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Discussion of Effectiveness

It would be useful to document the actual effectiveness of this flask, as that is not immediately obvious. A mod may consider adding the discussion or parts of it to the main page.

Let us call the total crit chance (including gear, charges, etc.) the crit chance, and the crit chance obtained by drinking the flask, the lucky crit chance.

The lucky crit chance is mathematically described as: lucky = 1 - (1 - crit)2 or 2crit - crit2. It is useful to analyze the lucky crit chance in terms of relative and absolute difference to the original crit chance.

Relative Increase

Relative increase = (lucky-crit)/crit = 1 - crit

In other words, the distance of crit chance to 100% is the effective multiplier you are getting through the diamond flask. E.g. with 70% crit chance, the flask will give you a 30% increase (just like a 30% more critical strike chance modifier would), for a total of 91% lucky crit chance.

But this is misleading for small numbers: if you have a 10% crit chance, a 90% increase will mean only 19% lucky crit chance, which -- while almost doubled -- is generally too low for critting.

Absolute Increase

Absolute Increase = lucky-crit = crit - crit^2

This gives us an overview of the largest absolute effect of the flask, depending on our crit chance (see the graph at google). Immediate observation indicates that the flask is the most effective when our crit chance is exactly 50% (lucky crit chance is then 75%). The absolute increase in total crit chance is symmetrical on both sides of the curve and approaches zero the closer you get to 0 or 100% crit chance.

Cut-off crit chance for diamond flask

What is a meaningful cut-off for crit chance when using the diamond flask? Obviously, yielding a lucky crit chance beyond 95% is meaningless so this should always be taken into account. In practice, the decision also depends on how useful another flask would be in place of the diamond flask.

To calculate the crit chance based on desired lucky crit chance: crit = 1 - sqrt(1-lucky). For 95% lucky, crit needs to be ~ 77.6%, and for 90% lucky, crit needs to be ~ 68%. See also the graph at google (inverse of the Absolute Increase formula).

Another decision could be to consider the flask only if it has the effect of at least X% more critical strike chance, which is to have crit at most 100% - X% (inverse of the Relative Increase formula). E.g. for the flask to have at least 30% more critical strike chance effectiveness, crit may at most be 70%.

--Irfy (talk) 16:49, 2 December 2016 (UTC)

The cut-off equation seems to be the most interesting one of these. The absolute increase can be explained easier by looking at the graph on the lucky page in my opinion. --Illviljan (talk) 17:36, 2 December 2016 (UTC)
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