The Last 5% of CDR is More Significant Than the First 10%

  • The last 5% of CDR is more significant than the first 10%

    Maths:
    Quote:
    <table cellpadding="6" cellspacing="0" border="0" width="100%"> <tr> <td class="alt2" style="border:1px inset; padding:10px;"> Take spell A with a base cooldown of 1 second. With 0% CDR, spell A can be cast 1 time per second, giving us 1 Cast / 1 second (1 CpS).
    With 5% CDR, Spell A cooldown becomes .95 seconds, giving us 1 Cast / .95 seconds (1.0526 CpS), an increase of roughly 5.26%

    The next 5% CDR makes Spell A cooldown become .9 seconds, giving us 1 Cast / .9 seconds, (1.1... CpS), an increase of roughly 5.85%

    Continuing with increments of 5% CDR, we get the following results.
    CDR | Cooldown | CpS | CpS Gained | % Increased | increased in %
    0.00% | 1.00 | 1.0000 | 0.00 | 0.00% |0.00%
    5.00% | 0.95 | 1.0526 | 1.05 | 5.26% |5.26%
    10.00% | 0.90 | 1.1111 | 0.06 | 11.11% |5.85%
    15.00% | 0.85 | 1.1765 | 0.07 | 17.65% |6.54%
    20.00% | 0.80 | 1.2500 | 0.07 | 25.00% |7.35%
    25.00% | 0.75 | 1.3333 | 0.08 | 33.33% |8.33%
    30.00% | 0.70 | 1.4286 | 0.10 | 42.86% |9.52%
    35.00% | 0.65 | 1.5385 | 0.11 | 53.85% |10.99%
    40.00% | 0.60 | 1.6667 | 0.13 | 66.67% |12.82%

    </td></tr></table>
    As we can see, going from 0-10% CDR yields about an 11.11% increase in CpS, while going from 35-40% gives us about 12.82% increase in CpS.


    Just thought people ought to know, I found it to be very useful information when trying to itemize certain champions.
  • Quote:
    <table cellpadding="6" cellspacing="0" border="0" width="100%"> <tr> <td class="alt2" style="border:1px inset; padding:10px;">
    Originally Posted by WonderBoy55 View Post
    I see what you mean, but using the flat values yields the following:

    From 0-10% you go from 1 CpS to 1.1111 CpS, a difference of .1111
    From 35-40% you go from 1.5385 to 1.6667 CpS, a difference of .1282

    I believe using these calculations, the statement in the title is still justified, as .1282 > .1111
    </td></tr></table>
    Using these calculations, I could justify that a pickaxe at 300 AD is more significant than a longsword at 50 AD because 25 > 10. The problem is that this lacks context and few people would actually argue that that pickaxe at 40 minutes is as significant as that longsword at 0 minutes. Taking a proportional approach lets you put the numbers in context and see that while 25 > 10, a 20% increase in damage output is more meaningful than an 8.33% increase in damage output.
  • Quote:
    <table cellpadding="6" cellspacing="0" border="0" width="100%"> <tr> <td class="alt2" style="border:1px inset; padding:10px;">
    Originally Posted by WonderBoy55 View Post
    The last 5% of CDR is more significant than the first 10%

    Maths:


    As we can see, going from 0-10% CDR yields about an 11.11% increase in CpS, while going from 35-40% gives us about 12.82% increase in CpS.


    Just thought people ought to know, I found it to be very useful information when trying to itemize certain champions.
    </td></tr></table>
    Looking at the additive increase in Casts per Second is actually a bit misleading here. When you go from 0% CDR to 10% CDR, you're going from 1.0 CpS to 1.1111 CpS, which represents an 11.11% increase to your spell casts, you got this part right. However, when you're going from 35% CDR to 40% CDR, you're going from 1.5385 CpS to 1.6666 CpS, which represents an 8.33% increase to your spell casts. So while your point that latter points in CDR are more valuable than early points in CDR is totally true, your thread title is actually wrong because you're comparing 1.1111 - 1 to 1.6666 - 1.5385 instead of 1.1111/1 to 1.6666/1.5385.
  • Quote:
    <table cellpadding="6" cellspacing="0" border="0" width="100%"> <tr> <td class="alt2" style="border:1px inset; padding:10px;">
    Originally Posted by WonderBoy55 View Post
    Ah, I see what you mean, and thank you for the response. But aren't proportional differences and flat differences just two different ways of comparing two numbers?
    </td></tr></table>
    Additive differences lack context and therefore tend to have less meaning than proportional differences.

    Quote:
    <table cellpadding="6" cellspacing="0" border="0" width="100%"> <tr> <td class="alt2" style="border:1px inset; padding:10px;">
    Originally Posted by WonderBoy55 View Post
    From either calculation you can still justify an increasing rate of change in CpS as you get more CDR. By showing the % more CpS you get at a certain amount of CDR from the base amount, you can see the growing significance of each point of CDR. By measuring the difference at points 0 and 10% then comparing to the difference between points 35% and 40%, we can justify the title of the thread. If we compared it proportional to the last step, we see a ratio of 1.0526 from 0-10% and a ratio of 1.0833 from 35-40%
    </td></tr></table>
    You're using 0-5% here, not 0-10%. 0-10% is a 1.1111 ratio.

    Quote:
    <table cellpadding="6" cellspacing="0" border="0" width="100%"> <tr> <td class="alt2" style="border:1px inset; padding:10px;">
    Originally Posted by WonderBoy55 View Post
    This doesn't apply to my comparison since it's using a different mathematical approach, but it still demonstrates the point that the more CDR you get, the "better" or more significant each point becomes.
    </td></tr></table>
    I'm not debating that the more CDR you have, the better each point is, that's objectively true, I'm just saying that the last 5% aren't better than the first 10%. The last 5% are better than the first 7%, but not as good as the first 8%.


    Quote:
    <table cellpadding="6" cellspacing="0" border="0" width="100%"> <tr> <td class="alt2" style="border:1px inset; padding:10px;">
    Originally Posted by ZedekiahCromwell View Post
    Hmmm. My TF build has recently been maxing at 39.00%. 35% from items+E and then 4% from the mastery.

    Should I swap out a MR glyph for a flat/scaling cooldown reduction glyph? It would seem to me that the 0.9% cooldown would probably be more worth it with this kind of scaling.
    </td></tr></table>
    The last point is pretty good and I'd advocate getting that last 1% through flat CDR Glyphs if that's your set build. I have several pages that run 2 flat CDR glyphs to get either 5% or 10% from pre-game setup so that my builds will put me at the full 40% CDR rather than falling short.