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How do +X% chance to reflect at Y% Weapon DPS enchantments add?

Example:

Base: x% chance to reflect at y% weapon dps
Add: w% chance to reflect at z% weapon dps

Result = ??

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1 Answer 1

up vote 2 down vote accepted

According to this runic forums post, each chance to reflect source is considered independently, like consecutive independent dice rolls or coin flips.

A simple test

Here is an example from a low level character using numbers displayed in the Arcane Statistics pane by the game itself.

Without gear, the character has 0% chance to reflect. I have a shield that has innate 30% chance to reflect at 50% weapon DPS and an enchant that has 6% chance to reflect, also at 50% weapon DPS. When that shield is equipped, the Arcane stats show 34.2% chance to reflect at 52.6% weapon DPS.

Based on the above information, here is my best guess as to where those numbers come from.

Combined chance to reflect

Assuming the 30% and the 6% reflect are independent events, then the chance that both of them fail is (100 - 30)% * (100 - 6)%, which makes a 65.8% chance to not reflect. In other words, that is a 100 - 65.8 or 34.2% chance to reflect. The number matches the in-game number.

Combined reflect DPS %

This appears to be simply a weighted average. With only two reflect events, it's possible to illustrate with a simple 2D diagram:

 DPS reflected |    30% reflected    |  70% not reflected
---------------+---------------------+---------------------
      6%       |  50% DPS + 50% DPS  |
   reflected   |     = 100% DPS      |       50% DPS
---------------+---------------------+---------------------
     94%       |                     |..... no reflect ....
 not reflected |      50% DPS        |....... 0% DPS ......

The weighted average of the reflected dps, ignoring the chance to not reflect anything, is (30% * 50% + 6% * 50%) / (1 - 70% * 94%) = 52.6%. This number also matches.

The above example was done with only 2 reflect chance sources, but it can be extended to multiple sources. The fact that the numbers match what is seen in game seems to suggest the "independent event" model is the correct one.

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It would seem likely, but there doesn't seem to be a confirmation from a developer, or actual tests shown, unfortunately –  Gnoupi Jan 25 '13 at 10:53
    
Interesting. I do hope it's calculated this way, as it means you have the chance for compound reflects. I'm planning on gemming out a bunch (maybe 8 or 10) gems for 7% missile reflect 50% dps each, that would mean that I would have a (albeit small) chance of reflecting for 150% or 200% dps. Even as much as 500% in very rare cases. While this might seem slim, when you have multiple machine gun bots firing at you, the chance to reflect adds up very quickly, to where they should start blowing up without me going near them. Steam username elektrohawk level 100 berserker –  user54903 Sep 7 '13 at 1:38
    
Yes, that does seem to suggest that you can get very high reflect damage if you get lucky and all of your reflect sources do indeed reflect. Berserker has the best reflect skill in the game (ice shield?), which goes up to 100% chance to reflect, so using reflect as a damage source may work. It would be too risky to try on anyone else though, I think. –  jw013 Sep 7 '13 at 23:06
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