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Recharge Guide

Everything you need to know about Recharge…and then some

By Bopper

Written: 17 Nov 2019

Updated: N/A

The purpose of this guide is to teach you everything you need to know about recharge. I have broken up this guide into chapters in an effort build up your understanding on how recharge works. My methods for building up your knowledge will be a bit backwards. Normally in a textbook, you will be given a formula, the formula will be derived, then you will see examples on how to use the formula. Instead, Chapter 1 will show you examples with step-by-step solutions in hopes of learning and observing all the details that goes into solving the Recharge Problem. In Chapter 2, I will introduce formulas that could be used for solving the examples from Chapter 1 in hopes that you can apply those formulas for your own needs. In Chapter 3, I introduce a new technique for solving the Recharge Problem that is faster and easier to implement, although it has its limitations. At that point, you will have all the knowledge you need to know. But if you would like to read on, Chapter 4 provides additional formulas that apply to the Recharge Problem that could be useful to you. Finally, Chapter 5 (not complete), will be additional examples that I will solve by request. If you have a specific problem and are having trouble, you can mention it in the comments and I will attempt to solve it and provide the solution in this chapter.

 

If you prefer the PDF version or Word document version (they are much more readable than the forum's formatting), they are attached below.

RechargeGuide.pdf

RechargeGuide.docx

 

Background information: I have discussed this topic previously, which you can check out here.

Edited by Bopper
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Chapter 1: Understanding How to Calculate the Time to Recharge a Power

by a series of examples

 

The first thing to understand about recharge is that we are working with two time domains: the real-world time domain (which is what you experience), and the cooldown time domain (which is what your power experiences). The recharge in the power is the rate at which the cooldown time domain experiences for every second that passes in the real-world time domain. This leads us to our first formula, which is the amount of cooldown time experienced.

image.png.44e97311532e214798bd4b5d65af3793.png

 

To understand how to apply this formula, let’s start with the most common example recharge question: How much recharge do I need to make Hasten permanent?

Example #1.1: Hasten has a base recharge of 450 seconds and a duration of 120 seconds. Thus, to make Hasten permanent, we need our power to experience 450s of cooldown within 120s of real-world time. To know the amount of recharge required to achieve that, we use algebra to tweak our above formula:

image.png.d61c8f503c7e4da59dbc5f53423b95aa.png

375% recharge may seem like a lot, however 100% comes from our base recharge and another 70% comes from Hasten, so that leaves us with needing an additional 205% recharge from other sources (enhancements, set IO bonuses, other powers).

 

Example #1.2: Now let’s say we only have 370% recharge (70% from Hasten, 300% from base and other sources). How long will it take for Hasten to recharge?

This requires us to analyze the problem in two parts. First part, we analyze when Hasten is active (370% recharge for 120 seconds) and the second part we analyze when Hasten wears off (300% recharge for some additional amount of time). Our power will still need to experience 450s of cooldown, so:

image.png.a876bfe37575c77791c50721beae771c.png

image.png.13920c7989691cf112865741ea043a0f.png

image.png.26138f9aca3ebdcac552489b9b2841d8.png

This tells us Hasten will recharge in 120 + 2 = 122 seconds.

 

Example #1.3: Now let’s do the same example, but this time a Force Feedback Proc (+100% recharge for 5 seconds) goes off once while Hasten is active. How long would it take for Hasten to recharge?

This adds some additional complexity as we don’t know if Hasten will become permanent or not, so we may have to analyze this in up to three parts: Hasten+FF active (for 5 seconds), Hasten active (120 seconds minus the 5 secs for FF proc), and nothing active (for possibly some additional amount of time). To make this simple, we will start from highest recharge then work our way down to calculate the amount of cooldown experienced for each time interval of differing recharge values:

image.png.541381b2d95991c2bf98f6717012071c.png

image.png.19807fa4df3ed14893ed4b2d599a26a8.png

image.png.341f786337ed798a35af9cd04c9ffa36.png

It turns out we still do not achieve permanent Hasten as it would take 120 + 0.33 = 120.33 seconds to recharge. If image.png.10ef3d5975124f2375e6539ec7edc359.png was equal to or less than zero, then we would have achieved permanent Hasten as this would tell us we achieved full recharge prior to 120 seconds.

 

Example #1.4: Now let’s assume we had two Force Feedback Procs occur (a total of 10 seconds worth of +100% recharge boost). What would become the final recharge for Hasten?

We do the same steps as above.

image.png.18ffa9b965fe6f7cea21b4aeb98ebc3c.png

image.png.5345fea963bc64982f12d06ced9210dc.png

Now we have a negative number in the additional time calculation. This tells us that Hasten actually finished recharging prior to the expiration of Hasten’s 120 second duration (yay, we achieved perma-Hasten). However, how long did it actually take to recharge? We need to tweak the numbers in the above formula by removing the 120 seconds from the Hasten duration, as we know we will never reach that time, and substitute it with our image.png.463786cb8e25af55bbcb762ce021ac8c.png:

image.png.103122f1c567768b5f050a8413a75e65.png

image.png.c5615883fc52faa5a1bd29bf0d96bc80.png

It turns out that the total time for Hasten to recharge in this example is 10 + 108.92 = 118.92 seconds.

 

Let’s do a few more examples by incorporating a Tier 4 Ageless Destiny incarnate power (Core Epiphany or Radial Epiphany). This power has a 120 second cooldown duration that is unaffected by recharge; and when it is cast, it will provide a recharge bonus that cascades from strongest boost to weakest boost. It provides a 70% recharge boost for the first 10 seconds, then 30% for the next 20 seconds, then 20% for the next 30 seconds, then 10% for the final 60 seconds (120 seconds in total).

Example #1.5: Let’s assume once again that we have 300% recharge in the Hasten power from outside sources. How long will it take for Hasten to recharge if we cast Ageless and Hasten back-to-back?

Once again, we break this down by time intervals of where the recharge in Hasten is different.

image.png.78e572d20e2e826064cfe4b8232c2965.png

image.png.f6d4de3fda13b1385ce97c06ce9f61fc.png

image.png.13a377e4b4528cbecde7996b4f4f7afc.png

This tells us Hasten will recharge in 10 + 20 + 30 + 55 = 115 seconds, thus achieving perma-Hasten.

 

Example #1.6a: Finally, let’s look at incorporating the Force Feedback Proc into this Ageless example. Now we care about when the Force Feedback Proc fires because if it fires within the first 10 seconds, then we will achieve a total recharge of 300%+70%+70%+100% = 540% which is over the maximum allowed recharge cap of 500%. So, let’s look at the impact of Hasten’s recharge if the FF Proc fires in the first 10 seconds and if it fires after 10 seconds.

For first 10 seconds we get the following recharge-capped result

image.png.9748629b270aab46e192167f8c1910c6.png

image.png.40d3934c5bec52bb8f560a8100893fd8.png

Thus, Hasten would recharge in 60 + 54.2105 = 114.2105 seconds.

Example #1.6b: Now let’s look at FF Proc firing after 10 seconds (thus, never surpassing recharge cap). It won’t matter where it fires as the math will not change the result, so let’s assume it happens in the subsequent 20 second window.

image.png.441b8c5532efd43d2f676db89076c1ee.png

image.png.15da46e4cb236464a603895e25946397.png

Thus, Hasten recharges in 60 + 53.6842 = 113.6842 seconds, which is slightly faster than the recharge capped scenario as we don’t waste any of our boosts.

Edited by Bopper
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Chapter 2: Formulas for Calculating a Power’s Recharge Time

by using Time Interval Analysis

I know that was a lot of math and a lot of examples I just threw at you. I didn’t do that for the purpose of triggering your math class PTSD, I did it because it is my goal to make you an expert in understanding how recharge works and how to calculate a power’s recharge for ANY situation. These examples covered everything ranging from static recharge, fluctuating recharge, and cap-saturated recharge; so, if you were able to follow the math in those examples, you will have an easier time following the formulas I’m about to introduce. All these formulas were used in the examples, but now I will call them out explicitly.

Recall our first formula,

Formula 2.1:

image.png.85fe0b84618614ecc06686f6cb6b586a.png

We tweaked this first formula by accommodating for times when the recharge changes:

Formula 2.2:

image.png.4383bf54e05e79ba6847bbd479b1b492.png

This simply shows that we are calculating the total cooldown time by summing the products of each (n-th) recharge amount with its respective real-world time duration. We used this formula in almost every example by plugging in the Base Recharge of the power as our image.png.f5c5dc718ca16f9e7adc3ff9e536ec54.png, then adding up the total recharge amount for each known time interval and multiplying them together, then solving for the last unknown time interval (where image.png.5b1564b4b849399c9979ef92a0c33861.png is the image.png.878a2fff87d72a7bd1a0ddfa7b4ea2b2.png in this formula). To show this explicitly, let’s recall Example #1.3 and apply it to Formula 2.2.

image.png.240f0e2fb5d07e1243747a81c0d0f7e2.png

image.png.7851627ba16e433b2f51467e8261c650.png

We have the following:

image.png.6473713162a3ace3c439b976ede6e491.png
image.png.5d6ad24754418f8b772aa62ed1fcd53f.png
image.png.1215b7de0ae4645f7e6237c04a1f4746.png
image.png.cf689201385be4e22a3281a075b25d79.png
image.png.895a0df669161cf3a08a21cba6608f13.png
image.png.f2b89fecb93bc3634bf71ac8076340d0.pngimage.png.1b5f759afb97221a4294cb3be8515055.png

We can rearrange the above formula to solve for image.png.75ec8f2e5d4a732ded909d5648b6122c.png directly.

Formula 2.3:

image.png.4d71b76a866d0abd98f8a5f4b2443d48.png

From this, we can calculate the total time it takes for a power to recharge by simply adding up all the time intervals together. This formula can go without saying, but I provide it for completeness.

Formula 2.4:

image.png.ab7e32673aa66a8bec5d8928522ecd96.png

Finally, the total recharge of the power for each time interval is simply the summation of each source of recharge that is present for the entirety of its time interval.

Formula 2.5:

image.png.f5b0391c693f22b54b5a64ceebba5eb5.png

Where we add up all permanent recharge boosts (image.png.a00857fe2bacf47e4264ed462c80103d.png, which represents the l-th permanent boost out of a total of L permanent boosts) and we add up all temporary boosts (image.png.e138b1197619aa49a965ea7c04f60609.png, which represents the m-th temporary boost out of a total of M temporary boosts) that are active for the entirety of the n-th time interval. If the total recharge boosts exceed 500%, then it is capped to 500%.

That’s admittedly a confusing statement and a confusing formula for something so simple. I’m sorry. So, let me put this in layman’s terms… the total recharge is calculated by adding up all the recharge sources for the power. You know how to do this, as I showed how to do it in each of the examples. Permanent boosts include your 100% base recharge, the power’s recharge enhancements (after enhancement diversification), global set IO bonuses (e.g. slotting a Luck of the Gambler: Defense/Increased Recharge Speed, or 5-slotting an Apocalypse set), or possibly auto powers (e.g. Quickness, or Lightning Reflexes). Temporary boosts include powers with a finite duration (e.g. Hasten, Ageless Destiny) and temporary buffs (e.g. Force Feedback Proc). Recall from Example #6a:

image.png.8b88c5601d0b8d895447a527ed5706b5.png

What we had in this example was the following:

image.png.16fd99f3384034691a286671cb13bbd4.png
image.png.4c4f5d790a22329e3ea81c73281259e8.png
image.png.a8500e4c2ce23804952756e43b1718c5.png
image.png.65f13d2fc2fc2db8bdc7a28f1eaf5040.png

image.png.cf6bd102a814129da3810df554528073.png

In this example, image.png.e83f9251df6536d8ac4f1a0743f3b5dd.png had its summation of boosts exceed the 500% cap, so the min-function capped the total boost to 500%. All the other image.png.419c3dc168a3ac4409b0e7cb29913d3a.png values did not exceed the cap.

Also, in this example, I had spelled out what all the temporary boosts were, so I was able to break them out here by their image.png.c36e1fb861db10454bd921f12ea0e572.pngetc. As for the 300% permanent boosts coming from other sources, I never did say where all those boosts came from. In actuality, we know our base is image.png.aab283b747e766469ab4ce25bc3f1c9b.png. Then we may have enhancements that make of image.png.0b61455712229b05353cccb9c8e9c5a0.png. We might have 4 Luck of the Gamblers in our build giving us image.png.3c229e28f9fc3d1061366d5fc6a50a2a.png. We might have global set IO bonuses that give us a total of image.png.b817d384b9e9f04e2e98078da0ff9d47.png. Finally, we might have an auto power such as Quickness that gives us .image.png.a0af38ae394a2b3b9c5806839b2cf3e7.png Thus, we achieve a total permanent recharge boost of

image.png.96ec5919566e1bba9c74a67920c89ce6.png

Overall, this is overkill for understanding how to calculate the total permanent recharge in a power. Honestly, you only need to check 2 things and you can do this in the game or in Mids’ Reborn: Look up the amount of recharge slotted in the power (the Enhancement Diversification amount), and look up your Global Recharge when no temporary boosts are active (so turn off Hasten and similar powers). If using Mids’ Reborn, you will see this as “+Recharge” in the Totals tab, or as “Haste” in the View Totals/Misc. Buffs panel. Once you have those 2 numbers, add them together with your base recharge and you will get your image.png.bb25c4a6c4c65a627803da0cb163241d.png

image.png.f9123d0110a9ec23edae53f84ca8b9fc.png

Edited by Bopper


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Chapter 3: Formulas for Calculating a Power’s Recharge Time

using Recharge Boost Duration Analysis

 

In Chapter 1, I used step-by-step examples to show how we can calculate the time it takes for a power to fully recharge by breaking up the analysis into time intervals where the total recharge in each time interval is constant. In Chapter 2, I showed the formulas we would use to do the type of analysis performed in those examples. Now I want to change course by breaking up the analysis by recharge boost as opposed to breaking up the analysis by time intervals. Below I use graphs to illustrate what I mean by this:

image.png

Figure 3.1: Time Interval Analysis

Figure 3.1 is the same as the analysis we did in Example #1.3, instead the total permanent boost was 300% in Example #1.3 whereas this figure shows it as 250%. Nonetheless, it illustrates how we analyzed the problem: For the first 5 seconds we calculated the cooldown time for when the Force Feedback Proc and Hasten were active at the same time (white), then the next 115 seconds was evaluated for when only Hasten was active (yellow), then an additional amount of time was evaluated for when only the permanent boosts were active (green). That additional amount of time was what we solved for.

image.png

Figure 3.2: Recharge Boost Duration Analysis

In Figure 3.2, we highlight how we can instead analyze for each individual recharge boost and its duration. The temporary boosts are evaluated for just amount and duration, while the permanent boosts are evaluated until the time the power becomes fully recharged (which is what we’ll solve for).

The benefit of this method is that it is time agnostic. We don’t need to worry about calculating time intervals for when each recharge boost is active/inactive, which makes for easier and faster calculations. The downside of this method, by ignoring when boosts are active (thus not knowing how much recharge is stacked up) we could go over the 500% recharge cap, resulting in inaccurate calculations. So, keep this in mind when considering using the following formulas as they will only be accurate if your boosts never go over the 500% recharge cap. Lucky for most of us, this will typically be the case…and even if we were to temporarily go over the recharge cap, it likely won’t be sustained long enough to change our final results by a whole lot (Examples #1.6a and #1.6b in Chapter 1 shows this).

Once again, recall our first formula

image.png.53c6508bf89c8f9c160317c7a1a60716.png

In Chapters 1 and 2, we used this principal formula to add up all the cooldown times from different time intervals and its respective total recharge amounts. By adding up all the cooldown times by recharge boost amounts with its respective boost durations does not change this math at all. We are just calculating area with different lengths and widths, essentially, but we will come to the same end result.

Formula 3.1:

image.png.95e5e9d0bb3e0d6480a7f6208acb5baa.png

Recall from Chapter 2, the image.png.94cdfffef80280c622f38a904a75ed16.png is the amount of the m-th temporary recharge boost and image.png.d55cc252ae584c357abec84467e48613.png is the amount of the l-th permanent recharge boost. For each of the temporary recharge boosts it has a duration which is represented as image.png.6db42dcc47113f0d86211e3fb83d9536.png. For all permanent recharge boosts, they are evaluated until the power is recharged.  Note: there is one caveat I should make to Formula 3.1, which is each duration of a temporary boost can’t be greater than the recharge time (similar to Example #1.4). If that is the case, then we must treat the temporary boost as a permanent boost and only evaluate it for the time until the power recharges.

Formula 3.1a:

image.png.7105063a805791f2e877a226a8c7793c.png

Since we are solving for image.png.a0850246d0ebaa435c88fb2a2f4e58ff.png, we unfortunately won’t know if the duration of a temporary recharge boost will be greater (perma’d) until we run the numbers. So, like the Example #1.4, if we find our solution to be in error, i.e.  image.png.23950c833ad07c18e998a6913ab986cd.png, then we must iterate through our analysis by changing the longest temporary boost duration to image.png.9fad23a6dcd1e0b4a178f41891146827.png, recalculate, then check the remaining temporary boost durations to see if any of those are still in error.

That sounds like a painful process, and it certainly can be, but you can save yourself some of the hassle if you know ahead of time which temporary recharge boosts will definitely be active for the entirety of your power’s recharge and treat those boosts as permanent right away (turn a image.png.2bc0d643732346224d7466bb82dfb438.png into a image.png.34f8ffb7ef28a682d6d14840981be870.png, basically). This could be done by identifying temporary powers that are already perma’d (if we know Hasten or ChronoShift are already perma’d, then treat them as permanent), or it could be your power has a base recharge less than the duration of a temporary boost. By handling those situations ahead of time, you can save yourself from a lot of the potential iterations you might need.

Let’s not dwell on Formula 3.1a. I will show how it works in a later example, but for now let’s use Formula 3.1 to define some other useful functions.

Since each permanent boost is being multiplied by the same time duration (image.png.1f2263037bf4bd722b753150c57f61b6.png), we can actually add up all the permanent boosts together first, then multiply. This tweaks our formula slightly:

Formula 3.1b:

image.png.f2c4f34d4dbb94858e03bfa1a0032f1d.png

This now makes it simple to solve for the time it takes a power to recharge.

Formula 3.2:

image.png.2131fd5d962581cddf3002385bdf9279.png

This is as simple as it comes with solving for a power’s recharge time. We merely take the base recharge of the power, subtract the product of each temporary recharge boost and its duration, then divide by the total permanent recharge boost.

Let’s revisit some of the examples we did before, now using the Formula 3.2.

Example #3.1: Recall in Example #1.3, we had a image.png.f1ee649e3e969c999454e1efa8b52265.png, and a single Force Feedback Proc. How long would it take for Hasten to recharge?

image.png.174ffefc5465c3ebfe3482d7e6bcaea0.png

Same answer as before.

 

Now let’s look at an Ageless Destiny example. If you recall from before, I said Ageless works as a 70% recharge for 10 seconds, then 30% for the next 20 seconds, 20% for the next 30 seconds, then 10% for the final 60 seconds. If you read the description of Ageless, that is not what it says. It actually says it provides a 40% recharge boost for 10 seconds, a 10% recharge boost for 30 seconds, a 10% recharge boost for 60 seconds, and a 10% recharge boost for 120 seconds. My original description simply added the stacks of recharge together, here we will use the actual description as four separate recharge boosts.

Example #3.2: Recall from Example #1.5, we have a image.png.06bcf1e21f6389d340a88a3d31478506.png and we cast Ageless and Hasten back-to-back. How long will it take for Hasten to recharge?

image.png.b250f643e1aa284a4eda08bf35090f2e.png

Oops, we have a image.png.fdf6b480d46a3b57b48a14a9ee5c59c9.png that is less than the duration of two of our temporary boosts (see Formula 3.1a). Since both boosts have a 120 second duration and we now know the recharge is less than 120 seconds, we must re-do our calculation with these temporary boosts treated as permanent boosts.

image.png.a95345645de09efbab0224ca53b4c020.png

Once again, this is the same answer as before.

From these examples we can see that using Recharge Boost Duration analysis is viable, if not ultimately more convenient. The nice thing with this method is that you can see a temporary boost and instantly know what its impact on a power will be. For example, the Force Feedback Proc’s 5 seconds of 100% recharge effectively takes off 5 seconds of a power’s base recharge. Hasten’s 120 seconds of 70% recharge effectively takes off 84 seconds. Those are numbers you can quickly calculate and apply whenever you need.

 

Edited by Bopper


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Chapter 4: Additional Useful Formulas

So far, I’ve taken you through an exhaustive journey in understanding how to do one calculation: Time to Recharge. Now I want to go through some of the formulas you can use to answer some of the more common questions that come up relating to recharge. For this chapter, I will format it more like a FAQ section.

 

How much will an extra 10% recharge give me?

Answer: Ok, this can be any percentage really, so we will just say an “extra X recharge”, where X is in decimal form (like the decimals I’ve been using in my examples). Anyways, this is pretty simple to apply.

Formula 4.1:

image.png.bb5ccc3bb8471e4e9526af1de5f133d3.png

Proof (using Formula 3.2)

image.png.5b244e116c59a892e401864a3627fde5.png

image.png.94fb5e8aad85129b73d4e0db7776e60d.png

image.png.3e5a0fe96838704c4bf79322872dd4a1.png

Pretty simple. You actually don’t even need to know your base recharge or the temporary boosts in the power. As long as you know what your current (“old”) recharge is, and you know your total permanent boosts (including any temporary boosts that are active the entire duration, Formula 3.1a), then you can directly calculate the effects of adding more recharge simply by using Formula 4.1. There is one potential gotcha, though. If your added recharge would turn a previously temporary boost into an effective permanent boost, then you’re out of luck. You’ll have to go ahead an incorporate the base recharge and temporary boosts and calculate the new recharge directly as shown in the above proof.

Example #4.1:

Spoiler

 

Let’s assume our power is Hasten with a image.png.e3b81df4d9a0ba7f0b9e833946282fd9.png. We assume we have one Force Feedback Proc occur. We calculate our recharge to be:

image.png.6f3812b50f86452a21fce79a43bb55f8.png

We want to know what our new recharge time would be if we added a 10% global recharge boost via 5-slotting a purple IO set.

Answer:

image.png.fdfed7ee5f87f7f5173be07753b00265.png

 

 

 

How much will a Force Feedback Proc give me?

Answer: Again, this can be any temporary recharge boost for any duration. So, we’ll assume the amount of boost is image.png.fee1c5ddaf5a53d06c70e07f509bb2c1.png (image.png.de3dd172247b058df42d8565084a125e.png for FF proc) and the duration is image.png.d99d04b5a1ad12897b17ec813829c375.png (image.png.3a36285e30421da25dd3d7ed388ec3b6.png for FF proc).

Formula 4.2:

image.png.b67bb06ac4984ecdad7f183f3a84f2f8.png

Proof (from Formula 3.2)

image.png.0c7f8c3a92325a1e3e57d78135737da1.png

image.png.3259322c5bd6cb668646b7a0c82a345d.png

image.png.ae8b2bc817a7a093526f28b65865f3dd.png

Once again, this is a very simple formula as you only need to know your current (“old”) recharge and your total permanent recharge boosts. However, once again, if the new boost winds up making a temporary boost effectively a permanent boost, then you will have to calculate the new recharge directly as shown in this proof and properly applying the Formula 3.1a caveat.

Example #4.2:

Spoiler

 

Let’s use the result from Example #4.1, but now let’s assume we get one additional Force Feedback Proc to occur. What is our new recharge for Hasten?

Answer:

image.png.5f7d5e12502c4c91fee626c8aedbe540.png

 

 

 

How much equivalent recharge does a Force Feedback Proc provide me?

Answer: Often I’ve seen the question come up of how helpful is a temporary recharge boost, compared to simply adding more global (permanent) recharge. Often you might see someone respond to this question with something like “a single Force Feedback Proc is equivalent to adding 6% global recharge”. Now, that response is not universal; it is specific only to power in question and the build it is applied to. But wouldn’t you like to know how people come up with those types of responses? Well, there’s a formula for that too…

Formula 4.3:

image.png.d21a4006625215b021a08082aa10114a.png

Proof (from Formula 3.2)

image.png.18c7f225684efe76c8d9d4d1e9c7ad53.png

image.png.3895168f58d9701b16f10680521db817.png

image.png.89f589acdf6880b6f365ea192afa7de4.png

image.png.a40b6ede42a65ee7cb87664aac4ea051.png

image.png.5830a5f5d9de37c0efea4a16701187db.png

image.png.806c16833e9a70a58a9aea857a3f201f.png

The proof is probably uglier than doing the actual brute force calculations themselves. In fact, once you calculate your new recharge from the temporary buff, you should simply solve directly:

Formula 4.3a:

image.png.e6038d39cb7966019d5b19d02f3b7b71.png

Proof (from Formula 3.2😞

image.png.236e844a6dbc221738bbe3be73739649.png

image.png.8deec5429d54822225a292fbc075c402.png

image.png.6592c74fd8d427f5353afe8878287a03.png

image.png.7752b51507100c90d76ec48d24b78461.png

Example #4.3:

Spoiler

 

Let’s reuse the results of Example #4.2. In it we had one additional Force Feedback Proc occur, which changed the recharge of Hasten from 138.85 seconds to 136.92 seconds. What amount of additional recharge would be required to replicate that one additional Force Feedback Proc?

Answer: Using Formula 4.3 we get:

image.png.e7d1b6adfc63b95eb22dc23df084e046.png

Using Formula 4.3a we get:

image.png.5bc85ed17ed5a20f8a6dfa1dbf975deb.png

Now let’s check our work. If we had added 3.65% recharge instead of the one additional Force Feedback Proc, would we get the same new recharge?

image.png.10abcc4b4e7bdb02528d3a70248db535.png

Indeed, in this specific example, the additional Force Feedback Proc provided the equivalence of 3.65% global recharge to Hasten. But if you used different numbers (different image.png.7a851b81b3ab5f7c8ae1f3ce4ff3cd1a.png, image.png.75bccbfa77fae64193940847d4f5bed1.png, etc), you would certainly get different results.

 

 

Edited by Bopper


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Chapter 5: Additional Examples

Solutions to Problems Submitted on the Forums

 

I've got nothing...so far. Actually there are a few interesting problems that I will write up in the near future. Stay tuned.

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Way too complicated for me.  I'd just take a goal, like say perma-Phantom Army on an Ill/Rad controller.  It takes just about 300% recharge to get that... 95% from ED capped recharge in the power, Hasten at 70%, Accelerate Metabolism at 30% leaves you with needing just about another 100% to find in global IO bonuses.  5x LotG = 37.5%, you need another 63% recharge from other bonuses.  On Live my Perma-PA Ill/Rad controller had a global recharge of 205% which was just over the amount needed.  I also had Perma Hasten and Perma AM as a byproduct.

 

Perma Hasten needs about 90% global recharge on top of the 70% provided by the power itself, for many characters it's not that hard to get.  I have it on my Elec/SD stalker and got it almost as a byproduct of the build rather than something I was specifically going for.  I imagine most players looking at recharge heavy builds are trying for something specific with Perma Hasten being among the most common.

 

The heavy math formulas aren't needed, Mid's will handle the number crunching for you.  The Force Feedback proc is too unreliable to count on for a goal, it's simply a bonus when it does fire... it also only lasts 5 seconds further limiting its value.   You can work all the complex mathematical formulas if you like but why bother?  Work out the build in Mid's and you'll get the numbers anyway without needing more advanced math.

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Don't listen to him, Bopper!

The math may be hairy, but basic science is its own reward!

 

Call, with the formulae here you could fix Mid's Reborn if it has the wrong numbers for something.

That's worthwhile.

I won't be calculating these by hand, either, but having the data here can benefit more than just players.

The devs may refer to this when creating new powersets.

 

Thanks  very much, Bopper!

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28 minutes ago, Call Me Awesome said:

Way too complicated for me

It's not for everyone, I understand.

 

29 minutes ago, Call Me Awesome said:

The heavy math formulas aren't needed, Mid's will handle the number crunching for you

I am unaware of Mids doing any accurate calculations of recharge when your recharge changes over the course of time. For example, if you click Hasten while not perma-Hasten, your numbers will show as if you are perma-Hasten. So that's wrong.

 

31 minutes ago, Call Me Awesome said:

The Force Feedback proc is too unreliable to count on for a goal,

Au contraire. You can make this very reliable if you design for it (my PPM Information Guide can give you some ideas). But in the example of Hasten, which has a 2 minute duration, is it not reasonable to assume it will proc one or two times during the course of the duration? My knockout blow can proc 90% of the time. My footstomp will proc similarly, assuming I'm hitting enough targets. My Hail of Bullets is practically 100%. You can make it reliable, if you want.

 

37 minutes ago, Call Me Awesome said:

it also only lasts 5 seconds further limiting its value.

I also beg to differ on that one. I showed in one of my examples that a single proc acted as a 3.65% recharge boost. We chase recharge like its gold, and something as simple as 1 proc achieved half a LotG. With my Knockout Blow (25 second recharge), 90% of the time I effectively turn it into a 20 second recharge. That's what each FF proc does, takes away 5 seconds from the base recharge.

 

40 minutes ago, Call Me Awesome said:

You can work all the complex mathematical formulas if you like but why bother?

For innovative build concepts. 

 

Thanks for the reply. I do like feedback on this stuff. It helps me try to write better.



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14 minutes ago, DoctorDitko said:

Don't listen to him, Bopper!

The math may be hairy, but basic science is its own reward!

 

Call, with the formulae here you could fix Mid's Reborn if it has the wrong numbers for something.

That's worthwhile.

I won't be calculating these by hand, either, but having the data here can benefit more than just players.

The devs may refer to this when creating new powersets.

 

Thanks  very much, Bopper!

Whatever works for you, I own a Video Production company, I'm not a Math Professor.  😉 

I was trying to give some simple thumb rules that most of the playerbase will get more out of.  For me and probably the majority of players the math is a "nooooo, it BURNS it does my Precious!"  I'll leave the specifics to the math geeks, I just want the practical numbers.


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24 minutes ago, DoctorDitko said:

Don't listen to him, Bopper!

The math may be hairy, but basic science is its own reward!

 

Call, with the formulae here you could fix Mid's Reborn if it has the wrong numbers for something.

That's worthwhile.

I won't be calculating these by hand, either, but having the data here can benefit more than just players.

The devs may refer to this when creating new powersets.

 

Thanks  very much, Bopper!

I also dont do it by hand per se, but there have been times I was able to reply to a forum post and provide an answer using just my basic calculator app on my phone. The formulas are that simple, once you're used to it.



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4 minutes ago, Call Me Awesome said:

Whatever works for you, I own a Video Production company, I'm not a Math Professor.  😉 

I was trying to give some simple thumb rules that most of the playerbase will get more out of.  For me and probably the majority of players the math is a "nooooo, it BURNS it does my Precious!"  I'll leave the specifics to the math geeks, I just want the practical numbers.

I totally understand where you're coming from. I'm an electrical engineer working for the Air Force and NASA, so the numbers are clearly what I love. 



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Just now, Bopper said:

It's not for everyone, I understand.

 

I am unaware of Mids doing any accurate calculations of recharge when your recharge changes over the course of time. For example, if you click Hasten while not perma-Hasten, your numbers will show as if you are perma-Hasten. So that's wrong.

 

Au contraire. You can make this very reliable if you design for it (my PPM Information Guide can give you some ideas). But in the example of Hasten, which has a 2 minute duration, is it not reasonable to assume it will proc one or two times during the course of the duration? My knockout blow can proc 90% of the time. My footstomp will proc similarly, assuming I'm hitting enough targets. My Hail of Bullets is practically 100%. You can make it reliable, if you want.

 

I also beg to differ on that one. I showed in one of my examples that a single proc acted as a 3.65% recharge boost. We chase recharge like its gold, and something as simple as 1 proc achieved half a LotG. With my Knockout Blow (25 second recharge), 90% of the time I effectively turn it into a 20 second recharge. That's what each FF proc does, takes away 5 seconds from the base recharge.

 

For innovative build concepts. 

 

Thanks for the reply. I do like feedback on this stuff. It helps me try to write better.

I'm not trying to be a Debbie Downer here at all, I'm just not a math guy.  I'm looking more at constant effects and the practical of "what do I need to get X".  Possibly a summary to the effect that "The FF proc will get you an average of x recharge" with some examples for the more math-challenged of us.

 

Like the old guy says "I don't care how the watch is built, what time is it?"


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Just now, Call Me Awesome said:

I'm not trying to be a Debbie Downer here at all, I'm just not a math guy.  I'm looking more at constant effects and the practical of "what do I need to get X".  Possibly a summary to the effect that "The FF proc will get you an average of x recharge" with some examples for the more math-challenged of us.

 

Like the old guy says "I don't care how the watch is built, what time is it?"

Absolutely, and I tried to show the effects in some examples. I showed that if you were 5% from achieving perma-hasten, one FF proc won't get you to perma, but 2 procs would. That is something tangible you can use when designing your build.



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1 minute ago, Bopper said:

I totally understand where you're coming from. I'm an electrical engineer working for the Air Force and NASA, so the numbers are clearly what I love. 

I figured you were something technical in your day job.  I've a couple friends like that and I appreciate their know how, I just don't follow them sometimes.  All the formulas are good for the math guys but most of the people reading the guide aren't going to have a clue what you're talking about.


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1 minute ago, Bopper said:

Absolutely, and I tried to show the effects in some examples. I showed that if you were 5% from achieving perma-hasten, one FF proc won't get you to perma, but 2 procs would. That is something tangible you can use when designing your build.

I guess I missed that in skimming over the math formulas.  May I suggest a "TL/DR" summary would be helpful?


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3 minutes ago, Call Me Awesome said:

I figured you were something technical in your day job.  I've a couple friends like that and I appreciate their know how, I just don't follow them sometimes.  All the formulas are good for the math guys but most of the people reading the guide aren't going to have a clue what you're talking about.

Yeah, I've seen the audience in the general discussion section. My hope is having it in the guide section helps others who understand the math better explain it to others. I saw the growth in PPM knowledge across the community and I hope something similar can happen with recharge. 

2 minutes ago, Call Me Awesome said:

I guess I missed that in skimming over the math formulas.  May I suggest a "TL/DR" summary would be helpful?

Certainly. The reason I reserved extra spots was for incorporating ideas like that. I'll see about producing a simple summary, and if folks still struggle in understanding, they can read the full guide



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Most of the clued in community understand the practical effects, not usually all the math behind it.  Look at how many players just know "45% defense" without knowing the reason behind it?

 

I always read what posters like Arcanaville posted on the old forums but mostly I looked for the summary rather than the frequently complex interactions behind it.  The concept of Arcanatime comes to mind there.


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Bopper I hate to suggest this, but I really think you've gone about explaining this in a way that is bass-ackwards for accessibility.  I'm not saying your formulas are wrong ... just that they're hard to parse if you're not intimately familiar with what you're looking at.

 

The way that I deal with this problem is to basically DITCH any kind of division arithmetic operations until the very last step ... and instead use an ADDITIVE process to do most of the heavy lifting for me, since it's easy(ier) to check the math for errors.

 

Here's my approach to this, which is hopefully easier to explain.

 

 

 

You want to think in terms of iteratively adding multiples of 100 per second until reaching a threshold.

So if you've got no +Recharge Reduction in a power (at all, from enhancements or globals) then you're adding +100 per second to the "recharge stack" for that power.  So the baseline starting point is +100 per second.

If you've got +100 Recharge Reduction in a power (from enhancements or globals) than you're adding +100 and +100 makes for +200 per second to the "recharge stack" for that power.  You essentially just ADD +100 to whatever the +Recharge percentage is to get the number you're going to use next.

 

With me so far?

 

You then look at the recharge time for a power (in seconds) and then multiply that amount by x100.

So if a power has a 600s recharge time then is will need 600x100=60,000 "points" of stacked up recharge using the calculation above (and I'm only using "points" here to help designate and differentiate the numbers to help keep them straight).

 

At 100 recharge "points" per second, where there's no recharge enhancement, it'll take 600 seconds to meet the 60,000 "points" of recharge threshold (because 600x100=60,000)

However, at 200 recharge "points" per second, where there's +100% recharge enhancement, it'll take only 300 seconds to meet the 60,000 "points" of recharge threshold (because 300x200=60,000).

 

Alright, still with me?

 

 

 

The reason why this is useful is because it gives you a "fixed" target to reach ... the number of recharge "points" to fill in an ADDITIVE manner ... combined with the notion that once the threshold is met the power is recharged ... meaning you can go "over" without creating a numeric issue for your math of the stack overflow/divide by zero variety.

 

 

 

So how does this work for something like Hasten, which is a temporary recharge buff?

 

 

 

Hasten has a 450s recharge and adds +70% global recharge for 120s after the power activates/animates.  Ideally speaking, you want to have a recharge time of LESS THAN 120s in order to account for the time it will take to animate in order to maintain perma status on the buff.

 

So the target to reach is 450x100=45,000 recharge points, and ideally speaking you want to reach that total within 118s (or so) to prevent downtime on the buff.

So we're aiming to ADD UP to 45,000 in 118 seconds.

That means that you're aiming for being able to achieve an average of 45000/118=381.36 recharge "points" per second.

 

Start with a base of 100.

Hasten itself adds +70.

2 Common Level 50 +Recharge Reduction IOs will add +83.32 to the Hasten power.  Note that a third slot will only increase this amount to +99.08 which is a mere +15.76 increase for adding an entire 42.4% Common IO, which is a really terrible return on investment for another slot.  For this reason I recommend slotting no more than 2 +Recharge Reduction Common IOs into Hasten.

 

So at this point we've got 100 + 70 + 83.32 = 253.32 recharge points per second just acting on Hasten itself.

 

Which means ... what?

 

Well, it means that in the absence of any other global recharge enhancement(s) ... during the 120s duration of the Hasten buff you'll build a stack of recharge points of:

120 x 253.32 = 30,398.4 ... leaving 14,601.6 to go after 120s of elapsed time.

 

So how long would it take to finish recharging Hasten with no other buffs in play?

Well, you'd have only 100 + 83.32 = 183.32 recharge points per second accumulating ... so ...

14,601.6 / 183.32 = 79.65 seconds

 

 

 

Okay ... so what? (I hear you cry)

Of what use is that to ANYONE?

 

 

 

Well ... it's just the first step foundational underpinnings to being able to do things like factor in Force Feedback procs into the process.

Huh, say wha?  How would that even work?

 

 

 

Actually, it's rather simple.

Each Force Feedback proc is +100% Recharge Reduction for 5 seconds.

Using the above "add up to a threshold" method that uses division at the end and you've got a simplified way to factor in temporary buffs to recharge.

 

Specifically ... each Force Feedback proc equates to +500 recharge "points" added onto the stack needed to reach the threshold.

 

In other words, take the 14.601.6 recharge remaning amount after 120s of Hasten buff time and simply reduce it by 500 for each Force Feedback proc.  In other words ... if you were able to proc Force Feedback 29.2 times (let's round up to 30 to keep things simple) during those 120s of Hasten buffing you wouldn't need any global recharge buffs to make Hasten perma.  And why is that?  Because 30x500=15,000 which is greater than 14.601.6 ... as you can see.

 

Now, the complication factor here is that each Force Feedback proc lasts 5 seconds and even under ideally perfect laboratory conditions you're only going to get 12 procs per minute(!) since 12x5=60 seconds, owing to the fact that Force Feedback procs DO NOT STACK.

 

 

 

But that was doing a very simplified example of how using an additive process can make the math easy and accessible to use, since (like the New Math™) you know what you're doing at each step of the process and it's intuitively obvious.

 

 

 

So to extend the example of what I was just doing ... let's say for the sake of argument and illustration purposes that we've got the same situation as above but with an extra +50% global recharge bonus from sets.  What happens?

 

Well, the first thing is that you move into a 100+70+83.32+50=303.32 recharge points per second during Hasten and a 100+83.32+50=233.32 recharge points per second outside of Hasten buffing regime.

What does this do to the "speed" of building the recharge stack in time for making Hasten perma?

 

120 x 303.32 = 36,398.4 recharge points over 120 seconds ... leaving 8601.6 recharge points remaining.

8601.6 / 233.32 = 36.87 seconds additional recharge beyond 120 seconds of Hasten buff duration ... for a total of 156.87 seconds of total Hasten recharge time.

 

How many Force Feedback procs would it take to bring that total of 36,398.4 recharge points over 45,000 within the 120 second window?

Answer (rounding up to next integer): 8601.6 / 500 = 17.2 = 18 procs within 120 seconds

This would be difficult to achieve ... since Force Feedback is a 2 PPM proc, but if it was slotted into multiple powers in a build it could be done.

 

 

Okay, then what about something like a +85% global recharge bonus?

100+70+83.32+85=338.32 recharge points per second during Hasten

100+83.32+85=268.32 recharge points per second outside of Hasten buffing

 

120 x 338.32 = 40,598.4 ... leaving 4401.6 recharge points remaining.

4401.6 / 268.32 = 16.4 seconds additional recharge beyond 120 seconds of Hasten buff duration ... for a total of 136.4 seconds of total Hasten recharge time.

4401.6 / 500 = 8.8 = 9 procs of Force Feedback during 120 seconds of Hasten buffing to achieve perma Hasten recharge stack of 45,000 within 120 seconds (doable with multiple powers slotted with Force Feedback procs).

 

 

 

In other words, you can use this additive method of computing recharge at different amounts over time in order to figure out how many procs of Force Feedback you'd need in order to reach a particular threshold.  You can also use this method to calculate the "value" of a Force Feedback proc relative to a global recharge buff (kinda sorta).  That's because ...

500 / 60 = +8.333% global recharge per minute ... per Force Feedback proc ... and Force Feedback has a base 2 PPM proc rate.

 

In other words ... if you can get 2 PPM out of a power using Force Feedback, that's the equivalent of adding 1000 recharge points over 10 seconds during that minute ... which is the equivalent to a +16.67% global recharge boost ... assuming an average of 2 procs per minute from that slotted proc in that power.

 

Name the other ways you can add +16.67% global recharge boosting for ONE SLOT available to you in this game?

The "catch" ... of course ... is that you have to USE the power(s) the Force Feedback procs are slotted into in order to get the benefits of those procs to your global recharge amounts.

 

 

 

Then again ... when do you "need" global recharge bonuses the most?

In combat.

 

When do you tend to be using your powers the most?

In combat.

 

Do you REALLY need your powers to be completely perma refreshing when out of combat?

DEPENDS ...

Sometimes yes ... sometimes no ... it depends on your build.

 

 

 

Anyway, the point I'm making with this additive system here is that it makes it a lot easier to figure out "how short" you are of being perma on buffs like Hasten ... and if you are "falling short" of being perma, how much global recharge you'd need in order to close that gap AND how many Force Feedback procs you'd need to make happen within that time frame in order to close that gap completely.  And best of all, the math is relatively accessible.

 

100 + enhanced recharge + global recharge modifiers = recharge "points" per second

100 x base recharge time = recharge "points" threshold to meet

Each Force Feedback proc = +500 recharge "points" over 5 seconds (theoretical max of 12 per minute)

 

 

 

Hope that helps you @Bopper ...


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31 minutes ago, Redlynne said:

Bopper I hate to suggest this

First off...where the hell have you been? I haven't seen you post in like a month. Either way, I'm honored to be crit'd by your wall of text response.

 

From your steps, you are literally doing everything I showed in the Chapter 1 examples (I used the additive approach until the last time interval, but I worked in decimal as opposed to you working in percents/points). The formula version of your steps are Formulas 2.2.-2.4, and that formula is further simplified with Formulas 3.1-3.2.

 

You actually showed that I took the right approach of working backwards, as I did the additive method up front then introduced formulas. I may need to revisit how I'm explaining the additive method, as I thought it was clear.



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The way I look at it is basically ask the question of whether or not the recharge is reduced enough to recharge the power during the effect in question.  If not, then how much time is left over once the effect expires so as to compute recharge time beyond effect duration.  The follow up to that is computing "how many" Force Feedback procs are needed to make up the shortfall ... and the easiest way to do that is using an additive process where you're trying to meet (or exceed) the threshold of total recharge rate over time needed to produce that yield.

 

For the layman, simply knowing "how many Force Feedback procs are needed" to make up any shortfall in having enough recharge to accomplish a perma effect is the useful number that even laymen can grasp ... kind of like knowing you need to add up to 45% Defenses for the non-incarnate softcap.


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