Calculations for refresh duration chance (e.g. Refresh Ignite)

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What platform are you running Path of Building on?

Linux - PoB Frontend

Is your feature request related to a problem?

Currently the chance to refresh ignite duration mods are not supported by PoB.

Describe the solution you'd like

Ailment duration refresh, such as the Mastery "50% chance to refresh ignite duration on critical strike" will on average result in an extended duration of the ailment, based on the chance to proc. From my testing, it can be calculated as follows:

Given:
D = base duration of the ailment (including all increases/decreases, faster/slower mods, etc.)
t = attack/cast time of the critting hit
p = probability that a refresh will occur (e.g. 50% refresh chance * crit chance * hit chance)
q = 1 - p
n = the number of hits during the ailment's base lifetime

n = \lfloor D / t \rfloor

Then the expected total duration is:

t \cdot \frac{1 - q^{n}}{p \, q^{n}} + (D - n \,  t)

This looks at the number of hits it would take for n attempts to refresh to fail in a row, and then basing the average on how long it will take for that to happen.

Describe alternatives you've considered

No response

Additional context

As an example of the impact of this, suppose you have:
D = 4 seconds (ignite duration)
t = 0.45 seconds (cast time)
p = 0.1 (50% of a 0.2 crit chance)

With this function it would mean that, on average, the time an individual instance of ignite would last is ~6.35s. This final value would then be used to impact certain other calculations, such as the number of ailment stacks.

Note that this does not handle the special case where p -> 1. If it's guaranteed to refresh the duration (or close to it), the duration is in essence infinite. I don't know what impact that would have on other calculations. There may be the need for an alternative metric to be used, such as the expected lifespan of the entity that is ignited.

L’issue non indica file, test o punti di ingresso. Inizia esaminando la formula proposta per la durata attesa e la sua limitazione quando p→1, quindi determina in che modo la probabilità di refresh e gli stack di ailment dovrebbero influire sugli altri calcoli. Il lavoro è completato quando gli effetti della durata del refresh sono supportati e il caso di refresh garantito ha un comportamento definito.