Guide to Calculating Recharge v1.0

Arcanaville · 03-13-2007 01:12 PM

How to calculate recharge.

The question of how recharge works comes up a lot, as does the question of how to calculate how fast a power will recharge, especially given the complexities of hasten. Moreover, I suspect more people are going to be fiddling with recharge when I9 goes live and players start experimenting with the recharge buffs that exist in the Invention System. I have a technique that works pretty well: its not the fastest computational technique, but it has the advantage of being relatively easy to understand and adapt to a lot of different complex situations.

How does recharge work?

First of all, recharge boosts are expressed (like lots of things in CoH) in terms of percentages, like 33% recharge buff (terminology note: speed buffs generally refer specifically to movement speed like running. Recharge buffs refer specifically to the speed boosting that reduces recharge). But in actuality, those buffs are really decimal numbers: in this case, 0.33. The way recharge buffs improve the recharge of a power is by formula:

NewRecharge = OriginalRecharge / (1 + RechargeBuffs)

So if you have +33% recharge and a power takes 10 seconds to recharge normally, with that recharge buff it will take 10 / 1.33 = 7.52 seconds to recharge. Recharge buffs are additive: if you have a +0.33 recharge buff, and a +0.2 recharge buff, the new recharge will be the old recharge divided by (1 + 0.33 + 0.2) or 1.53.

Something important to know: powers have an activation time and a recharge time. And recharge buffs only speed up recharge time: they do not affect activation times at all. So if a power takes two seconds to activate, and eight seconds to recharge, it can be used every ten seconds. A 0.33 recharge buff does not mean the power can be used every 7.52 seconds: it means the power recharges in 8 / 1.33 = 6.02 seconds, and can be used every 2 + 6.02 = 8.02 seconds. Notice that because recharge cannot work on activation times, its always a little weaker than you might expect in terms of speeding up things like attack powers.

Actually, its a little more complex than that: powers can have interrupt periods, activation times, cast times, root times, and all manner of complex mechanics. But for our purposes, we will call the time from the moment the power is activated, until the moment it fully discharges and begins recharging the activation time.

How to Calculate Recharge

Now, that's how recharge works. How do you calculate how long a power takes to recharge. Well, the simple way is what I just said: add up all the recharge buffs operating on the power, and divide the recharge time of the power by the factor (1 + TotalRechargeBuff). But what if it isn't that simple? What if you have variable recharge buffs.

When do you have variable recharge? When you have recharge buffs that aren't on all the time. And there are examples of that in the game. The most prominent example is hasten. Hasten is a recharge buff that has 450 second base recharge time, and 120 second duration. While its up, it offers +0.7 recharge buff. Because hasten isn't up all the time (as of ED its no longer perma-able with just slotted recharge) we can't just divide hasten's 450 recharge time by the recharge buff operating on the power: that recharge buff is one thing when hasten is up, and another thing when hasten is down. So how would we calculate hasten's uptime?

Answer: we use an alternate method for calculating recharge. We tend to think of recharge buffs as reducing the total time necessary to recharge a power. But there is an alternate way to think about it. When a power has 450 seconds of recharge, we can say that without speed buffs, that power earns one tick every second towards recharging to full. After 450 seconds, the power earns 450 ticks, and is fully recharged.

If the power is operating under a speed buff, it earns more ticks per second. With a +0.33 recharge buff, it earns 1.33 ticks per second. Theoretically, after 338.35 seconds, the power would earn 450 ticks, and be fully recharged.

Trust me: it works. And its useful. Suppose we have hasten, with no slotted recharge at all. How long does it take to recharge? Easy:

When hasten first activates, it offers a +0.7 recharge buff for 120 seconds while its up. Then it drops, and offers no speed buff until it recharges.

For the 120 seconds it is up, hasten earns 120 * (1 + 0.7) = 204 ticks towards being recharged. That means it has 450 - 204 = 246 ticks to go. It has to earn those at one tick per second, so it has 246 seconds to go until its fully recharged. So the total cycle time for hasten is 120 + 246 = 366 seconds.

So hasten, with no slotted recharge, takes 366 seconds to recharge. Its activation time is 0.73 seconds, so hasten's total cycle time is 366.73 seconds. Thats how often you can use it.

What if we slot it with recharge? Well, if we slot 3 even SOs of recharge, that is a +95% recharge buff, or more properly a +0.95 recharge buff. Now, its cycle time changes: during its 120 second uptime, it now earns 120 * (1 + 0.7 + 0.95) = 120 * 2.65 = 318 ticks. That means it has 450 - 318 = 132 ticks to go. These remaining ticks have to be earned without hasten being up: it will earn those ticks at a rate of 1.95 ticks per second (because of the slotted recharge). So it takes 132 / 1.95 = 67.7 seconds to earn those ticks. That means hasten recharges in 120 + 67.7 = 187.7 seconds. Its total cycle time is 187.7 + 0.73 = 188.43 seconds.

Okay, time to move to slightly harder problems. How long does it take for Elude to recharge, if you have hasten, and hasten is 6-slotted with even recharge SOs for recharge (+110% recharge buff), and Elude is 3-slotted with even recharge?

First, we tackle hasten. Hasten earns 120 * (1 + 1.1 + 0.7) = 336 ticks when up, leaving 450-336 = 114 ticks to go, which takes 114 / (2.1) = 54.3 seconds to earn. Hasten's total cycle time is 120 + 54.3 + 0.73 = 174.03 seconds.

Now, in one hasten cycle, Elude is going to earn a certain amount of ticks towards its recharge. When hasten is up, Elude will earn 120 * (1 + 0.95 + 0.7) = 318 ticks. When hasten is down, which it will be for 54.03 seconds, Elude will earn 54.03 * (1 + 0.95) = 105.36 ticks. So in one complete cycle of hasten, Elude will earn 318 + 105.36 = 423.36 ticks. Now, Elude and Hasten will not be perfectly lined up all the time: sometimes Elude will see more of hasten's uptime than at other times. But what will Elude's recharge be on average?. Well, on average, Elude will need 1000/423.36 = 2.36 cycles of Hasten, slotted the way described, to fully recharge (423.36 ticks per hasten cycle, so that's how many cycles it needs). So Elude will recharge in 2.36 cycles of Hasten, or 2.36 * 174.03 = 410.71 seconds. Elude has 1.5 second activation, so Elude's total cycle time will be 410.71 + 1.5 = 412.21 seconds. Basically, Elude can be used once every 412.21 seconds, and its up for 180 seconds, so it has 412.21 - 180 = 232.21 seconds of downtime: 3 minutes up, 3 minutes, 52.21 seconds down.

We can do this for other powers, like dull pain, even when the average number of hasten cycles required is less than one: consider hasten 3-slotted with (even) recharge, and dull pain slotted with 3 even recharge enhancers also.

Hasten with 3-slot recharge has 188.43 cycle time, as mentioned above. Dull Pain earns 120 * (1 + 0.95 + 0.7) = 318 ticks when hasten is up. It earns 68.43 * 1.95 = 133.44 ticks while hasten is down. But it only needed 360-318 = 42 ticks to fully recharge. That means while Dull Pain earns 451.44 ticks per hasten cycle, it only needs 360 ticks to recharge, and it therefore only needs 360/451.44 = 0.797 hasten cycles to recharge, or 150.18 seconds on average. Sometimes a little faster, and sometimes a little slower, depending on how Dull Pain and hasten align.

One little bit of subtle complexity for the mathematically inclined: when recharge powers are up, powers like Elude earn more ticks faster, so all other things being equal, its much more likely that a power like Elude will complete its recharge while a recharge power is up, rather than down. That means the *number* of times the power will recharge at below average times (faster) is going to be higher than the number of times it will recharge at above average times (slower). But the times when it is slower will weigh heavier on the average, because they will obviously happen for longer periods of time. Overall, this is a wash: the average recharge rate per unit time is going to be the computed average. But it might *seem* like its faster, because you'll see more instances where its faster than slower, and are less likely to factor in the fact that when its slower, you are spending more time waiting (especially for long duration/long recharge powers like Elude).

Multiple Recharge Boosting Powers

Time to graduate to the hardest problem. Suppose you have accelerate metabolism and hasten? Each has recharge buffs. How do you calculate the recharge times of either, when each speeds the other up?

Unfortunately, I don't have a nice simple calculation that determines this. I'm forced at this point to switch to algebra. AM is a +0.3 recharge buff for 120 seconds, and has 422 base recharge time and 2.03 activation time. Hasten, as before, is a +0.7 recharge buff for 120 seconds, and has 450 base recharge time and 0.73 activation time.

First of all, we presume that AM has an average recharge buff, call it a, and hasten has one, call it h. We can then create two expressions based on those average recharge buffs.

The average recharge buff of AM is based on its average cycle time. Its 0.3 * 120 / (cycle time). And its average cycle time is based on the average recharge buff it experiences. If its 3-slotted, it always has a 1.95 recharge. On top of that, it gets the average buff from hasten, and also its own average buff. So the total recharge it experiences on average is (1.95 + a + h). That reduces its recharge from 422 to 422/(1.95 + a + h). Its total cycle time is 2.03 + 422/(1.95 + a + h). So its average buff is 0.3 * 120 / (2.03 + 422/(1.95 + a + h)), which reduces to:

a = 0.3 * 120 * (1.95 + a + h) / (2.03 * (1.95 + a + h) + 422)

Now, I like precision as much as the next person, but I'm not really interested in solving quadradic equations just to find the recharge of AM. I'm willing to estimate. AM's activation time is very small relative to its cycle time, so I'm going to assume its zero for the purposes of this calculation. It will only alter the numbers by a second at most. That reduces that expression further to:

a = 0.3 * 120 * (1.95 + a + h) / 422

Similarly, you can derive an expression for the average recharge buff of hasten:

h = 0.7 * 120 * (1.95 + a + h) / 450

Two equations, two variables. All you need to do is solve. Having a calculator helps multiplying all the terms through. What you get is:

h = 0.500, a = 0.228

So the average recharge buff of hasten is 0.500, and the average recharge buff of AM is 0.228. That makes it easy to calculate average recharge times.

Hasten: 450 / (1.95 + 0.500 + 0.228) = 168.04 seconds
AM: 422 / (1.95 + 0.500 + 0.228) = 157.58 seconds

The total cycle times become just activation time plus recharge time:

Hasten: 168.04 + 0.73 = 168.77 seconds
AM: 157.58 + 2.03 = 159.61 seconds

This algebraic method is extensible to any number of speed boosting powers operating simultaneously. You could use it to see what happens when 8 rads all use AM on each other, for example.

a = 0.3 * 120 * (1.95 + 8a) / 422
a = 0.524

When you calculate the average recharge buff of a power to be higher than its actual base buff, that's saying the buff is recharging fast enough to be self-stacking. What the math doesn't know is whether or not the buff is actually capable of self-stacking. In this case, AM doesn't self-stack. Therefore, its maximum average buff is the case where its up permanently, in which case its average buff is equal to its base buff, or 0.3.

AM recharge: 422 / (1.95 + 8 * 0.3) = 97.01 seconds
AM cycle time: 99.04 seconds

More than perma, with no hasten.

The algebraic method above pretty much works all the time, with one caveat: if the recharge buffing powers you're looking at have downtimes that are low relative to their uptimes, what you see in game will tend to be about the calculated average. But the larger the downtimes are relative to the uptimes, the more likely it is you'll see wilder extremes in recharge, with sometimes much longer and sometimes much shorter ones. A good rule of thumb is that if the recharge buffing power is up at least half the time, you'll likely see recharge rates near the computed average most of the time.

Summary

How to calculate recharge:

* With no recharge boosting powers, or with constant recharge buff, take the base recharge of the power, and divide by the total recharge factor, which is (1 + All Recharge Buffs)

* With one recharge boosting power that is not perma (up and down), use the tick method. Calculate how much ticks the power earns while the recharge boosting power is up, how much when its down, and then calculate how many total cycles the power in question needs. Even if it turns out to be only a fraction of one cycle, the method still works.

* With two or more non-perma recharge powers, you have to resort to the algebra method above.

Edit: Thanks to Plasma for correcting a major calculation error.

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RagManX · 03-13-2007 03:39 PM

Mmmmmmmm. Numbers.

Most of my characters have given up hasten, just because I typically solo and prefer even performance. I recognize that I could perform better on average with hasten, and would still have worst case performance equal to my typical performance now with regards to power availability, but I like the evenness I have now and still enjoy playing as I am built. All that said (and quite poorly, I recognize), I'm seriously reconsidering hasten after reading this. Thanks, Arcana. Well written as always, and certainly something to get me thinking about hasten again. Now, is it worth dropping recall friend on my DDD to get hasten? Hmmmm.

RagManX

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The_Gamemaster · 03-13-2007 04:50 PM

Very useful, general information; nice work. I was hoping for some graphs, but the algebraic method works .

I notice that you already have a link to this guide in your sig; hopefully those who need it will notice this fact as well.

SuperBull · 03-13-2007 06:28 PM

Nice guide

Bill Z Bubba · 03-14-2007 08:00 AM

Woot! Now me go back to smashing rocks together.

<grunt>

Be well, people of CoH.

Plasma · 03-14-2007 08:50 AM

[ QUOTE ]

This algebraic method is extensible to any number of speed boosting powers operating simultaneously. You could use it to see what happens when 8 rads all use AM on each other, for example.

a = 0.3 * 120 * (1.95 + 8a) / 422
a = 0.170

AM recharge: 422 / (1.95 + 8 * 0.170) = 127.49 seconds
AM cycle time: 129.52 seconds

Very nearly perma, with no hasten.

[/ QUOTE ]

I was with you until here, and then my brain red-flagged this because I know that AMx8 is nearly perma without even slotting recharge SOs.

a = 0.3 * 120 * (1.95 + 8a) / 422
a = .522

Of course, this is wrong, since the factor [a] for a buff cannot be higher than its maximum buff; it reflects the fact that with 3 SOs and 8xAM, AM is up WAY before it expires (about 20 seconds early). So we have to cap any recharge factor at the maximum of its own buffage before we insert it into the next part of the formula:

a = max (.3,0.3 * 120 * (1.95 + 8a) / 422), which is .3 since our .522 > .3.

So then the actual recharge:

AM recharge: 422 / (1.95 + 8 * 0.30) = 97 seconds
AM cycle time: perma, baby

If we run the numbers without the 0.95 from the SOs in place, we get a = .268, and then:

AM recharge: 422 / (1.00+ 8 * 0.268) = 134.2 seconds
AM cycle time: 136.23

That about jibes with my experience.

Arcanaville · 03-14-2007 10:37 AM

[ QUOTE ]
a = 0.3 * 120 * (1.95 + 8a) / 422
a = .522

[/ QUOTE ]

Yikes. You're right, I must have pushed the wrong calculator button on that one. Also, it didn't feel right either, but I let it go. Grr...

Just to make sure:

a = 0.3 * 120 * (1.95 + 8a) / 422
422a = 36 * (1.95 + 8a)
422a = 70.2 + 288a
134a = 70.2
a = 0.524

[ QUOTE ]
Of course, this is wrong, since the factor [a] for a buff cannot be higher than its maximum buff;

[/ QUOTE ]

To be specific, the calculation is implying that this level of recharge is so high that the powers are self-stacking: if the recharge buff doesn't self-stack (and AM doesn't) then its actual average recharge buff contribution cannot exceed its base recharge buff. So 0.524 implies its actually up all the time and giving 0.3 all the time.

Thanks for the correction: I've updated the guide with a proper rendition of this calculation and an explanation for what's going on.

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EvilGeko · 03-14-2007 11:04 AM

Does this make Plasma the Dread Pirate Roberts?

Probably only Scrapper forum junkies will understand.

The City of Heroes Community is a special one and I will always look fondly on my times arguing, discussing and playing with you all. Thanks and thanks to the developers for a special experience.

Plasma · 03-14-2007 11:24 AM

Good night. Sleep tight. I'll most likely kill you in the morning.

Bosor · 03-14-2007 01:56 PM

Excellant guide Arcanaville, as always.

Enantiodromos · 03-14-2007 04:30 PM

Nice guide. Consumed virtual seconds is a useful tool indeed.

It's worth noting (if you did, I didn't notice) that some of the really long recharge powers (which frankly, are what we worry about most), may well have recharges close to 232 seconds; which makes it feasible for them, at least, to assume a flat .36 recharge out of hasten. A convenient shortcut in the rare case its useful-- e.g., recharges on click accolades and perhaps, leaving long-recharge powers like EMP and controller AoE Holds unslotted or minimally slotted.

Even if you're close to 232 seconds, it can be a convenient kludge. If you have 1 recharge in a 240 second hold, for example, you know you'll burn at LEAST 68 real seconds at the increased recharge.

Arcanaville · 03-14-2007 04:44 PM

[ QUOTE ]
Nice guide. Consumed virtual seconds is a useful tool indeed.

It's worth noting (if you did, I didn't notice) that some of the really long recharge powers (which frankly, are what we worry about most), may well have recharges close to 232 seconds; which makes it feasible for them, at least, to assume a flat .36 recharge out of hasten. A convenient shortcut in the rare case its useful-- e.g., recharges on click accolades and perhaps, leaving long-recharge powers like EMP and controller AoE Holds unslotted or minimally slotted.

Even if you're close to 232 seconds, it can be a convenient kludge. If you have 1 recharge in a 240 second hold, for example, you know you'll burn at LEAST 68 real seconds at the increased recharge.

[/ QUOTE ]

My motivation for posting the guide was to lay out the basics of looking at recharge in potentially unconventional situations. That's why I didn't just say "this is 3-slot hasten, this is 3-slot dull pain with hasten" etc. My suspicion is that when I9 goes live, a lot more players are going to be experimenting with recharge, and asking questions like "can I get perma-DP back"? or "what's the best possible uptime for Elude?" or "if I slot up these IO sets in order to get these set recharge buffs, what does that do to hasten?" There's going to be a lot more "weird" recharge out there, and that will mean the "standard" speed questions might not be the norm anymore.

Hopefully, this guide will help a lot more players be able to figure their recharge questions out for themselves, and will allow more players to help more players that can't.

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Bystander · 03-14-2007 05:07 PM

[ QUOTE ]
[ QUOTE ]
Nice guide. Consumed virtual seconds is a useful tool indeed.

It's worth noting (if you did, I didn't notice) that some of the really long recharge powers (which frankly, are what we worry about most), may well have recharges close to 232 seconds; which makes it feasible for them, at least, to assume a flat .36 recharge out of hasten. A convenient shortcut in the rare case its useful-- e.g., recharges on click accolades and perhaps, leaving long-recharge powers like EMP and controller AoE Holds unslotted or minimally slotted.

Even if you're close to 232 seconds, it can be a convenient kludge. If you have 1 recharge in a 240 second hold, for example, you know you'll burn at LEAST 68 real seconds at the increased recharge.

[/ QUOTE ]

My motivation for posting the guide was to lay out the basics of looking at recharge in potentially unconventional situations. That's why I didn't just say "this is 3-slot hasten, this is 3-slot dull pain with hasten" etc. My suspicion is that when I9 goes live, a lot more players are going to be experimenting with recharge, and asking questions like "can I get perma-DP back"? or "what's the best possible uptime for Elude?" or "if I slot up these IO sets in order to get these set recharge buffs, what does that do to hasten?" There's going to be a lot more "weird" recharge out there, and that will mean the "standard" speed questions might not be the norm anymore.

Hopefully, this guide will help a lot more players be able to figure their recharge questions out for themselves, and will allow more players to help more players that can't.

[/ QUOTE ]

It's already been asked. But well, you knew that since you posted in that thread. And I agree with the others. Very nice guide.

Plasma · 03-14-2007 06:08 PM

[ QUOTE ]
My suspicion is that when I9 goes live, a lot more players are going to be experimenting with recharge, and asking questions like "can I get perma-DP back"? or "what's the best possible uptime for Elude?" or "if I slot up these IO sets in order to get these set recharge buffs, what does that do to hasten?"

[/ QUOTE ]

Insightful! I was already thinking this way, but I hadn't thought about how confusing this can be if you're not a bit of a numbers junkie.

Teeto_K · 03-17-2007 02:09 AM

I had recently switched over to "consumed virtual seconds" in my own recharge calculations. It's good to see this in guide form. Definitely worth a /favorite, and I'll remember to link people to this if they start getting questiony.

Top grade work, as always.

Mission Arc: Metatronic Mayhem (Id 1750): A tale of robots gone wrong, rogue robots gone right, and madmen gone every which way but loose.

Frozen_Horizon · 03-17-2007 03:31 AM

Nice guide!!! Very good layout and it is understandable...

Ars Valde · 04-03-2007 07:56 PM

Arcanaville you are my Savior. Ive been having issues for a while now with Recharge problems, I might have to bookmark this to help when Im stumped.

Agonasty · 05-31-2007 09:48 PM

[ QUOTE ]
Trust me: it works. And its useful.

[/ QUOTE ]

I was skeptical for a while, but I think I just proved you right trying to disprove it. It really does work. I'm excited and extremely greatfule.

I was confusing the hell out of myself yesterday over the relation of Quickness, Hasten, Elude, and how I might benefit from IO sets. I just happend to stumble apon this today.

Montu · 05-07-2008 12:14 PM

Post deleted by Montu

Dagmo · 05-07-2008 12:51 PM

[ QUOTE ]
I would like ask where you got your formula for calculating a modified recharge rate. If a power's RECH is reduced by 33% (.33), then it means it will recharge 33% (.33) faster.

[/ QUOTE ]
Hmm...
[ QUOTE ]
Therefore, the formula should be [Modified RECH = Original rate - (Original rate X Boost %)]. So 10 - (10 X .33) = 6.7 not the 7.52 in your calculation which would only be 24.8 % boost. 6.7 is 33% (.33) faster than 10. Better example to illustrate my point is using 100 sec. 33% (.33) of 100 is 33. [100 - (100 X .33) = 67]. 67 sec is 33% faster than 100. Reduce the RECH by 50% (.50) and it will be twice as fast. [100 - (100 X .50) = 50]. 50 is 50% faster than (twice as fast as) 100.

[/ QUOTE ]
Well heck, you're right! Why don't I just three-slot all my powers with Single Origin Recharge enhancements (100%) so they're all recharged instantly!

I tease.

However, you must understand that enhancements that reduce an attribute--like recharge or endurance cost--cannot be a straight percentage reduction or they'll eliminate the attribute--and then go negative!--after just three enhancements. If three Endurance Reduction enhancements caused a 99% reduction in endurance cost for each power, no one would ever need to take Stamina.

Thus, Arcanaville's post is right on the money. Ye Olde Formule:

(Original Value) / (1 + Enhancements) = (New Value)

is quite correct.

So, ignoring Enhancement Diversification for ease of calculation, slotting three 33% recharge enhancements (even level SOs) into a power than normally takes 30 seconds to recharge will subsequently recharge in 15 seconds.

It's pretty easy to see this in action. Slot three single origin recharge or endurance reduction enhancements in a power and see if it recharges instantly or costs nothing to use.

Luminara · 05-07-2008 10:20 PM

[ QUOTE ]
I would like ask where you got your formula for calculating a modified recharge rate.

[/ QUOTE ]

Thousands of tests, hundreds of calculations, developer confirmations when she decides that there's something she needs to verify.

She's Arcanaville. She understands the mechanics of this game at least as well as the people who coded it, if not better in some respects. Really, questioning her math is like asking Albert Einstein to prove his work on E=MC².

Montu · 05-08-2008 09:50 AM

Post deleted by Montu

Plasma · 05-08-2008 02:02 PM

[ QUOTE ]
Please see my previous post. I didn't question the formula. Just wondered how she came upon it. The point I was making was how the % listed on the enhancements are misleading. Arcanaville's formula is dead on the money. It's the flaw in what we were led to believe that is my issue. Sorry I confused you on that.

And I hate to break it to you, but calculating enhancement boosts is no where near E=MC². And unlike a theory, they are proveable. Once you get past the fact that the % are not as stated.

[/ QUOTE ]

If your complaint is that the devs have made recharge enhancement numbers deceptive, why are you posting it in Arcana's guide thread? It doesn't belong here.

First you ask a question, and then it gets answered, and then you admit your question was disingenuous and you knew all along what the answer was, and just want to gripe. It's rude.

Arcanaville · 05-08-2008 04:36 PM

[ QUOTE ]
I would like ask where you got your formula for calculating a modified recharge rate. If a power's RECH is reduced by 33% (.33), then it means it will recharge 33% (.33) faster. Therefore, the formula should be [Modified RECH = Original rate - (Original rate X Boost %)]. So 10 - (10 X .33) = 6.7 not the 7.52 in your calculation which would only be 24.8 % boost. 6.7 is 33% (.33) faster than 10. Better example to illustrate my point is using 100 sec. 33% (.33) of 100 is 33. [100 - (100 X .33) = 67]. 67 sec is 33% faster than 100. Reduce the RECH by 50% (.50) and it will be twice as fast. [100 - (100 X .50) = 50]. 50 is 50% faster than (twice as fast as) 100.

[/ QUOTE ]

The way recharge works has been known for a very long time: far longer than I've ever been calculating numbers in the game.

The english descriptions for many things are ambiguous or strictly speaking mathematically incorrect, however in this case the english phrase "recharges 33% faster" is actually (probably coincidentally) correct.

If something has a recharge of 100 seconds, and its reduced to 67 seconds, then the proper way of describing that is that the power "recharges in 33% less time." That is *not* the same thing as "33% faster."

"Faster" is a word used to describe rates. A rate can be faster or slower. A time cannot be faster or slower. So the question is, what thing is happening that can happen faster when something is recharging. The metaphoric answer is, if you picture the power starting from zero, and "moving" towards being fully recharged, that rate is what's being increased by 33%. Basically, imagine if powers had recharge progress bars. 33% faster recharge has only one logical meaning: the progress bar moves from left to right 33% faster.

Under that perspective, "33% faster" does not mean "recharge is 33% less time" it means "recharge at 33% higher rate" which is mathematically "recharge in 75% of the original time." Similarly "100% faster" does not mean "recharge in zero time" it means "recharge in half the time" because that's what would happen if the recharge progress bar moved twice as fast.

Your own post actually shows the fact that even you wouldn't ordinarily describe 50% less time as 50% faster:

[ QUOTE ]
Reduce the RECH by 50% (.50) and it will be twice as fast. [100 - (100 X .50) = 50]. 50 is 50% faster than (twice as fast as) 100.

[/ QUOTE ]

"Twice as fast" and "50% faster" are not synonymous. "Twice as fast" is 100% faster. That situation is "twice as fast" and "executing in half the time." Its not "50% faster."

The person who wrote the text descriptions for many things erred in many ways (most notoriously: confusing "percent" and "percentage points") but in this case, he got it exactly correct.

Now, as to what confirmation I have that the equations are correct: I have three:

1. My own testing confirms that recharge works the way the formula specifies
2. The devs have confirmed that is the way recharge is intended to work.
3. The devs have also confirmed that my understanding of the mechanics of the game scheduler are correct, which means this is the *only* way that recharge can work.

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Montu · 05-09-2008 06:17 AM

Thanks Arcanaville. I think I got the gist of what's going on now. I was just thinking of it from the wrong angle. Numbers really can be frustrating at times (especially when I am right and too frustrated to see it as you pointed out) and I never have liked mixing words with numbers ie word problems, algebra etc.. I really didn't mean to insult anyone or, as Plasma pointed out, to be rude. Just very hard to figure things out sometimes. I am going to remove my previous posts as, again Plasma pointed out, they don't belong here and will remove this one after you have had a chance to read it. I hope you will accept my apologies for bringing my frustration and, in hind-sight, lack of judgement to your work in such a manner. Again, i apologize for any and all things out-of-line on my part. And thank you again for helping me get a better understanding of what's going on with the numbers game here.