Diminishing returns? (Paging Theorycrafters!)

cdnbison · August 2016

So, I'm a well-geared DC (3300iL), but still looking to improve. I know what gear I want to get / need to improve, but I'm curious about my stat allocation. Right now, I'm at about 9k for both recovery and CS (~40%), 26k power.

The question I have is about when do DR kick in and make REC / CS stacking sub-optimal to stacking power? Would I be better off dropping some of either in place of power?

Thanks much!

putzboy78 · August 2016

There is no diminishing returns for recovery or critical strike. What you do have is:

Critical Strike Chance - A relationship between power and crit severity that gives you an optimal critical strike chance. However, that does not account for some skills that only proc on crit (fire of the gods for example) or powers that only proc on non-crits (owlbear cub).

Recovery - This you need to tweak based on your needs and playing style. 200 recovery is a 1% decrease in encounter cooldowns. If you are never waiting for stuff to come off cooldown you may have to much recovery conversely if you are always waiting you may have to little. As you stack recovery the actual time decreases. Let's say for example you put on 200 recovery and your current cooldown is 10s, now its 9.9s. If you have a lot of recovery already stacked and have already reduced that CD to 8s and you add 200 recovery you won't reduce your CD by .1s, you will reduce it by .08s. So its not a direct diminishing return but effectively stacking recovery becomes less and less effective.

Power - Power is typically your least effective stat (if you don't account for power buffing your party) and most would consider it your garbage stat. It's where you dumb stats when everything else is optimized. It's mostly linear 400 power = 1% damage increase.

I would checkout @thefabricant stat theory and associated calculators for a more in depth look

rapo973 · September 2016

[EDIT]
Wrong: forget it.

I've tried to show how recovery works against cooldown (I know it was already discussed somewhere else, but I love excercises).
Let's assume that you start from 1000 recovery and you cumulate it up to 9.200.
Overall, the recovery increases by 820%, but the cooldown decreases by -33.8% only: but this doesn't explain the recovery diminishing return yet.

If you analyze the behavior of the cooldown explained by @putzboy78 , then the general formula is:
Curr_CD=Init_CD * [(CHA-10)/100] * (1-0.01)^(Rec/200)
where
Curr_CD = Current Cooldown
Init_CD = the initial cooldown of the encounter power with no bonus.
CHA = your charisma
Rec = your current recovery
0.01 (1%) = the cooldown decreasing rate for each +200 recovery step forward. If you divide your recovery by 200, you have the number of steps.

Finally your current recovery is the exponent of a number < 1: that's the "diminishing return" component (see the graph hereunder by looking at the lenght of each segment before it steps down: shorter at the beginning, longer at high recovery)

That's why CHA may be important if your playstyle requires to decrease the cooldown: it's a linear decrease of the cooldown for each CHA point added with no diminishing return.
Unfortunately that's the behavior of the iterated linear functions (widely used to calculate the interest of a mortage loan against you )

If you see any mistake/error, let me know.

thefabricant · September 2016

rapo973 said:
I've tried to show how recovery works against cooldown (I know it was already discussed somewhere else, but I love excercises).
Let's assume that you start from 1000 recovery and you cumulate it up to 9.200.
Overall, the recovery increases by 820%, but the cooldown decreases by -33.8% only: but this doesn't explain the recovery diminishing return yet.

If you analyze the behavior of the cooldown explained by @putzboy78 , then the general formula is:
Curr_CD=Init_CD * [(CHA-10)/100] * (1-0.01)^(Rec/200)
where
Curr_CD = Current Cooldown
Init_CD = the initial cooldown of the encounter power with no bonus.
CHA = your charisma
Rec = your current recovery
0.01 (1%) = the cooldown decreasing rate for each +200 recovery step forward. If you divide your recovery by 200, you have the number of steps.

Finally your current recovery is the exponent of a number < 1: that's the "diminishing return" component (see the graph hereunder by looking at the lenght of each segment before it steps down: shorter at the beginning, longer at high recovery)

That's why CHA may be important if your playstyle requires to decrease the cooldown: it's a linear decrease of the cooldown for each CHA point added with no diminishing return.
Unfortunately that's the behavior of the iterated linear functions (widely used to calculate the interest of a mortage loan against you )

If you see any mistake/error, let me know.

The mistake/error you are making is in your basic equation:

Curr_CD=Init_CD * [(CHA-10)/100] * (1-0.01)^(Rec/200)

Lets plug in some values.

Initial CD = 20 seconds
CHA = 20
Recovery = 18000

If this equation was correct, the cooldown would be:

Current CD = 20*[(20-10)/100]*(1-0.01)^(18000/200)

Which would simplify to:

Current CD = 20*0.1*0.99^90

= 0.8094639454 seconds cooldown. By stacking it higher you could get it to the point where cooldowns round to 0, even in the games system.

Realistically, the equation is Base CD/(1+Recharge Speed Increases).

This means that with the above numbers, your cooldowns will look as follows:

20/(1+0.1+0.9) = 20/2 = 10.

You won't see any 0 second cooldowns. I WISH recovery worked the way you plotted it

bvira · September 2016

Power vs Crit you can download the speadsheet in my signature to see how to stack power and crit optimally (Note: it doesn't consider secondary effects related to power and crit such as owl bear cub active bonus, Fire of the Gods etc).

If you want to share your power with feats then stacking power is a no-brainer; if you want higher HPS/DPS & faster debuff via FotG+Bear your Sin then crit is generally more favorable (unless your power is ridiculously low).

Recovery IMO just roll with what your basic gears provide you without intentionally stacking it unless you want your cooldown to be a certain number. For example, if you want Astral Shield to have no down time then you can stack enough recovery/CHA/INT to drive its CD down to ~10s. Note that skills with high base CD would benefit more from high recovery and skills that already have low base CD would suffer serious diminishing return.

putzboy78 · September 2016

yeah as a right dc that doesn't rely on 24/7 Astral Shield, you can find that divinity mode can offset the CD on powers from having low recovery. I can't even imagine what I would do with high recovery on my DC.

mrtehpuppy · September 2016

Well and as rigneous DCS our capstone provides a seriously hefty chunk of CDR. Personally able to have a "100% uptime" on AShield with 4.4k Recovery (that fluctuates up to 5.9k via bindings) with 15 Int and 18 cha but ONLY while the capstone is active. Once the capstone expires there is a casting gap in AShield of what *feels* like 1 or 2 seconds (never bothered to time it as I typically only run into this during PvP matches which is something I do rather sparingly on the righteous DC).

But to your point Putz about not knowing what you'd do, I can say I've run alongside DCs that stacked Recovery into the 9k range and I was rather envious of their ability to have AA ready for every single trash clear in CN, but other than that, I didn't really notice them doing anything exceptionally different than me. I would parse higher on paingiver but that was simply due to them sacrificing ArP to get the Recovery where as I have too much ArP for PvE (and besides, it's not about who is where on paingiver, it's about those 7 minute CN clear times).

What I'm curious about though in regards to this Recovery discussion, is how much Recovery would it take to match the Righteous capstone? Basically I guess what I'm asking here is, is Avatar of the Divine a multiplicative boost or additive?

rapo973 · September 2016

thefabricant said:

The mistake/error you are making is in your basic equation:

Curr_CD=Init_CD * [(CHA-10)/100] * (1-0.01)^(Rec/200)

Lets plug in some values.

Initial CD = 20 seconds
CHA = 20
Recovery = 18000

If this equation was correct, the cooldown would be:

Current CD = 20*[(20-10)/100]*(1-0.01)^(18000/200)

Which would simplify to:

Current CD = 20*0.1*0.99^90

= 0.8094639454 seconds cooldown. By stacking it higher you could get it to the point where cooldowns round to 0, even in the games system.

Realistically, the equation is Base CD/(1+Recharge Speed Increases).

This means that with the above numbers, your cooldowns will look as follows:

20/(1+0.1+0.9) = 20/2 = 10.

You won't see any 0 second cooldowns. I WISH recovery worked the way you plotted it

Thank you @thefabricant
It's definitely wrong, formula and everything else. There were two more mistakes.
1) It's not Init_CD * [(CHA-10)/100], but Init_CD * [1-(CHA-10)/100].
2) I forgot the intelligence stat. At least for the DC, this is another source of recharge speed increase.

michela123 · September 2016

mrtehpuppy said:
Basically I guess what I'm asking here is, is Avatar of the Divine a multiplicative boost or additive?

It's additive, it's like 8k recovery.

mrtehpuppy · September 2016

Thank you @michela123

rapo973 · September 2016

[EDIT] Amended.
Here a simple simulator for DCs (and not only) that I've created to show how the cooldown decreases as a function of the recovery.
https://www.desmos.com/calculator/fnyimsihlf

There are some sliders you have to configure to match your roll and power cooldown.
- b = Base Cooldown
- c = Charisma
- i = Intelligence
- d = HL cooldown decrease (example, if you have hastening light, that has an effect on the cooldown).
You can also "play" such parameters and change the ranges as you like.

If you click on the red plot you can see the coordinates (recovery, cooldown).
Example: you want to know how your recovery improves the BtS cooldown, knowing that you have 13 INT and 18 CHA, then

b = 12 secs
c = 18
i = 13
d=0

thefabricant · September 2016

rapo973 said:
Here a simple simulator for DCs (and not only) that I've created to show how the cooldown decreases as a function of the recovery.
https://www.desmos.com/calculator/yxijzovg9c

There are some sliders you have to configure to match your roll and power cooldown.
- b = Base Cooldown
- c = Charisma
- i = Intelligence
- d = generic cooldown decrease or power duration (example, if you have hastening light, that has an effect on the cooldown).
You can also "play" such parameters and change the ranges as you like.

If you click on the red plot you can see the coordinates (recovery, cooldown).
Example: you want to know how your recovery improves the BtS cooldown, knowing that you have 13 INT and 18 CHA, then

b = 12 secs
c = 18
i = 13
d=0
It can be used to calculate what is needed to have the perma astral shield (set d as power duration and check where the line crosses the recovery axis).

Hastening light is subtracted before cooldown increases is applied. For example, if you have 100% recharge speed increase from all sources and 4 seconds CD reduction from hastening light on an encounter with has a base CD of 20 seconds, the equation is:

(20-4)/2=8

rapo973 · September 2016

thefabricant said:

rapo973 said:
Here a simple simulator for DCs (and not only) that I've created to show how the cooldown decreases as a function of the recovery.
https://www.desmos.com/calculator/yxijzovg9c

There are some sliders you have to configure to match your roll and power cooldown.
- b = Base Cooldown
- c = Charisma
- i = Intelligence
- d = generic cooldown decrease or power duration (example, if you have hastening light, that has an effect on the cooldown).
You can also "play" such parameters and change the ranges as you like.

If you click on the red plot you can see the coordinates (recovery, cooldown).
Example: you want to know how your recovery improves the BtS cooldown, knowing that you have 13 INT and 18 CHA, then

b = 12 secs
c = 18
i = 13
d=0
It can be used to calculate what is needed to have the perma astral shield (set d as power duration and check where the line crosses the recovery axis).
Hastening light is subtracted before cooldown increases is applied. For example, if you have 100% recharge speed increase from all sources and 4 seconds CD reduction from hastening light on an encounter with has a base CD of 20 seconds, the equation is:

(20-4)/2=8

Tested: unfortunately it doesn't work as you say.
Power: Astral Shield, Base Cooldown 20 seconds
Recharge speed increase = +135,9%
Hastening light slotted.

Test case:
1) Cast AA
2) Hastening light should apply -> 20 - 4 = 16
3) Recharge speed increase effect -> 16/2,359
4) Calculated cooldown = 6,78 sec

In game cooldown > 8 sec.

thefabricant · September 2016

rapo973 said:

thefabricant said:

rapo973 said:
Here a simple simulator for DCs (and not only) that I've created to show how the cooldown decreases as a function of the recovery.
https://www.desmos.com/calculator/yxijzovg9c

There are some sliders you have to configure to match your roll and power cooldown.
- b = Base Cooldown
- c = Charisma
- i = Intelligence
- d = generic cooldown decrease or power duration (example, if you have hastening light, that has an effect on the cooldown).
You can also "play" such parameters and change the ranges as you like.

If you click on the red plot you can see the coordinates (recovery, cooldown).
Example: you want to know how your recovery improves the BtS cooldown, knowing that you have 13 INT and 18 CHA, then

b = 12 secs
c = 18
i = 13
d=0
It can be used to calculate what is needed to have the perma astral shield (set d as power duration and check where the line crosses the recovery axis).
Hastening light is subtracted before cooldown increases is applied. For example, if you have 100% recharge speed increase from all sources and 4 seconds CD reduction from hastening light on an encounter with has a base CD of 20 seconds, the equation is:

(20-4)/2=8
Tested: unfortunately it doesn't work as you say.
Power: Astral Shield, Base Cooldown 20 seconds
Recharge speed increase = +135,9%
Hastening light slotted.

Test case:
1) Cast AA
2) Hastening light should apply -> 20 - 4 = 16
3) Recharge speed increase effect -> 16/2,359
4) Calculated cooldown = 6,78 sec

In game cooldown > 8 sec.

So here is a brief test case with Divine Glow. Notice my DC currently has 43.4% recharge speed increase (this includes the benefit from wisdom in it, if you don't believe me, remove points in wisdom and look at the result.)

Tooltip CD: 11.1s

11.1*1.434=15.917, I imagine it is actually 16 seconds and there is some rounding.

So, working with 16 as the base CD:

(16-4)/(1+0.434) = 8.36820083682

Vs 16/1.434 - 4 = 7.15760111576

You can very clearly see in this little demonstration here that the cooldown goes down to 8 and not 7 seconds:

https://youtu.be/lRhTntXbbNo

From this point on, I am abbreviating recharge speed increase to RSI btw.

This does of coarse mean that for the sake of calculating them as separate components, you need to write it as Base CD/(1+RSI) - Hastening light/(1+RSI) and whenever you cast your daily, the equation is then:

Current CD - Hastening light/(1+RSI).

Note, that hastening light on allies counts their RSI and not your own (I can post footage of this as well if you like.)

I can also do a frame by frame reference of this video for you if you like for exact time stamps for when HL kicks in etc.

rapo973 · September 2016

ok, there's a misundersting:
I understood that HL applies before you cast the power...uhm..quite strange.

Ok here another test @75.3% with Astral shield. I removed the mount bonuses to be more clear.

In the follwing video you can see that the cooldown goes down to 7 seconds (6 due Avatar of the Divine, my assumption) and not to 9 seconds. It seems to me that this result is more in line with the HL tooltip.

https://youtu.be/-L2dzu6L35w

michela123 · September 2016

This happens because if you hit mobs when you cast AA or Flame Strike the cooldown reduction is higher (I think it's 8 seconds instead of 4, or something close to that). In your video you can see that the cooldown goes down to 9 and then to 7; that's because HL is applied twice due to a bug.

rapo973 · September 2016

michela123 said:
This happens because if you hit mobs when you cast AA or Flame Strike the cooldown reduction is higher (I think it's 8 seconds instead of 4, or something close to that). In your video you can see that the cooldown goes down to 9 and then to 7; that's because HL is applied twice due to a bug.

Thank you for this.
Tested again and it's correct what you both are saying.
Too hard to test things...probably I've to give up and stop testing: too many frustrations

Diminishing returns? (Paging Theorycrafters!)

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