Orignally posted this in another thread, but as I computed out the numbers I realized this is not just a disproof of the diminishing returns statement, it is even counter-intuitive. Because of this, I thought I should post it in its own thread so people can see it.
CDR does NOT suffer from diminishing returns, and it is NOT less effective. at 0% CDR you can cast 180 Serenities in an hour. At 10% CDR you can cast Serenity every 18 seconds, or 200 Serenities in an hour. At 19% (2x10%) CDR you can cast Serenity every 16.2 seconds, or 222 Serenities in an hour. At 27.1% (3x10%) you can cast Serenity every 14.58 seconds, or 247 Serenities in an hour. At 34.39% (4x10%) you can cast Serenity every 13.122 seconds, or 274 Serenities in an hour. Things continue at this rate, there is no diminishing returns from CDR; if anything, stacking more is worth MORE (20 more casts for first 10%, 22 for second 10%, 25 for third 10%, 27 for fourth 10%). PERIOD.
To go from 66.67% CDR to 70% CDR requires 10% more CDR. at 66.67 CDR you have a 6.67 second CD on Serenity, or 540 casts per hour. At 70% CDR you have a 6 second CD on Serenity, or 600 casts per hour. In other words, CDR is much more effective at high CDR than at low CDR (20 more casts per hour vs 60 more casts per hour).
I think people are saying 'diminishing returns' in the sense that it's harder to go from 60-70 than it is to go from 40-50, in terms of gear slots, and eventually you have to max CDR on nearly everything, thereby giving up a lot of damage. To some, it's not worth it.
Also, to Autocthon--I see people post on a daily basis that CDR suffers from "Diminishing Returns" (check the Flow of Eternity thread for today's entry, for example). Making this post to show that they are mis-informed. To be honest, because I had never done the math via casts, I did not realize that high end CDR was better than low end CDR; I always thought they were approximately equivalent.
Diminishing means "lesser". Return means "what you get". You are correct that the term has its roots in MMORPGs, but it is not in regards to "more statpoints to achieve another percent"; older MMOs had softcaps built in that made it so that above a certain statpoint, you literally got less per point out of it than below that statpoint. "What you get" when you stack CDR is more casts per hour; this does not diminish, it increases exponentially. There are no diminishing returns here unless you literally want to change the definition of the term. That would be ironic, wouldn't it?
CDR works a bit strangely really...If I remember right each piece of gear reduces the current cd by its listed %, compounding to create a total cdr%.
So the calculation looks like CD=CD*(1-CDR1)(1-CDR2)(1-CDR3) and so on.
What this means is that a single CDR rating of X % allows for 1/(1-X%) more uses of a skill, scaling asymptotically up to 100% which would give 0 cd and therefore infinite use (But no cdr is approaches that high, its usually 50% at most, and thats for single skills as a legendary affix, 10% is the highest general CDR rating)
However when compounding CDR ratings, each rating allows successively more uses creating an exponential scale, two separate 25% CDR boosts will reduce the CD to ~56% of what it was, allowing for 77% more use of the skill. This is consistent with math as each 25% CDR boost gives you 33% more use of the skill from the previous value, and 1.33^2 gives ~1.77.
So what the hell does this mean...
CDR scales differently when you are increasing a single rating (upgrading gear for instance) versus stacking different ratings across different pieces. These differences in scaling also make a smaller amount of higher CDR ratings more effective than a large amount of small CDR ratings (Using the former numbers as an example. 2 25% CDR boosts give 77% more uses, while a single 50% will give 100% more). However it still effectively stacks with itself, growing exponentially more powerful the more that is gathered.
The biggest reason people's dps begins to suffer after stacking so much CDR is because they have to give up other damage affixes that compound with so many other factors that they are more effective at their current levels than what the new CDR would give.
CDR does NOT suffer from diminishing returns, and it is NOT less effective. at 0% CDR you can cast 180 Serenities in an hour. At 10% CDR you can cast Serenity every 18 seconds, or 200 Serenities in an hour. At 19% (2x10%) CDR you can cast Serenity every 16.2 seconds, or 222 Serenities in an hour. At 27.1% (3x10%) you can cast Serenity every 14.58 seconds, or 247 Serenities in an hour. At 34.39% (4x10%) you can cast Serenity every 13.122 seconds, or 274 Serenities in an hour. Things continue at this rate, there is no diminishing returns from CDR; if anything, stacking more is worth MORE (20 more casts for first 10%, 22 for second 10%, 25 for third 10%, 27 for fourth 10%). PERIOD.
To go from 66.67% CDR to 70% CDR requires 10% more CDR. at 66.67 CDR you have a 6.67 second CD on Serenity, or 540 casts per hour. At 70% CDR you have a 6 second CD on Serenity, or 600 casts per hour. In other words, CDR is much more effective at high CDR than at low CDR (20 more casts per hour vs 60 more casts per hour).
interesting. need some more excel graphics and piecharts. fraggin love piecharts! =))
MeatHeadGaming - YouTube - Twitch - Facebook - Web
Who the hell thinks otherwise?
Hopefully I am not breaking any ToS here, I read the ToS and didn't see anything wrong with posting a link to a GoogleDrive spreadsheet--
https://docs.google.com/spreadsheets/d/15_h_IG5Uz2zNVPXIValODYhspmNKS2C7coD0phbv_Kk/edit#gid=0
Excel graphics!!
Also, to Autocthon--I see people post on a daily basis that CDR suffers from "Diminishing Returns" (check the Flow of Eternity thread for today's entry, for example). Making this post to show that they are mis-informed. To be honest, because I had never done the math via casts, I did not realize that high end CDR was better than low end CDR; I always thought they were approximately equivalent.
If you like math and graphs, then understand this: CDR is based on a logarithmic escale.
So the calculation looks like CD=CD*(1-CDR1)(1-CDR2)(1-CDR3) and so on.
What this means is that a single CDR rating of X % allows for 1/(1-X%) more uses of a skill, scaling asymptotically up to 100% which would give 0 cd and therefore infinite use (But no cdr is approaches that high, its usually 50% at most, and thats for single skills as a legendary affix, 10% is the highest general CDR rating)
However when compounding CDR ratings, each rating allows successively more uses creating an exponential scale, two separate 25% CDR boosts will reduce the CD to ~56% of what it was, allowing for 77% more use of the skill. This is consistent with math as each 25% CDR boost gives you 33% more use of the skill from the previous value, and 1.33^2 gives ~1.77.
So what the hell does this mean...
CDR scales differently when you are increasing a single rating (upgrading gear for instance) versus stacking different ratings across different pieces. These differences in scaling also make a smaller amount of higher CDR ratings more effective than a large amount of small CDR ratings (Using the former numbers as an example. 2 25% CDR boosts give 77% more uses, while a single 50% will give 100% more). However it still effectively stacks with itself, growing exponentially more powerful the more that is gathered.
The biggest reason people's dps begins to suffer after stacking so much CDR is because they have to give up other damage affixes that compound with so many other factors that they are more effective at their current levels than what the new CDR would give.