Illusionary Dice MoI Area 11 Treasure Effect

When I first heard that the Maze of Illusion treasure was increase in attack speed, my first thought was, "oh really, again?" :P My second thought was that it was one of two possible effects:

1. DPS (damage per second) of the ranger would remain the same, but the hit rate increases. Exmaple: Without the treasure, if Ranger X's DPS is 10000 and he hits once every 5 seconds, then his damage per hit is 50000. Assume that with the treasure his hit rate doubles, then he would hit once every 2.5 seconds while his DPS remained the same, then each hit would cause only 25000 damage. This scenario causes no total damage gain, but has its perks as hitting more often can be advantageous. 
2. Damage-per-hit remains the same while the hit rate increases. Example: If without the treasure Ranger X's DPS was 10000, he hits once every 5 seconds, then his damage per hit is 50000. With the treasure, assume the treasure causes hit rate to double, then he is doing 50000 every 2.5 seconds. His new DPS would be 20000, effectively doubling it.

One way gives us just marginal benefits while the other gives us significant gains. So which way is it?

Our friends at LINE Rangers 台灣社團 has done the research for us! The text you find contained in the box below is an interpretation of their new article, Increased Attack Speed Treasure Comparison.

Article comes from: LINE Rangers 台灣社團
Author: 小為，黃郁弘
Research participants: 黃郁弘，小為，為執著，張家銘，黃名楊
Editor: 小為

Summary

LINE Rangers 台灣社團's testing has indicated that Maze of Illusion's treasure effect increases the rate of attack while preserving the amount of damage per hit. Each ranger's "attack" in the profile card represents its DPS (damage per second), and the damage per hit is derived from this number. The treasure preserves the ranger's damage per hit value according to its original DPS, but because the treasure causes an increase to the number of hits the ranger produces in a time period, it effectively is increasing its "true" DPS value. We can multiply the profile DPS value by the ranger's attack speed to find out how much the DPS has increased. For instance, Alice's profile lists her DPS as 53128. With 100% Illusionary Dice benefit, her DPS becomes 96693*.

* This value was obtained by using the attack speed value discovered via research method discussed below.

So how good is this treasure? Since this area is so tough, many players have had trouble getting it. Once you get to stage 129, you have a chance to unlock it 100%. Not to disappoint, the raid team has finally obtained 100% of the treasure and solved the mystery of its benefits.

The Method

The test method used recordings of the rangers attacking as researchers watched them in 10x slow motion to see the attack speed of each ranger. They recorded it many times and took averages of their observations so as to minimize error. Their original attack speed values were posted in their first article on the topic here, which I discussed on my blog here. Here is a sampling of their findings post-treasure (measured in time between hits):
  - Sol's speed is now 2.38 seconds, down from 4.33 s
  - Witch Cony's speed is now 1.47 seconds, down from 2.67 s
  - Alice's speed is now 2.55 seconds, down from 4.63 s
  - Opera James's speed is now 1.50 seconds, down from 2.73 s

Compare that to the original attack speed and you will see that obtaining 100% Illusionary Dice results in a 0.55 attack time reduction.

100% Illusionary Dice Attack Speed Coefficient

By battling a friend who does not have the Illusionary Dice treasure unlocked, the testers (who all obtained 100% of the treasure) saw that the Damage-Per-Hit value has not been changed, which is key to understanding how the treasure changes our ranger's damage.

Example: Level 70 Witch Cony

  - Without treasure, Witch Cony's damage-per-hit against the tower is 35648 

  - With 100% Illusionary Dice treasure, Witch Cony's damage-per-hit against tower is still 35648

From this, we can deduce that the treasure does not affect base damage values. Witch Cony's original no-treasure attack speed is one hit every 2.67 seconds while with 100% treasure, she hits once every 1.47 seconds. Since the treasure increases attack speed while preserving her damage-per-hit value, it means that her true DPS value has been increased. Based on damage-per-hit:

  2.67 sec/1.47 sec = approximately 1.82 times

...which means that if you take her profile DPS and multiply it by 1.82, you will get her new DPS. The treasure increases DPS by 1.82 times. 

Other rangers' attack speed changes also reflect the 1.82 coefficient:

  Sol 4.33/2.38 ~ 1.82

  Witch Cony 2.67/1.47 ~ 1.82

  Alice 4.63/2.55 ~ 1.82

  Opera James 2.73/1.50 ~ 1.82

This is how we arrived at the previous example with Alice: 

   53128 (original listed DPS) * 1.82 = 96693

Afterword

Line Ranger stages 109 - 120 of the Skyscraper area originally released with the treasure "increase attack speed" but because they reduced the damage at the same time, they finally changed the treasure altogether to something else, increase attack range. The present treasure for Maze of Illusion carries the same description as the old treasure, but it is vastly different and very beneficial to players. Once you obtain 100% of the Illusionary Dice, go back to Skyscraper and you will realize just how much easier the area becomes with the treasure effect. 

But the treasure effect is not just a DPS increase. It has substantially decreased the amount of time it takes for previously "slow/very slow" attack speed rangers to produce one hit. For instance, before the treasure, there was a very good chance that Sol would be knocked back or totally killed before landing even 1 hit of his red bomb. But now his hits are only 2.38 seconds apart (down from 4.33 seconds), so one quick burp and the enemy loses 250k! 

Conclusion

Long story short, the new treasure is the second scenario that I posed at the start, the effective DPS is increased by a factor of 1.82. 

Regarding Castle in the Sky

What about the 1.4545 multiplier from the Castle in the Sky treasure? Where does it fit in? 

Rest assured, the Castle in the Sky treasure is still in effect and it is still a factor in our rangers' damage-per-hit. The new attack speed is simply doing that amount of damage-per-hit more often.

The calculation of our rangers' damage is getting more and more convoluted as they add more treasure effects and multipliers. And it's getting all the more challenging to backtrack because they took away the enemy tower HP values that we used to measure against >:O It's all bit mind boggling, but we're getting more powerful all the same so I can't complain! 

Thanks again to the gurus at LINE Rangers 台灣社團. They work tirelessly to find out all this cool information.