The strange interface damage procs
By
Ardrea,
Posted on: 2011-12-27 01:57 in Archetypes and Powers General Discussion
Quote:
I think you did your math almost perfectly correct. I produced this table:|
Originally Posted by UberGuy
Edit: If correct, and if I did my math right, that would mean you have the following odds of each number of damage ticks.
0 Ticks: 25% 1 Ticks: 18.75% 2 Ticks: 14.25% 3 Ticks: 10.547% 4 Ticks: 7.910% 5 Ticks: 23.730% It doesn't seem like that lines up with reported observations, since it makes five ticks the most likely outcome. |
Ends doing 0 ticks: 25.000% (0.25)
Ends after doing exactly 1 tick: 18.75% (0.75*0.25)
Ends after doing exactly 2 ticks: 14.0625 (0.75^2*0.25)
Ends after doing exactly 3 ticks: 10.54875 (0.75^3*0.25)
Ends after doing exactly 4 ticks: 7.9101563 (0.75^4*0.25)
Ends after doing exactly 5 ticks: 23.7304688 (0.75^5)
Which adds up to 100%, with roundoff.
Quote:
The trouble here is these are not the probabilities of that number of ticks -- they're the probabilities of that many ticks -or more-. The probability of -exactly- 4 ticks, for instance is the probability of four or more minus the probability of five or more -- 31.65-23.73 = 7.91%, which is Uberguy's probability for exactly four ticks.|
Originally Posted by Mistress Rue
This is what I come up with in determining the chance of a given number of ticks from a 75% proc:
0 Ticks: .25 = 25% 1 Ticks: .75 = 75% 2 Ticks: .75^2 = 56.25% 3 Ticks: .75^3 = 42.18% 4 Ticks: .75^4 = 31.65% 5 Ticks: .75^5 = 23.73% The largest difference of course being that the chance for 1 Tick doesn't need to be determined mathematically - that's already been given to us - 75% I haven't a clue how you got the above numbers - nor do I have a clue if my own are correct - could somebody page Arcanaville to set us all straight?  |
In the general case of probability p per tick and n ticks, you'd have p(n)=p^n-p^(n-1), for n>0, which simplifies to p(n)=p^n * (1-p), which is the formula Uberguy used. It's correct, and no other answer is correct unless it's answering a different question about the probabilities; e.g., what's the chance of getting n or more ticks, or the probability of getting n or fewer ticks.
The termination of the series is a special case of course, the value of p for n=6 and greater is zero; whereas it was a non-zero constant (0.75) for n from 1 to 5.
I think the main question is: does that math really model the way it's working? Is five ticks really the most common outcome? Based on pre-necro observations, it doesn't seem like it.
Blue
American Steele: 50 BS/Inv
Nightfall: 50 DDD
Sable Slayer: 50 DM/Rgn
Fortune's Shadow: 50 Dark/Psi
WinterStrike: 47 Ice/Dev
Quantum Well: 43 Inv/EM
Twilit Destiny: 43 MA/DA
Red
Shadowslip: 50 DDC
Final Rest: 50 MA/Rgn
Abyssal Frost: 50 Ice/Dark
Golden Ember: 50 SM/FA
If a "tick miss" terminates the chain, and there's a 25% of such a miss, we know there's a 25% chance that there's no ticks at all - that 's the odds that the very first tick "misses". The odds of getting exactly one tick "hit" is the odds of getting one tick followed by a miss, which is 75% (the odds of not missing on the first tick) times 25% (the odds of missing on the second tick) which is 18.75%. And so on.
Edit: A hint that you've got the numbers right is that all your probabilities have to add up to 100%. If they don't, you forgot one of the combinations (in which case it will be too small), or just calculated the odds of each incorrectly. Overshooting 100% is probably a clear sign the calculation is just plain in error.
On an unrelated note I tried to use reactive today to see how many ticks I get at min and max and something odd happened. It started to tick normal and after second tick it stopped for a few second (didn't count seconds but it was definitly longer than two or ticks usual activation) than a third tick happened and it stopped I am not sure if this was just a coincidence or not but I realised there were times when ticks of DoT started a little longer than usual or there were some blanks like one or two tick were missing and the visiual fire on mob was going on eventhough tick of damage was stoped but the visual usually kickis in when -res proc activated too so I am not sure if its an indicator or not.