# Thread: 20 hits, 20 crits

1. ## 20 hits, 20 crits

I was doing an MSV LFR today, the part at the beginning with the big dog pull. I used arcane explosion, and got the message on my MSBT - 20 hits, 20 crits. What exactly is the chance of this happening?

My crit was around ~20% for simplicity's sake.

would it really be (1/5)^20 like I am thinking?

What i mean is that there were 20 dogs, and i crit all of them. I got 20 total crits.

2. Originally Posted by Yertillon
I was doing an MSV LFR today, the part at the beginning with the big dog pull. I used arcane explosion, and got the message on my MSBT - 20 hits, 20 crits. What exactly is the chance of this happening?

My crit was around ~20% for simplicity's sake.

would it really be (1/5)^20 like I am thinking?
More like
(1/5)^20*(4/5)^20
your scenario is 100% crits on 20 attacks
not 50% on 40 hits.

Maybe you even need to take a combination of possible outcomes...
Probability theory has been a while... lemme check

Ok, say you do 2 hits.
You either have:
Hit crit = 80%*20% = 16%
crit hit = 20%*80% = 16%
hit hit = 80%*80% = 64%
crit crit = 20%*20% = 4%
All of these combined 16+16+64+4=100 So these 4 options are the only four that can occur.

So the chance of having 1 crit and a hit is 16%+16%=32%
This means we have to multiply our original chance by the possible ways we can write 20 hits and 20 crits after one another.
Which can be calculated by a derivation of Newton's Binomial theorem, the multinomial theorem.

If we have 2 possible outcomes, and they both manifest 20 times.
Our equation becomes 40!/(20!*20!).
Which gives us a total of (1/5)^20*(4/5)^20*40!/(20!*20!).

Looking for my calculator... back in a sec

This gives me rougly 0.00167% chance of that happening.

If you want to create some more events, just change the formula to your needs.
Say you do 1 crit and 39 hits.

(0.2)^1*^(0.5)^39*40!/(39!*1!)=0.133%

The more acceptable form would be 20% crits and 80% hits this would give us:

(0.2)^8*(0.8)^32*40!/(32!*8!)=16%

These numbers may seem low but this is just the 1 case scenario that you do these exact amount of crits, normally you would take an event in which you crit 6-10 times (with 20% crit chance) thus increasing your pool of possible outcomes. These chances should then be added, not multiplied, giving a higher chance (a more natural chance).

/Endofmathrant
sorry for the long post, i get carried away sometimes.

3. Before you go any further, what i mean is that there were 20 dogs, and i got 20 crits. sorry for the confusion.

4. To add some more graphical terms:

This is the pure definition

With p=0.2, n=40, and k=20.

And to clarify:

which is the 40!/(20!*20!) in our equation.

- - - Updated - - -

Originally Posted by Yertillon
Before you go any further, what i mean is that there were 20 dogs, and i got 20 crits. sorry for the confusion.
Hitting 20 dogs 1 time, is the same as hitting 1 dog 20 times. It's just the way you look at the actual problem.
Nvm thats stupid.
You mean you hit 20 dogs twice right?
Because that might make it a bit more complicated.

5. Originally Posted by CenariusTheForestLord

Hitting 20 dogs 1 time, is the same as hitting 1 dog 20 times. It's just the way you look at the actual problem.
Nvm thats stupid.
You mean you hit 20 dogs twice right?
Because that might make it a bit more complicated.
I hit all 20 dogs with one arcane explosion, and it crit on every one of them. So 20 total crits.

So it would be the same as hitting one dog 20 seperate times, and having it crit each time? which is (1/5)^20 chance of that happening with 20% crit right?

6. Originally Posted by Yertillon
I was doing an MSV LFR today, the part at the beginning with the big dog pull. I used arcane explosion, and got the message on my MSBT - 20 hits, 20 crits. What exactly is the chance of this happening?

My crit was around ~20% for simplicity's sake.

would it really be (1/5)^20 like I am thinking?

What i mean is that there were 20 dogs, and i crit all of them. I got 20 total crits.
UVLS blah blah blah

7. Originally Posted by Normie
UVLS blah blah blah
I dont have that, here is my mage:

8. What i mean is if you hit each dog twice, you could either have:
Crit every dog once, hit once
crit some dogs once, some twice and some never.
This might make the computation larger because the definition doesn't hold up in more than one event.
These are 20 events combined.

9. Ahh alright, well nah it was just one cast of the attack, not 2.

10. Originally Posted by Yertillon
Ahh alright, well nah it was just one cast of the attack, not 2.
aha i was under the assumption you did 20 hits 20 crits, in total 40 attacks.
Didn't know you labeled attacks as hits sorry.
That makes the equation very simple indeed and of course what you wrote at the beginning holds up.

0.2^20*0.8^0*20!/(20!*0!)=0.2^20*1*1=0.2^20=1*10^-12%

Damn all that mathwork for nothing

11. Originally Posted by CenariusTheForestLord
aha i was under the assumption you did 20 hits 20 crits, in total 40 attacks.
Didn't know you labeled attacks as hits sorry.
That makes the equation very simple indeed and of course what you wrote at the beginning holds up.

0.2^20*0.8^0*20!/(20!*0!)=0.2^20*1*1=0.2^20=1*10^-12%
It's alright, I could have worded it better. :P that is really just insane though. I don't think I'll ever have that kind of "luck" again.

12. Or were they all frost novaed?

13. Originally Posted by Yertillon
It's alright, I could have worded it better. :P that is really just insane though. I don't think I'll ever have that kind of "luck" again.
Yes, that is some chance
Glad to have been able to share some probability theory with you though.
Have a nice night.

14. Yes thank you for the wise words, cenarius! I appreciate it, good night!

Mormo they might have been, although I know I didn't do it so another Mage would have had to do it the split second before I AE'd. Before they all broke by damage. It might've happened but I'm not sure

15. If the dogs had been frozen the numbers would be:
0.2*2+0.5=0.9
0.9^20=12.15%

So in the event of a frost nova that feat wouldn't be very impressive compared to the previous odds of 10^(-12) %.
Sorry.

16. There is no chance that OP rolled 1-2 on d10 20 times in a row.

So if there is any question it is what did actually happen that OP didn't notice or isn't telling us.

17. Originally Posted by Normie
There is no chance that OP rolled 1-2 on d10 20 times in a row.

So if there is any question it is what did actually happen that OP didn't notice or isn't telling us.
Um, not to be a dick but I think people have just been calculating what the chance of rolling 1-2 on a d10 20 times is... in fact thats the point of this thread.

Could it not just be that they roll once for the spell - if its a crit its a crit to everyone?

18. You had a trinket proc and someone used frost nova.

19. Chances are a DK hungering colded them.

20. I kind of picture OP like those guys in movies, where they kill 5 flies with one hand and stand up and yell out "Five....WITH ONE BLOW!" lol.

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