion with players, the devs came to a compromise and decided to only use the enhanced recharge (recharge buffs from enhancements or the Agility/Spiritual Alpha incarnates). The devs also compromised by incorporating a minimum Proc probability of at least 5% and dampened the negative effects of Area Factor so that AoE powers are not too severely punished. This was all incorporated into the i24 Beta when the game abruptly shut down.

 

PPM Mechanics

Procs Per Minute (PPM):    

PPM is roughly the average number of times per minute an effect from a Proc should fire. Each Proc enhancement will list this number in its description info and is used directly in calculating the Proc’s probability to trigger.

 

Modified Recharge Time (MRT):    

Modified Recharge Time (MRT) is the power’s actual recharge time when no global recharge boosts are present. If you’re not sure what your MRT is, you can check this in the game. Just right-click on the power, select “info”, and see what is listed as the recharge time. This recharge time will incorporate the recharge enhancements and alpha enhancements installed in the power, after enhancement diversification is factored in (again, global recharge boosts will not affect this).

 

Sometimes an example is worth a thousand words, so let’s do a few. Let’s assume we look at a power that has no recharge boosts from enhancements nor alpha incarnates, thus its enhanced recharge is 0%. If we look at the same power slotted with a T4 Agility Alpha and 2 Level 50 Invention-Origin Recharge Enhancements, the enhanced recharge is 114% after enhancement diversification. Let’s look at what the actual recharge time would be and the what the MRT would be if we also incorporate a 100% global recharge (achievable with Hasten and 4 LotGs).

 

Base Recharge	Enhanced Recharge	Global Recharge Bonus	Actual Recharge Time	Modified Recharge Time
10 sec	0%	0%	10 sec	10 sec
10 sec	0%	100%	5 sec	10 sec
10 sec	114%	0%	4.67 sec	4.67 sec
10 sec	114%	100%	3.18 sec	4.67 sec

 

As we can see, the global recharge bonus has no effect on the modified recharge time. This also highlights how added recharge has diminishing returns. Notice how going from 0% enhanced recharge to 114% enhanced recharge while already having 100% global recharge only decreased the actual recharge time by 1.82 seconds, yet the MRT decreased by 5.33 seconds. If your build already has managed high global recharge, you might be better off not slotting any recharge enhancements into your Proc powers as your actual recharge time will not decrease by much but your Proc performance can greatly decrease due to the significant decrease in MRT.

 

Activation Period (ActivatePeriod):    

Activation Period is the time between when the effects of an ENHANCEMENT trigger. Notice the not-so-subtle all-caps there? That's to emphasize the fact that the Activation Period has nothing to do with the power itself (ok, not exactly, but I'll get to that), but rather how the enhancement functions. When an enhancement is slotted, its effects trigger every 10 seconds (this is the ActivatePeriod) and those effects will last a duration of 10.25 seconds. There is some history to this that I don't recall, but I believe Procs used to work off of the Activation Period of the power, which resulted in silly Proc rates when slotted into powers with a high tick rate (Caltrops was cutely referred to as Proc-trops, if I recall correctly). Anyways, a change was made that resulted in powers such as toggles, autos, etc would only have the Procs pulse once every 10 seconds. Apparently this is how they incorporated it, by using the enhancement's activation period. I apologize for my shoddy description there, but my memory is fuzzy and I just recently discovered this functionality. I bring this up with emphasis because I've seen everywhere else folks talking about using the Activation Period of the power for calculating Proc probabilities (I was also guilty of that). Hopefully this clears that up.

 

There is one more thing worth mentioning, which does not impact how we calculate the Proc probability, but does detail something about the PPM mechanics. The Proc can only trigger when the power ticks, but will still be able to trigger once in every 10 second interval. That is a mouthful and not necessarily clear, so let me describe an example that I had tested repeatedly to confirm this mechanic. World of Confusion has an Activate Period of 4 seconds, so when you cast it (assuming a mob is present), World of Confusion will tick at 0 seconds, 4 sec, 8 sec, 12 sec, 16 sec, 20 sec, and so on. Where I highlighted in yellow is when the Procs will be eligible to trigger. Even though the time between the 2nd and 3rd proc is only 8 seconds, they fall into different 10 second intervals (which cover from 0-9.9 secs, 10-19.9 secs, and 20-29.9 secs). I don't know if this is intended behavior, but you can rest assure that when you attempt to calculate your Proc rates with toggles (or the like) you can expect on average one Proc opportunity per 10 seconds. 

 

Area Modifier (AreaMod):    

Area Modifier (AreaMod) is an unofficial term used to help distinguish itself from Area Factor, which is used in the game for things outside of PPM mechanics (such as Design Formulas). Basically, AreaMod is the new Area Factor for PPM calculations, which uses the 0.75 weight to dampen the effects on Proc probabilities (per Synapse's design). This is entirely an i24+ concept. It's worth noting the AreaMod (and the Area Factor that feeds into it) is entirely dependent on the area of effect of the power, and has no dependence on the maximum number of targets the power can hit.

 

Area Factor (AF):    

Area Factor (AF) is used in the game to discount the impact of Area of Effect (AoE) powers in relation to Single Target (ST) powers. For example, when it comes to power design formulas, the damage for an AoE attack should be equal to an equivalent ST attack's damage divided by the area factor (in this case, equivalent means having the same recharge time). This same concept was incorporated into the original PPM mechanics, however the impact proved to be more detrimental than anticipated; which is why Synapse proposed dampening its effect in i24 (thus creating the new PPM Area Factor...AreaMod).

 

Single Target - AF:    

The Area Factor of a Single Target attack is always 1. Obviously. It's the thing area attacks are being compared to.

 

Sphere - AF:    

The Area Factor of a Sphere attack applies to any non-cone AoE. These attacks are centered on a location (self, target, or patch) and can hit any target within its radius. 

 

Cone - AF:    

The Area Factor of a Cone attack is always less than its Sphere counterpart (same radius). This is simply due to the fact a sphere has 360 degree coverage and a cone has less than that, so it gets a discount. For ranged cone powers, the radius is always equal to the base range of the power (enhancing the range of the power will not change the radius of the power, so no impact on PPM calculations).

 

Chain - AF:    

The Area Factor of a Chain attack depends entirely on the maximum number of targets it can hit. From what I know, there were no Chain attacks prior to i25 (powers described as Chains actually summon numerous pet attacks, resulting in a chain visual effect, but those summoned pets use the Sphere - AF for PPM calculations). Now that we are in i25+, it seems this feature is starting to be implemented. As of this date (14 Aug 2019), only Refractor Beam (Sentinel, Beam Rifle) and Rehabilitating Circuit (Sentinel, Electric Mastery) might (MIGHT!) be tagged with the kEffectArea_Chain that would use the Chain - AF. Also, on Beta, there is mention that among the Dominator changes, Trick Shot (Martial Assault) "...is now a proper chain attack, hits up to 10 targets". This suggest its mechanics may be tweaked to a kEffectArea_Chain. Now, if you were getting excited by the prospects of utilizing Procs in Chain attacks - don't. It is a huge nerf. If Trick Shot does in fact become a Chain Attack with a maximum of 10 targets, its AreaMod would be 6.625. That's equivalent to a Sphere attack with a 50 (FIFTY!) foot radius. The dev team will seriously need to tweak the Chain - AF formula for it to become viable for Proc usage.

 

Frequently Asked Questions:

 

1) How much enhanced recharge can I put into a click-power and still achieve the maximum 90% Proc probability?

 

If the Proc has a greater than 90% probability to Proc without enhancement, you can calculate the maximum allowed enhanced recharge as follows:

 

 

For those interested, here is the derivation:

Spoiler

 

Other versions of the same formula include:

 

2) What is the impact of adding just a little bit of recharge enhancement into my click-power?

 

A lot, actually. The formula shows this already, but MRT will decay rapidly with just a little added recharge enhancement, then will slow its decay rate as it approaches its CastTime limit. Since there are an infinite number of combinations for BaseRecharge and CastTime, I will only do a few examples to demonstrate this point. In the below examples I will assume a 3.5 PPM proc (since it’s the most common), and I will look at Base/Cast pairings of: 10s/1s, 10s/2s, 4s/1s, 20s/2s. You'll notice the general trend is the same throughout.

 

Figures:

Spoiler

 

 

 

 

In the first 3 figures I wanted to highlight the first 20% drop off then the next 20% drop off. In each case you hit the 80% mark very quickly (~30% enhancement), but the 60% mark is not hit until much later (approximately triple the 80% mark’s enhancement value). So basically, the lesson here is to either go all in on not adding enhanced recharge, or put as much recharge as you want knowing that the drop off in Proc probability will have diminishing returns (the same could be said of the power’s cool down, so perhaps it’s a wash). In Figure 4, I wanted to show that if you are over the maximum probability (90%) you should go ahead and add enhanced recharge up to that limit (in this case, 48% enhanced recharge still kept the 90% Proc probability).

 

Lastly, please understand what these graphs are speaking to. It is merely suggesting the impact of your Proc probability whenever that power is clicked. It does not speak to your actual in game performance. Ultimately*, the goal is to maximize Proc rate (Procs per minute) which is a function of Proc probability (Procs per activation, which these figures show and requires recharge to be minimized) and Proc opportunity rate (activations per minute, which requires recharge to be maximize). There is a balance between Proc probability and opportunity rate that can be calculated using simple calculus, the parameters of the powers and your attack chain; however that is a unique calculation for every scenario and is outside the scope of this guide.

*Ok, so maximizing Proc rate is not really THE ultimate goal…but you get the point.

 

Update History:

Spoiler

*Update 1: Improving Range for Cones (via Enhancement or Boost) has NO IMPACT on proc performance*

 

*Update 2: Updated Title of Subject. Originally was "Calling all Testers: Can we confirm how Procs Per Minute (PPM) really works?"*

 

*Update 3: Max probability is confirmed at 90%. Minimum probability is confirmed at 5% + PPM x 1.5%*

 

*Update 4: Updated Title of Subject. Previously was "Testing on How Procs Per Minute (PPM) really works" (9 Aug 2019)*

 

*Update 5: Added the Scope, Background and History. Started to incorporate the PPM Mechanics section (12 Aug 2019)*

 

*Update 6: Finished PPM Mechanics section. Added FAQ Section (14 Aug 2019)*

 

*Update 7: Corrected misinformation in the ActivatePeriod section. Testing showed Procs in toggles can trigger once per 10 second intervals, but are not required to wait 10 seconds between Procs (16 Aug 2019)*

 

Original Post (27 June 2019, kept for Historical Purposes)

Spoiler

Hello to all, especially the ever so important testers.

 

I have been diving as deep as I could into the message boards (new and archived) as well as outdated paragonwiki pages, trying to get an understanding of how the Procs Per Minute (PPM) mechanic works. It seems i24 was supposed to have some new algorithms used for calculating PPM, but I am unsure as to whether or not anything was finalized prior to server shutdown. Below I will provide resources to the different algorithms I have seen:

 

This is the standard search for PPM, which is a hodgepodge of i23 mechanics with projected i24 mechanics sprinkled in. There's not much to say about this, other than folks seem to not pick up on what is from i23 and what is actually in the game today. Basically, we need to get away from thinking the calculations are using Base Recharge, but rather Enhanced Recharge (recharge that gets slotted into the power, including the agility alpha incarnate, but does not factor in the recharge boosts provided by buffs and Set IOs).

 

 

This source shows much of the same formulas as those provided in the previous link, however it tweaks it with a 1.25 and a 0.75 factor. This was cited around April of 2012.

i24 Proc Chance = (Enhanced Recharge + Activation Time)*(Current PPM * 1.25)/(60*Area Factor)

Area Factor = 1 + 0.75*(0.15*Radius - 0.011*Radius*(360-Arc)/30)

Doing some algebra simplification we can show Area Factor to be:

Area Factor = 1 + 0.75*(R*(11A + 540)/30000)

 

 

 

This thread, which seemed to go up until the day NCsoft terminated the Paragon Studios development team, used a version of the formula above; however, Hopeling's formula did not include the 0.75 muliplier. Also it seems the 1.25 multiplier to Current PPM was expected to occur with i24, so for example, the Force Feedback proc had a 1.5 PPM in i23 and it was expected all PPMs would increase by 25%. In i25, the Force Feedback proc is 2 PPM, so I suspect the PPMs shown in game today (i25) are correct for use in the following formula:

 

i25 Proc Chance = PPM * (Enhanced Recharge + Activation Time) / (60*Area Factor)

Area Factor = 1 + (Radius*(11*Arc + 540)/30000)

 

 

 

As you can see, I am getting a lot of information from old sources and there is no confirmation on anything that is currently implemented. This does not include the other nuances that come with calculating Proc Probability, such as ticks from powers that are toggled, a "pet" such as bonfire that does multiple ticks of damage, powers that have DoT ticks, summoned pets with procs slotted, etc.

 

Are there any good and curious testers who have the experience to take on this type of project? To be able to verify how PPM is calculated, how it works for different types of powers, and to get the story straight once and for all on how PPM works?

 

I thank you all for your time and consideration. I greatly hope good answers can come from this.

 

 

 

 

Still Not a Guide Writer!

Edited August 3, 2020 by Bopper

[SwitchFade]

We now have 3 ppm threads, mods, can we close/consolidate them?

[Bopper]

We now have 3 ppm threads, mods, can we close/consolidate them?

 

I would happily update this to a FAQ page if we can in fact get confirmation on the mechanics. You're right there are 3 threads on the topic, but there are dozens of other threads where PPM is discussed and people are using wrong assumptions. With paragonwiki outdated, there is no good source for this relatively new in game mechanic. For that reason I hope a developer or a tester can come out and provide us with the facts and have it consolidated in one place so that misinformation isn't spread across so many forum posts.

[Gaidin]

I'm bumping this thread because this particular thread contains the most useful info and Bopper's call for testing deserves attention; there is a dearth of info on effectively leveraging procs in i25.

 

Thanks, Bopper!

[Hopeling]

I was pretty involved in discussions about PPM close to shutdown. I have no idea if the .75 factor in question was actually implemented, but I suspect it was, since Synapse's other proposed changes (raise base PPM, calculate from enhanced recharge, cap proc chance at 90%) did go through.

 

It should be straightforward to test directly: slot a proc into a power, cast it a few hundred times, and see how many procs you get. Once you have enough data points, it should be pretty clear which of the two formulas is giving the correct value. Doing this by hand sounds super tedious, but I seem to recall that HeroStats could keep logs of things like that, which would let you get that data through regular play. If anybody remembers how to do it, go for it; otherwise I'll see if I can figure it out.

[Bopper]

I was pretty involved in discussions about PPM close to shutdown. I have no idea if the .75 factor in question was actually implemented, but I suspect it was, since Synapse's other proposed changes (raise base PPM, calculate from enhanced recharge, cap proc chance at 90%) did go through.

 

It should be straightforward to test directly: slot a proc into a power, cast it a few hundred times, and see how many procs you get. Once you have enough data points, it should be pretty clear which of the two formulas is giving the correct value. Doing this by hand sounds super tedious, but I seem to recall that HeroStats could keep logs of things like that, which would let you get that data through regular play. If anybody remembers how to do it, go for it; otherwise I'll see if I can figure it out.

 

I do see HeroStats listed as one of the Stick Messages. I believe it is up and working. If it works on the beta server, I can test it out this weekend once I figure out how to use it.

[Bopper]

Testing using HeroStats:

 

Assumed Formula: PPM * (EnhancedRecharge + CastTime) / (60 x AreaMod)

AreaMod = 1 + Radius*(11*Arc + 540) / 30,000

 

Executioner Shot

Base Recharge: 10s

Enhanced Recharge: 8.44s (18.5% added recharge)

Cast Time: 1.67s

FF Proc: 2PPM

Probability to Proc (with assumed formula): 33.7%

 

Number of Hits: 323

Number of Procs: 111 (34.4%)

 

In short, the formula seems to match what's tested

 

 

Bullet Rain

Base Recharge: 18s

Enhanced Recharge: 18s (0% added recharge)

Cast Time: 1.67s

FF Proc: 2PPM

Radius: 15ft

Arc: 360 degrees

Probability to Proc on each target (with assumed formula): 20.2%

 

Number of Hits: 1170 Number of Procs: 205 (17.5%)

 

This appears to be substantially different from the expected results. Throughout the testing, the average moved between 16-18% and never really approached the 20% the formula suggests. I am very curious as to why we would see underperformance when using the original formula when Synapse had suggested making improvements to the AreaMod formula (0.75 factor).

 

 

Other Discoveries

When testing Bullet Rain, I would potentially hit 4 targets with every attack (used the Combat Dummies at RWZ base). From the combat log a Hit Roll would occur for each target when Bullet Rain is cast. After, the Force Feedback Chance to Recharge will possibly Proc. On rarer occasions (15% of the time?) I would see a 2nd Proc hit after the 1st Proc wore off (after 5 seconds). This occurs prior to casting Bullet Rain again. This suggests to me that using Bullet Rain could proc more than once when cast (if there are multiple targets hit), and the 2nd proc will stack with the 1st proc (essentially 10 seconds of buff). If this can be confirmed, it would be major. All previous descriptions of how this proc included refreshing but not stacking. If that was the case, 2 simultaneous procs would look like 1.

 

 

Tomorrow I will look more into this. I'll test a cone power (Empty Clips) and I will see what Bullet Rain does against a mob of 16 targets (could 3 or 4 procs stack?). We shall see...

[Bopper]

Empty Clips

Base Recharge: 10s

Enhanced Recharge: 10s (0% added recharge)

Cast Time: 1.67s

FF Proc: 2PPM

Probability to Proc: 18.0%

 

Number of Hits: 761

Number of Procs: 175 (23.0%)

 

Once again, a large discrepancy from the formula, but this one is on the other end of the spectrum, greatly out-producing the expected results. This test was done only against a single target. I am re-running the test against 5 targets and will update this post with those results.

 

*UPDATE*

More details are mentioned below from discoveries of the multi-target test for Empty Clips. It appears there is a good chance Synapse did tweak the AreaMod formula, which would mean the true formula is possibly AreaMod = 1 + Radius x (11 x Arc + 540) / 40000.

 

If this is the case, the probability to proc off of 1 target would be 20.8% for Empty Clips (if no recharge enhancements). That value is still less than the 23% I observed from testing, but it's not nearly as egregious.

 

 

Empty Clips (5 targets):

 

Number of Attacks: 906

Number of Hits: 4307

Number of Procs: 597

 

Procs/Attack: 65.9%

Procs/Hit: 13.9%

 

It is worth noting that I did not see the double FF Proc stacking like I saw last night with Bullet Rain. This makes me suspect that a Damage over Time element may have played a part in that. I will revisit Bullet Rain and update my analysis in the near future. This does tell me something about the mechanization, however. I suspect that when multiple targets are hit with one attack, the Proc is checked on each target, and if any are hit, the Proc is fired (keep in mind, this is purely in terms of the Force Feedback Proc which only affects the Hero. Damage procs and others alike will likely behave differently and will be tested later).

 

After observing the results for Procs/Attack, it makes me wonder what the actual formula could be. If we use the formula where the AreaMod is 1 + R(11xA+540)/30000 (as I've been using so far), I would expect to trigger a FF proc 62.9% of my attacks if I were to hit all 5 targets 100% of the time. Obviously, I only hit my targets about 95% of the time, yet my Procs/Attack were greater than this optimum case as I saw Procs 65.9% of the time.

 

This makes me think, perhaps Synapse did in fact change the AreaMod formula. If he did in the way he described he would, we can expect the AreaMod to be 1 + R(11xA+540)/40000. When using this formula, I would expect Procs/Attack to be 68.8% if I hit 5 targets 100% of the time, and 60.7% if I hit only 4 targets every time. The fact my actual results falls between these numbers is very promising. If you care to see how I'm calculating my numbers, I'll provide them below.

 

The math:

 

Empty Clips:

PPM: 2

CastTime: 1.67

EnhancedRecharge = 10s

Radius = 40

Arc = 30

 

AreaMod3 = 1 + 40(11x30+540)/30000 = 2.16

AreaMod4 = 1 + 40(11x30+540)/40000 = 1.87

 

ProbToProc = PPMx(CastTime+EnhancedRecharge) / (60xAreaMod)

 

Prob3 = 2x(11.67) / (60x2.16) = 0.180093

Prob4 = 2x(11.65) / (60x1.87) = 0.208021

 

Probability to Proc at least once against 5 targets:

Prob2PALO_3 = 1 - (1 - Prob3)^5 = 0.629469

Prob2PALO_4 = 1 - (1 - Prob4)^5 = 0.688422

 

Probability to Proc at least once against 4 targets:

Prob2PALO_3 = 1 - (1 - Prob3)^4 = 0.548082

Prob2PALO_4 = 1 - (1 - Prob4)^4 = 0.606582

[Bopper]

Hail of Bullets (5 tgts):

Prob3K = 62.2%

Probability if 4 hit: 98.0%

 

Prob4k = 77.4%

Probability if 4 hit: 99.7%

 

 

Number of Attacks: 87

Number of Hits: 418

Number of Procs: 90

 

Procs/Attack: 103.4%

Procs/Hit: 21.5%

 

So that's not a typo...every attack had a proc and on 3 occasions I observed a 2nd proc go off right after the 1st one wore off, giving me 10 seconds of 100% recharge boost. It is rare, but there is something to attacks that have ticks of damage getting more opportunities to hit and potentially stacking the Proc (not refresh).

 

 

Hail of Bullets (1 tgt):

 

Number of Hits: 66

Number of Procs: 53

Number of Stacked Procs: 3

 

When factoring in the stacked procs, we had 66 attacks on a single target and 50 times there was atleast 1 proc. That is 75.8%. That lines up almost exactly with the updated Synapse formula for AreaMod (1 + Radius x (11 x Arc + 540) / 40000. At this point, I suspect this is the correct formula, but I will continue to monitor. In my next test I will attempt a chain to maximize uptime of the FF proc and try to determine if it could remain seamless with all attacks, or if the seamless stacking I've been seeing is only if it's from the same power.

 

[Bopper]

Now that Justin is back, I am able to re-attack some of the questions I had about PPM mechanics. The big test I wanted to look at was whether or not buffing the range on cone powers will result in diminished performance by your procs. Good news, enhancing range does not impact a cone's proc performance!. Now that I gave away the conclusion, folks who don't like math can go ahead and move on. For those who like the math, let's take a look at the results.

 

Just a reminder, I still am assuming the formula for calculating proc probability is Prob = PPM x (MRT + Cast) / [60 x (1 + Radius x (11xArc + 540)/40,000)]. My previous testing showed the divide by 30,000 version does not come close to the actual proc performance. The results of this test further proved this.

 

For this test I wanted to compare three scenarios: Default Range Proc Performance, Range Boosted Proc Performance, and Range Enhanced Proc Performance. For this reason, I decided to use a Dark/Energy/Leviathan Blaster. This offered me 4 cones to test, all with unique range/arc combinations. Also, Energy Manipulation offers the Boost Range power, which grants a 59.6% boost to all range attacks. For the default test I looked at all 4 cones, however given the performance of Bile Spray, I decided to just focus on it for the Range Enhanced and Range Boosted scenarios because any change in performance would be obvious. In each of these tests I slotted a single Positron Blast Proc (3.5 PPM).

 

Test 1: Umbral Torrent. No Range Enhancement. No Recharge Enhancement.

MRT: 15s

Cast: 1.03s

Range: 80 ft

Arc: 30 degrees

Prob = 34.1271%

 

Results:

# Procs: 75

Hits: 223

Percent: 33.63%  (Only 1 proc less than expected for 223 Hits)

 

Test 2: Tenebrous Tentacles. No Range Enhancement. No Recharge Enhancement.

MRT: 10s

Cast: 1.67s

Range: 40 ft

Arc: 40 degrees (In game says 40, City of Data says 39...I used 40 for my calculations)

Prob = 34.3813%

 

Results:

# Procs: 129

Hits: 387

Percent: 33.33%  (Only 4 procs less than expected for 387 Hits)

 

Test 3: School of Sharks. No Range Enhancement. No Recharge Enhancement.

MRT: 20s

Cast: 2.37s

Range: 50 ft

Arc: 30 degrees

Prob = 62.511%

 

Results:

# Procs: 113

Hits: 172

Percent: 65.70%%  (Only 5 procs more than expected for 172 Hits)

 

Test 4: Bial Spray. No Range Enhancement. No Recharge Enhancement.

MRT: 32s

Cast: 2.67s

Range: 60 ft

Arc: 30 degrees

Prob = 87.7404%

 

Results:

# Procs: 139

Hits: 156

Percent: 89.10%  (Only 2 procs more than expected for 156 Hits)

 

Test 5: Bial Spray. Range Boosted 59.6%. No Recharge Enhancement.

MRT: 32s

Cast: 2.67s

Range: 60 ft

Arc: 30 degrees

Prob = 87.7404% (Assuming Range Boosting has no impact)

Prob = 65.6037% (Assuming Range Boosting has impact, thus modified range becomes 95.76 ft)

 

Results:

# Procs: 60

Hits: 69

Percent: 86.70%  (Exactly expected for 69 hits)

 

Test 6: Bial Spray. Range Enhanced by 56.1%. No Recharge Enhancement.

MRT: 32s

Cast: 2.67s

Range: 60 ft

Arc: 30 degrees

Prob = 87.7404% (Assuming Range Enhancing has no impact)

Prob = 66.595% (Assuming Range Enhancing has impact, thus modified range becomes 93.65 ft)

 

Results:

# Procs: 51

Hits: 56

Percent: 91.07%  (Only 2 procs more than expected for 56 hits)

[Sunsette]

Thanks so much for your continued research.

 

I'm curious, can you confirm/deny that there's an ICD on Force Feedback? I see the stacked proc and I'[ve observed that fact myself, but the reddit thread on PPM suggested there was a cooldown on how often it can activate aside from stacking.

[jack_nomind]

this conforms with the best knowledge i have on internal cooldowns.

[Bopper]

Thanks so much for your continued research.

 

I'm curious, can you confirm/deny that there's an ICD on Force Feedback? I see the stacked proc and I'[ve observed that fact myself, but the reddit thread on PPM suggested there was a cooldown on how often it can activate aside from stacking.

 

Can you provide a link to what you saw? But ultimately, jack_nomind provided you with the same link I would have. It seems to be an urban legend. My actual build uses so many FF procs that when I'm farming with it (mobs are almost limitless) my +100 % recharge buff seems like it is almost always up. That's not test results though, just personal experience. I'll have to look at my combat attributes next time I farm and see how often my buff is up (HeroStats, I don't know how to look at time logs of when buffs are active, but if there is a way, let me know).

[Bopper]

Super excited about something that came across my way just now. It seems someone (I might know who, waiting to confirm) found the formulas in the source code. I'm not a programmer by trade, so I can't say I understand the entirety of this code, but it certainly seems to show the formulas I've been posting are correct.

 

 

The base Area Factor formula is the AF = 1 + Radius(11xArc + 540)/30000. This is simply an easy to read version of the formula given in the "Design Formulas" thread stickied in the Guides section which states:

 

Standard Area Factor

Spheres: (1+(Radius*0.15))

Cones: ((1+(Radius*0.15))-(((Radius/6)*0.011)/5)*(360-Arc))

 

The important part of the formula is the 0.75 dampening factor. Basically the code is showing this:

NewAF = OldAF x 0.75 + 0.25

 

This is equivalent to the post I referenced where Synapse (Phil) mentioned wanting to tweak the Area Factor such that:

NewAF = 1 + 0.75(OldAF - 1)

This is equivalent to the formula I use: NewAF = 1 + Radius(11xArc + 540)/40000

 

The 2nd most important thing is the confirmation that not only is the max probability to proc 90%, the minimum probability to proc exists too with the following formula:

Min Probability to Proc = 5% + PPM x 1.5%

 

Originally, I saw Synapse suggest he wanted a Min = 5% + PPM x 1.2%. It seems prior to i24 Beta coming out he tweaked the numbers. This is very cool, especially for wide radius AoEs.

 

It also appears we have a formula for toggles as well. It is simply:

Prob = PPM x ActivatePeriod / (60 x AreaFactor)

 

The one mystery that remains is the last functions used "ChanceModAccumulate()". I have some ideas as to what this is, but I am really hoping to just see its code and determine it explicitly.

 

Anyways, I hope to update the front matter soon with this new information. Today is my daughter's birthday so I won't get to these updates for at least a day. Nonetheless, I wanted to pass this info down.

 

[_NOPE_]

Yeah, reading through the thread, I was wondering why y'all were guessing and testing, when the code is there. It's always just a matter of finding where it is in code, that's always the trick.

 

Honestly, someone with more Time™ than me could go through the code and release a new City of Data site that's accurate to today.

[Bopper]

Yeah, reading through the thread, I was wondering why y'all were guessing and testing, when the code is there. It's always just a matter of finding where it is in code, that's always the trick.

 

Honestly, someone with more Time™ than me could go through the code and release a new City of Data site that's accurate to today.

 

That (City of Data) would probably be the 2nd best tool created, behind Mids. I'm not a coder/programmer, reading through it doesn't come natural. But if someone pointed me where to look, I could sift.

[Hjarki]

Have you confirmed that pets/pseudo-pets base their PPM on the recharge slotted into the power even though that recharge doesn't increase their attack rate? From informally testing, this seems to be the case (and it may well be the case with toggles as well).

[Bopper]

1 hour ago, Hjarki said:

Have you confirmed that pets/pseudo-pets base their PPM on the recharge slotted into the power even though that recharge doesn't increase their attack rate? From informally testing, this seems to be the case (and it may well be the case with toggles as well).

I have not done so yet, but this would be the next thing on my list. I've been away from home so haven't done any testing since my last update. Hopefully next week I can attack this. I suspect click pet powers use the standard click power formula on the initial cast, then uses the toggle formula for the remainder of the pet's duration.

 

For example, I somewhat tested my Distortion Field with about 5 damage procs in it, and it seemed upon cast I usually saw a burst of procs, then I would see a few trigger randomly for the next 45 seconds or so. It will take a lot of time to get statistical significance of this test as I can only cast it once per duration of the pet. 

 

edit: I should strike my above example. I haven't properly tested it and I rather not pass along bad info based on gut feel. I'll test it soon and I'll update this thread with the results. If there is a particular power you'd like me to check out, let me know.

Edited July 27, 2019 by Bopper

[Redlynne]

Bopper ... I have a curiosity that you might be able to satisfy ... AND ... which would seem to be pertinent to some of your other research on this topic since this might make for a useful test case.

 

Behold ... ENFLAME ... from the Sorcery Pool.

Quote

 

Range: 80 feet
Cast time: 2.07 seconds
Recharge time: 90 seconds

 

Target:

• Summon Level 50 Enflame (PL_StaticObject) at Target for 5s
• Summon Level 50 Enflame (PL_StaticObject) at Target for 5s (after 3 second delay)
• Summon Level 50 Enflame (PL_StaticObject) at Target for 5s (after 6 second delay)
• Summon Level 50 Enflame (PL_StaticObject) at Target for 5s (after 9 second delay)
• Summon Level 50 Enflame (PL_StaticObject) at Target for 5s (after 12 second delay)
• Summon Level 50 Enflame (PL_StaticObject) at Target for 5s (after 15 second delay)

 

Common Enhancement types accepted: Accuracy, Damage, Endurance Reduction, Range, Recharge Reduction

Set types accepted: Target AoE, Universal Damage

 

Procs that can be slotted:

Positron's chance for Energy damage

Ragnarok chance for Knockdown

Javelin Volley chance for Lethal damage

Annihilation chance for Resistance debuff

Frozen Blast chance for Immobilize

Overwhelming Force chance for Knockdown plus Knockback to Knockdown

Personal note: it would seem to me that slotting both the Ragnarok AND Overwhelming Force procs together in this power would be an example of unnecessary redundancy.

 

This power seems to have all the markers you'd expect from a "toggle that isn't actually a toggle" in that it instead cues up a collection of successively time delayed clicks that spawn pseudo-pet flame patches in the location that the $Target happens to be at at the time (so as to "leave a trail" of them (at 88 mph?)).

 

 

Now, in the context of this thread about PPM on Set IOs, I have to wonder how the PPM would "work" for Enflame, and if there's a particularly "good fit" for the power from any of the procs that can be slotted into it ... particularly given the fact that the 5s duration on the 3s delays means that you can potentially have multi-stack chances for procs going on ... or it could be a "check once, use repeatedly" kind of multiplier situation, due to how the power is coded to function under the hood (resolve first, animate after).  Also, that long recharge time of 90 seconds for the base power, coupled with a 5+15=20 second overall duration for the effects which can be repositioned after casting (!) would seem to me to be something of a prime research opportunity for PPM monsterification of an otherwise somewhat lackluster power.

 

For example, the chance for Immobilize in a "burn patches" power would seem to make for a pretty decent starting point ... particularly if coupled with chance for a Resistance Debuff ... particularly if the chance of getting those procs on the initial casting is high (approaching 90%?) and thereby helping to maximize the damage throughput onto the $Target(s) affected by the Enflame patches.  And that's before tossing a chance for Energy and/or Lethal damage into the mix (let alone a chance for Knockdown).

 

 

 

Your thought(s) on the potential for clever use of game mechanics ...?

[Bopper]

2 hours ago, Redlynne said:

Your thought(s) on the potential for clever use of game mechanics ...?

I love where your head is at. I'll definitely test it this week, hopefully Monday. Given its unique mechanics, there could be some very interesting exploits available.

Edited July 28, 2019 by Bopper

[Redlynne]

  My plot to take over the builds forums is thickening ... 

[Sir Myshkin]

15 hours ago, Redlynne said:

For example, the chance for Immobilize in a "burn patches" power would seem to make for a pretty decent starting point ... particularly if coupled with chance for a Resistance Debuff ... particularly if the chance of getting those procs on the initial casting is high (approaching 90%?) and thereby helping to maximize the damage throughput onto the $Target(s) affected by the Enflame patches.  And that's before tossing a chance for Energy and/or Lethal damage into the mix (let alone a chance for Knockdown).

Posted this in another spot, but I'll add it here too:

Irradiated Ground (which it sounds like Enflame is doing basically the same principle effect) drops a pseud-pet patch on the ground. The power itself is a toggle, the toggle is a trigger into (every 5/s) dropping the pet in the current position of the character. When I tested Fury of the Gladiator -Res proc in this ability against a Pylon, through watching with a Power Analyzer, I could see it hit and apply the debuff regularly. Any time there may have been a gap I often only caught it for 5/s (basically until the next trigger). I cannot confirm the regularity of this application, however, because the duration of the debuff overlaps greater than the amount of triggers I have, and the combat logs don't show anything for it.

[Sunsette]

We need to get a master list of these toggles that aren't toggles. 

[Bopper]

4 hours ago, Sir Myshkin said:

Posted this in another spot, but I'll add it here too:

Irradiated Ground (which it sounds like Enflame is doing basically the same principle effect) drops a pseud-pet patch on the ground. The power itself is a toggle, the toggle is a trigger into (every 5/s) dropping the pet in the current position of the character. When I tested Fury of the Gladiator -Res proc in this ability against a Pylon, through watching with a Power Analyzer, I could see it hit and apply the debuff regularly. Any time there may have been a gap I often only caught it for 5/s (basically until the next trigger). I cannot confirm the regularity of this application, however, because the duration of the debuff overlaps greater than the amount of triggers I have, and the combat logs don't show anything for it.

Great work. If you ever redo your test and you have numbers, please post them here. I think it helps everyone learn about how some of these procs work in different powers.

[Bopper]

I did some testing with Distortion Field. Tracking numbers is a bit difficult as I am unable to track hit rolls for each tick (maybe I'm doing something wrong). Anyways, it seems Distortion Field acts completely like a toggle and there is no initial burst probability from a long recharge cast. 

 

Some possible additional findings, I used 3 hold procs in my powers, the purple smashing proc (4.5 PPM), the PVP lethal proc (3.5 PPM), and a psionic proc (3.5 PPM). This could be a small sample size issue, but the PVP lethal proc seemed to outperform the rest, hitting far more frequently. Also, the purple proc did worse of them all. Again, this could be small sample size, but it might be worth monitoring the actual proc performance of these.

 

Edit: I did follow on testing the the striked out paragraph above seems to just be a small sample size experience. New testing shows results that are more in line with expectations.

Edited August 1, 2019 by Bopper
New Findings from recent testing