... and in which I presented some calculations about enhancements; after getting feedback in that earlier thread I found out that I had made some errors in the calculations presented. The newly re-formulated calculations are given below, and I'm looking for feedback to verify that they're correct this time.
This will ultimately be part of a longer post about enhancements, the markets, and influence / infamy sinks, although this particular part of that longer post is quite narrow in its focus.
Thank you in advance for any feedback provided.
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I'll work with the defender version of the Empathy set power “healing aura” for the calculations that follow, with one arbitrary modification; I'll set the amount of healing done to 100 hit points, to make the following calculations a little easier. That means the base stats to work with become 100 points of healing, 2.03 seconds of activation (or casting) time, 13 endurance casting cost, and there's a base recharge time of 8 seconds listed in the “real numbers” provided in-game. Lets work with the assumption that a player uses set IOs to enhance healing aura to produce a 90% level of enhancement to healing power, endurance cost, and base recharge rate. How much do these enhancements to healing aura improve its performance?
Each enhanced attribute, by itself, is easy to calculate using a spreadsheet. Enhancing healing by 90% means that a base level of 100 hit points of healing becomes 190 hit points, for a 90% increase in healing power, per casting. The endurance cost falls to 6.84 endurance ( 13 / (1 + 0.9) = 6.84 ), for a 47% drop in endurance cost, per casting. The recharge time drops from 10.24 seconds to 6.45 seconds, leading to a 37% improvement in recharge time^.
^ The base recharge time is listed as 8 seconds in terms of “Real Numbers” (ie: in the game). But, powers don't start to recharge until their activation time has completed, and the activation time for healing aura is 2.03 seconds. There is also Arcanatime to factor into recharge times, as powers don't actually start to recharge immediately after their activation time completes; there is a small delay before a new action is begun, after a triggering event has occurred. Thus, the calculation used to generate the average recharge time for healing aura was as follows: 8 + ( [RoundUp(2.03 / 0.132) + 1] * 0.132 ) = 10.24 seconds. A similar calculation was used to determined the recharge time after healing aura has its recharge time enhanced by 90%.
The most valuable help provided by enhancements, of course, comes in how enhancements to individual power attributes work together. If you look at healing efficiency, measured as hit points of Healing Per Endurance point spent (HPE), with an unenhanced healing aura you spend 1 point of endurance for 7.69 points of healing, which translates into a HPE of 7.69 ( 100 / 13 = 7.69 ). If you slot healing aura as indicated earlier, you end up using 6.84 endurance to do 190 hit points of healing, for a HPE of 29.44 ( 190 / 6.84 = 29.44 ). In summary, the enhancement levels outlined earlier lead to healing aura being 3.83 times as endurance efficient for the amount of healing provided ( 29.44 / 7.69 = 3.83 ). If you care less about efficiency and more about the raw amount of healing that can be done during a single battle, then enhancements boost the amount of healing that can be done from 300 hit points in 32 seconds (with no enhancements)* to 760 hit points in 32 seconds (enhanced as described earlier); a well enhanced healing aura provides 2.53 times as much healing as the unenhanced power could provide in the same time frame ( 760 / 300 = 2.53 ).
* A 30 second time frame would reduce the “unenhanced” amount of healing to 200 hit points, which would compare even more unfavorably to the enhanced healing aura under discussion, as that would still come in at 760 hit points over 30 seconds, just as it does for 32 seconds.
Next, I'll use the calculations just done to provide an exact answer to the question “How much of the benefits available from using healing aura are due to enhancements, and how much are due to the base attributes of the power itself?” In the above example, the healing efficiency (HPE) of healing aura is 26% due to base power attributes and 74% due to enhancements ( 7.69 / 29.44 = .2613 and 1 - .2613 = .7387 ). Enhancement totals being used here ( 90/90/90 ) would account for 60.53% of the raw amount of 760 hit points of healing done over 32 seconds (( 760 – 300) / 760 = .6053 ), while the base power attributes would account for 39.47% of that same healing (( 300 / 760) = .3947 ).
The upshot? If you focus on examining healing efficiency (HPE), then enhancements account for about three quarters of the healing efficiency achieved. If you factor in the option to use healing aura substantially more often, one could quite reasonably argue that enhancements are much, much more important in determining the performance of healing aura than the base attributes of healing aura itself. Furthermore, it bears mentioning that the values used for calculations made earlier are not as high as they can be; enhancement values can actually be higher for characters using higher level set IOs, and players can do better than the 90/90/90 enhancement levels used for these calculations, through the use of set IO bonuses.
I'm following up on an earlier thread about enhancements, for which the link is given here:
http://boards.cityofheroes.com/showthread.php?t=221433
... and in which I presented some calculations about enhancements; after getting feedback in that earlier thread I found out that I had made some errors in the calculations presented. The newly re-formulated calculations are given below, and I'm looking for feedback to verify that they're correct this time.
This will ultimately be part of a longer post about enhancements, the markets, and influence / infamy sinks, although this particular part of that longer post is quite narrow in its focus.
Thank you in advance for any feedback provided.
------------------------------------------------
I'll work with the defender version of the Empathy set power “healing aura” for the calculations that follow, with one arbitrary modification; I'll set the amount of healing done to 100 hit points, to make the following calculations a little easier. That means the base stats to work with become 100 points of healing, 2.03 seconds of activation (or casting) time, 13 endurance casting cost, and there's a base recharge time of 8 seconds listed in the “real numbers” provided in-game. Lets work with the assumption that a player uses set IOs to enhance healing aura to produce a 90% level of enhancement to healing power, endurance cost, and base recharge rate. How much do these enhancements to healing aura improve its performance?
Each enhanced attribute, by itself, is easy to calculate using a spreadsheet. Enhancing healing by 90% means that a base level of 100 hit points of healing becomes 190 hit points, for a 90% increase in healing power, per casting. The endurance cost falls to 6.84 endurance ( 13 / (1 + 0.9) = 6.84 ), for a 47% drop in endurance cost, per casting. The recharge time drops from 10.24 seconds to 6.45 seconds, leading to a 37% improvement in recharge time^.
^ The base recharge time is listed as 8 seconds in terms of “Real Numbers” (ie: in the game). But, powers don't start to recharge until their activation time has completed, and the activation time for healing aura is 2.03 seconds. There is also Arcanatime to factor into recharge times, as powers don't actually start to recharge immediately after their activation time completes; there is a small delay before a new action is begun, after a triggering event has occurred. Thus, the calculation used to generate the average recharge time for healing aura was as follows: 8 + ( [RoundUp(2.03 / 0.132) + 1] * 0.132 ) = 10.24 seconds. A similar calculation was used to determined the recharge time after healing aura has its recharge time enhanced by 90%.
The most valuable help provided by enhancements, of course, comes in how enhancements to individual power attributes work together. If you look at healing efficiency, measured as hit points of Healing Per Endurance point spent (HPE), with an unenhanced healing aura you spend 1 point of endurance for 7.69 points of healing, which translates into a HPE of 7.69 ( 100 / 13 = 7.69 ). If you slot healing aura as indicated earlier, you end up using 6.84 endurance to do 190 hit points of healing, for a HPE of 29.44 ( 190 / 6.84 = 29.44 ). In summary, the enhancement levels outlined earlier lead to healing aura being 3.83 times as endurance efficient for the amount of healing provided ( 29.44 / 7.69 = 3.83 ). If you care less about efficiency and more about the raw amount of healing that can be done during a single battle, then enhancements boost the amount of healing that can be done from 300 hit points in 32 seconds (with no enhancements)* to 760 hit points in 32 seconds (enhanced as described earlier); a well enhanced healing aura provides 2.53 times as much healing as the unenhanced power could provide in the same time frame ( 760 / 300 = 2.53 ).
* A 30 second time frame would reduce the “unenhanced” amount of healing to 200 hit points, which would compare even more unfavorably to the enhanced healing aura under discussion, as that would still come in at 760 hit points over 30 seconds, just as it does for 32 seconds.
Next, I'll use the calculations just done to provide an exact answer to the question “How much of the benefits available from using healing aura are due to enhancements, and how much are due to the base attributes of the power itself?” In the above example, the healing efficiency (HPE) of healing aura is 26% due to base power attributes and 74% due to enhancements ( 7.69 / 29.44 = .2613 and 1 - .2613 = .7387 ). Enhancement totals being used here ( 90/90/90 ) would account for 60.53% of the raw amount of 760 hit points of healing done over 32 seconds (( 760 – 300) / 760 = .6053 ), while the base power attributes would account for 39.47% of that same healing (( 300 / 760) = .3947 ).
The upshot? If you focus on examining healing efficiency (HPE), then enhancements account for about three quarters of the healing efficiency achieved. If you factor in the option to use healing aura substantially more often, one could quite reasonably argue that enhancements are much, much more important in determining the performance of healing aura than the base attributes of healing aura itself. Furthermore, it bears mentioning that the values used for calculations made earlier are not as high as they can be; enhancement values can actually be higher for characters using higher level set IOs, and players can do better than the 90/90/90 enhancement levels used for these calculations, through the use of set IO bonuses.