#531
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At 170 Dex you get 1.5 PPM. At 47 delay, that means a swing every 4.7 seconds, or 12.76 swings/minute. At 1.5 PPM, that's 1.5 procs per 12.76 swings, or a proc rate of 11.75% for each swing. I know very little about both weapon delay and proc calculations, so please correct me if I'm wrong here.
JBB has an 8 second cast, and with 132 seconds per fight, that's 16 casts. Let's assume you take a swing before first cast, and lets say you have excellent reflexes, and click JBB almost simultaneously with swinging. Note I see you've fiddled some more with the numbers since I did this calculation; I can update it if you'd like. Let t=0 be when the mob has been pulled, slowed, and first engaged in melee. A proc here will last 132 seconds, or 22 ticks. A proc here will do 40 + 24 * 22 or 568 damage. At t=8, second chance to proc. There's (132 - 8) / 6 = 20 (rounded down) ticks left. If there's been no prior proc, a proc is worth 40 + 24 * 20 = 520. If there's a prior proc, only the DD component counts: 40 damage. So we can build a table: Now, what are the probabilities of each possible outcome? At t=0, it's simple: there's a 11.75% chance of a proc. At t=8, the chance of a proc is 11.75%. There's a 11.75% chance there was a proc at t=0, and an 88.25% chance there was no prior proc. At t=16, we get to the real meat of the problem. To calculate the chance of a prior proc, there's an 11.75% chance of a proc at t=0, and a 11.75% chance of a proc at t=8, but these are independent possibilities. 1) The chance of a proc at 0 and 8 is 11.75 * 11.75. 2) The chance of a proc at 0 and not 8 is 11.75 * 88.25. 3) The chance of no proc at 0 and a proc at 8 is 88.25 * 11.75 4) The chance of no proc at 0 and no proc at 8 is 88.25 * 88.25 This is a classic binomial distribution. You can also think of this as flipping a coin every 8 seconds, where the chance of heads is 11.75% and the chance of tails is 88.25%. The relevant formula is the probability mass function: https://en.wikipedia.org/wiki/Binomi...on#Definitions The vertical (n k) notation is spoken as "n choose k" or sometimes written as nCk and described in more detail here: https://en.wikipedia.org/wiki/Binomial_coefficient To apply this to our problem, we can use this formula to calculate the probability of no prior proc, i.e. setting k=0 (n choose 0) * p^0 * (1-p)^(n-0) (n choose 0) is always 1, so this simplifies to (1 - p)^n So at each 8 second interval (the variable n), the damage of a proc will be 44 * (1 - (1 - p)^n) + (44 + 24 * (132 - 8*n) / 6) * (1 - p)^n p is the chance of a proc, or 0.1175 Over a 132 second fight, there's 16 casts, so we need to sum this over n = 0 to 15 inclusive. Let's implement this in Python; perhaps that will be easier to follow: Code:
p = 0.1175 def no_prior(n, fight_length = 132): """" 44 dd plus 24 per tick remaining in the fight """ from math import floor ticks_remaining = floor((fight_length - 8 * n) / 6) return 44 + 24 * ticks_remaining def prior(n): """" if there's been a prior proc, only the dd matters """ return 44 expected_damage = 0 for n in range(0, 16): prior_probability = pow(1 - p, n) expected_damage_this_interval = prior(n) * prior_probability + no_prior(n) * (1 - prior_probability) expected_damage += expected_damage_this_interval print(expected_damage) | ||
#532
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I am right. EVERYBODY ELSE IS WRONG.
Especially at math, but especially at math. | ||
#533
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The reason why people can use "PPM" as a metric is because when you have 1 PPM, you get 1 proc per minute on average. It's really that simple. You wouldn't be able to say that if the average never came out to be 1 proc per minute.
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Shamwowi Wipesalot (60 SHM) | Bazgek Bonebreaker (60 SK) | Sznake Pliszken (52 MNK) | Laanfear (30 ENC)
Do you have questions about Shaman races? Read my guide: https://wiki.project1999.com/Shamwow...man_Race_Guide Want to see Shaman videos? Check out my youtube channel: https://www.youtube.com/channel/UCFU...zEFJVBIH3-jUog | |||
Last edited by DeathsSilkyMist; 01-29-2024 at 04:15 PM..
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#534
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Do we need to go through this more slowly? | |||
#535
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The assumption that this mob will do 10dps to you swinging a 2handed weapon instead of wearing a shield is also a farce. You will take more damage without the shield ac. You will also have to deal with some degree of ripostes.
I bet the JBB shaman would likely fair better by just equipping a shield and not trying to land 2hb procs to begin with. However much damage you think you’ll be taking … you’ll be taking more if you equip that hammer.
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#536
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This is great. I dont actually know the answer. But I have clues.
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#537
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#538
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Let me go a bit more slowly for you. In our example, you basically get 6 swings per minute with a 1/12 chance of proccing. It is like rolling a D12 six times in a row, hoping to get a specific number. Let's say a "success" is rolling twelve. Since the fight lasts 2 minutes, that means we get twelve chances to roll a d12. We are not looking for a set of numbers to roll in a sequence (what are the odds of rolling a 6 and then a 3). This means each dice roll has a 1/12 chance of succeeding equally. Worst case is you roll the twelve after 12 dice rolls. Best case is you roll the twelve on the first attempt. 1 roll + 12 rolls / 2 = 6.5 rolls on average to get your number. So on average you will proc it roughly half way through the fight.
__________________
Shamwowi Wipesalot (60 SHM) | Bazgek Bonebreaker (60 SK) | Sznake Pliszken (52 MNK) | Laanfear (30 ENC)
Do you have questions about Shaman races? Read my guide: https://wiki.project1999.com/Shamwow...man_Race_Guide Want to see Shaman videos? Check out my youtube channel: https://www.youtube.com/channel/UCFU...zEFJVBIH3-jUog | |||
Last edited by DeathsSilkyMist; 01-29-2024 at 04:26 PM..
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#540
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Look man he already spelled it out for you very comprehensively:
https://www.project1999.com/forums/s...&postcount=531 It is absolutely ok to admit it went over your head. I imagine that level of math would go over most college educated adults heads. There is no shame in that. I’ve got a doctorate and it have me a slight headache trying to follow him. But he is correct. You aren’t going to win a math fight with a senior engineer bro
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