Handle Atlatl / Full Eclipse set burn effect

[Cheeseyx]

What feature would you like to see?

I'd like if burn damage from the full eclipse moon set + atlatl was included in the dps displayed. It's a little more complicated than other dps, but still very reasonable to account for:

• The effect on Average hit can be approximated as +2 * accuracy
• The effect on DPS can be approximated as +10/9 * accuracy dps, while at 3t attack speed
• The damage "lost" due to burn stacks that don't go off before the enemy dies averages to 14.666 * accuracy at 3t attack speed (against enemies that survive at least 40 ticks/24s), so TTK estimates can fudge the enemy HP up by this amount to account for the DPS loss towards the end of the kill. (Or ignore it, like with ruby bolts)

I don't have any perfect answer to accounting for the few enemies that interact strangely with burn damage (some fully immune like Zuk, some that become periodically immune to damage like Zulrah or Hespori, some that cleanse burn/status effects like I think Vorkath does). But, the vast majority of enemies don't cause issues, and it'd be nice if the DPS could be properly displayed against the 95% of foes for which it's not that complicated.

Evidence

• Each successful hit has a 20% chance to deal 10 damage via burn, which provides an expected value of +2 * accuracy per hit (towards the expected hit), and +2 * accuracy / 1.8 = accuracy * 10/9 dps at a 3t attack speed
• For "lost" burn damage: If you could attack every tick with 100% accuracy and 100% proc chance, you would miss out on 220 theoretical burn damage over those last 40 ticks. Since you instead attack every 3t, with a 1/5 proc chance, the expected "lost" damage is 14.666 * accuracy.
• Technically, all burn damage estimates should also account for a "discarded proc factor" since any burn beyond the 5th stack will be discarded. This is effectively a reduction on the 20% * accuracy proc chance by whatever the chance is that the previous 12 attacks had at least 5 burn procs, which fluctuates pretty significantly by accuracy
  • At 100% accuracy, my estimate is that this would be at most a 7.25% decrease in the on-paper damage (20% burn chance per hit -> 18.55%, 0.08 dps loss), but should be less severe than that. At 66% accuracy, it should be at most a 1.5% decrease in damage (20% -> 19.7%, 0.01dps loss). Not fully negligible, but a very very small factor given how much complexity it adds to the math

[Cheeseyx]

Out of curiosity I did some simulations, to get a rough estimate in how often burn procs are cancelled due to already having 5 active stacks (since calculating an exact formula for that is extremely difficult). Here's the data I got of efficiency (successful burn procs vs ideal (20% * accuracy), with n=10,000,000 simulations and going out to 150 attacks

• 100% accuracy: 95.6682% efficiency
• 90% accuracy: 96.9694%
• 80% accuracy: 98.0033%
• 70% accuracy: 98.7807%
• 60% accuracy: 99.3283%
• 50% accuracy: 99.6803%

I tracked the per-attack proc chance too, to see how quickly it flattened out, and it seemed to hit the overall average after around 15-20 attacks - which makes sense to me, given that each burn stack ends after ~13 attacks.

FWIW I also threw these rates into wolphram alpha to get a fit:
0.0216434 x^4 - 0.11126 x^3 + 0.056392 x^2 - 0.0107511 x + 1.00064 (quartic)
-0.0636441 x^3 + 0.0215462 x^2 - 0.00122803 x + 0.999897 (cubic)

[jmyaeger]

While the lack of an analytical solution for the effect of the 5-burn cap is definitely part of the reason it hasn't been implemented in the calc, the main thing is that it's not currently feasible to include in TTK calcs given the enormous expansion to the state space it incurs. The wiki calc has in general tried to avoid situations where an effect is only partially implemented and/or approximated, which is why things like the 10/9 * accuracy DPS approximation haven't made it into the calc despite having been known for a long time.

Since you mentioned it, ruby bolts are a bit of a different situation because they actually are calculated correctly in the TTK distribution plot, and it's not an approximation in that case. That calculation just isn't used in the results table/loadout comparison plots at the moment due to performance concerns, since the TTK distribution function is much more expensive than the normal TTK function (so things can go awry when you, say, generate a TTK vs. ranged level plot against Nex).

I'll add that I'd love to see burn in the calc and have spent a decent amount of time trying to come up with an exact rather than approximate burn DPS expression. But unless the main devs have changed their minds recently, I wouldn't expect an approximation that doesn't solve the TTK problem to be accepted.