Druid Amping at High Speed

Someone had a question about the last bit of my post yesterday: where did you get the numbers for the boost to damage that a Druid gets when hitting at maximum speed?  This is fairly easily computed, but it relies on information about the game that not everyone knows.  So I thought I'd show the work.

Druid's boosts per proc at various skill levels can be seen in game (look in the Hero Compendium) or at the wiki.  That's the easy part.  The harder part is understanding how speed boosts work in conjunction with energy and the proc system.

Heroes accumulate 15 energy per hit.  Thus, absent any outside energy source, and assuming that they are immobile hitting as often as they can, heroes proc every 7 hits  (7*15 = 105, 105>100 and extra energy is discarded).  Castle Clash has quantized time steps of 200ms.  7 hits at max speed is thus 1.4 seconds.

The stack of procs that a hero can create is a function of his proc's duration and his skill cooldown.  Most heroes have a cooldown that is longer than their proc's duration.  So they don't stack at all.  Druid, however, has no cooldown.  His proc lasts 5 seconds.  1.4 divides 5 into 3 plus a remainder of .8 seconds; that .8 second is 8/14 of the 1.4 seconds between procs.  Thus, we find that Druid will stack 3 times about 43% of the time (.43 = 6/14), and he will stack 4 times about 57% of the time (.57 = 8/14).

To compute the average boost we get from Druid, therefore, we need to average the effects of a stack of three of his boosts and a stack of four of his boosts.  (To be more precise, we don't literally average them but compute a weighted average with ~.43 weight on 3 stacks, and ~.57 on 4 stacks.)

Here's a table showing the net damage boost Druid gets at maximum speed.  The "Weighted Average" column is the multiplier.  For example, my Druid has skill 7, so once spooled up he creates a team multiplier of 2.5.

Druid Attack Boost, Max Speed

In practice, if you have a Valentina and/or Cupid you will do somewhat better than the attack boost computed above, since your Druid will proc somewhat more often.  Druid by himself generates 375 energy over 5 seconds.  Cupid (skill 9) adds 0 to 55 to that, every 6 seconds; so Druid should be getting closer to 4 procs continually.