MC Math

[Euronymous 2]

In this thread I will attempt to analyze the math behind Thunderfury drop rates, and answer burning questions such as "Will ycb ever get a Thunderfury?", "will payo get tf?", "is there a hot grill in the raid?", "what does WD mean?".

<Dankk Budz Collective> has had a staggering 79 MC clears where both Geddon and Garr have been killed, dating all the way back to 2015/04/26 (trust me I dug up the logs). A good portion of those happened during grueling months of double MC every weekend. Throughout these runs there's been a single binding; Garr's, currently in possession of Mokes (who is busy getting his items ninjaed from him on Elysium right now)

This is a typical chance simulation, where we need to determine the number of successes in a series of independent binary experiments. This is by definition a binomial distribution with parameters n (number of MC runs) and p(chance for a binding drop on each Garr/Geddon kill). According to http://db.vanillagaming.org/?npc=12056 the chance is 3%, therefore p=0.03 (same for Geddon's binding).

Let's now take the binomial formula for the cumulative distribution function:

This allows us to calculate the probability of the event occurring k or less times. In order to calculate its complement (k or more times) we need only invert the summation's bounds. Thus we get:

(I'm shamelessly ripping shitty images off the web cause I cba to TeX - variable names have changed but you get the picture)

We'll figure the chance for one binding first, then generalize. So let's throw some numbers in there: N=1,  M=79, p=0.03.
Throw these into wolfram and you get P(K≥1) ≈ 0.909849735135229574839800563581749468165469647727020038080...

That's a 91% chance for one binding up to now - hey that's not too bad. We can make a Thunderfury when Ge≥1 AND Ga≥1, where Ge is the number of Geddon bindings and Ga is the number of Garr bindings. Since we can treat boss kills as independent events in a single raid and across every single raid in between all possible pairs, P(Ge≥1, Ga≥1) = 0.91^2 = 0.828.

That's an 82% chance to have had one Thunderfury by now. Maybe we're just unlucky. I'm now going to plot P(Ge≥X, Ga≥X), where X is the number of desired thunderfuries.

 

Note that Team Blackout's chance is even lower in actuality, as I'm pretty sure they've done less MC than we have.

I will now extrapolate the number of required MCs for us to reach 1 TF with 90% 95% and 99% probability.
Please note that in no way do results of previous experiments have any bearing whatsoever on future ones. This is just the chance to make one WITHIN X runs. You can mostly use this to gloat over tanks' misfortune when we hit the 150 run hallmark.

 P(Ge≥1, Ga≥1) ≈ 0.9 → 97 runs
 P(Ge≥1, Ga≥1) ≈ 0.95 → 120 runs
 P(Ge≥1, Ga≥1) ≈ 0.99 → 173 runs

Payo's TF would probably be the 3rd or 4th one.  The chances for 3 TFs in the same amount of runs are:

97 runs: P(Ge≥3, Ga≥3) ≈ 0.31304025
120 runs: P(Ge≥3, Ga≥3) ≈ 0.49210225
173 runs: P(Ge≥3, Ga≥3) ≈ 0.79937189

Through advanced math beyond the scope of this post I can deduce that Shakuur will not get a Thunderfury before the cold death of the universe with 9 sigma certainty.

[execution526 0]

rly doe calmdown

[YcbshadowE 1]

So there is like a 90% chance we will get a binding next run right?

[Undertanker 88]

Also bindings were not available to drop since the first MC.  They were added to the loot tables later.

 

To be more specific, bindings were not available until BWL.

Edited January 30, 2017 by Undertanker

[Euronymous 2]

If that is correct I'll have to adjust the math to this

I was going off this post: https://forum.nostalrius.org/viewtopic.php?f=2&t=4&p=4830&hilit=bindings#p4830

 

[Drakbak 3]

For the record, Team Blackout doesn't have 5 thunderfuries.  I know some of our guys like to exaggerate the number.  No doubt we've been really lucky so far, but we're at 3.5 currently.  Had 3 completed before Nost went down in April, then have received 1 binding since returning (funny enough it was when the Raid IDs got reset and we pugged the reset MC on an off-night).  Granted, we only run 1 MC per week, so the chances are still ridiculously low.

At the same time, we haven't seen any Eye of Sulfuras, so there's that.

[Gryffin 0]

We are doing MC with Inheritance weekly since 2015 october. Before the server got shut down, we managed to get 2 Geddon bindings. Since the server restart we had around 15 Molten Core runs without any kind of Binding dropping. Not counting the server downtime, we can say no Garr bindings - aka TF-s in 2 years of raid history with weekly clears. 3.5 seems a great number to me compared to that. So where are all those thunderfuries coming from that started popping up like crazy since the server got relaunched? Compared to the average 4k peak population on the server, feels like I see a bit too many. Feelsbadman.

[Eagger 0]

i think u should focus more on killing cthun first :)

[Haestingas 30]

Convulsion has had 1 binding despite doing double MC for 6+ months, Dreamstate same thing. When you have such a low drop rate there's bound to be unlucky people. For fucks sakes Convulsion had no t2 belt drop for 23 vael kills in a row, and the droprate on that is 12x higher than a binding. Fact is when there's no pity timer and % based drop rates, there's bound to be outliers of bad luck and good luck.

[NoGnomo 7]

what does WD mean??

[Storfan 24]

Gnarly GM-guild = CONFIRMED

:D

[Alyndra 3]

is there some math that explains how in all raids since nost launch a guild can have _ZERO_ enchant drops and others 5?

where can i send my yuans?

[Balar 0]

What's funny is we at the blooders just got both bindings in only 3 MC runs.  It's ok to be salty.

[Netherfrost 1]

Dreamstate has never completed a full TF in the whole lifespan, of the vanilla servers we've played on, in neither Nost/anathema NOR Emerald Dream (ED release -> ~AQ release where we made the transition), spreading our tanks on up to 3-4 different MC runs, and when not, typically split raiding. The only exception being tanks we recruited who already had a Garr binding. We started MC raiding around October/September 2012, and then theres ~10 months of nost being down.

Bitch pls.

[sumeht 9]

1 hour ago, Netherfrost said:

Dreamstate has never completed a full TF in the whole lifespan, of the vanilla servers we've played on, in neither Nost/anathema NOR Emerald Dream (ED release -> ~AQ release where we made the transition), spreading our tanks on up to 3-4 different MC runs, and when not, typically split raiding. The only exception being tanks we recruited who already had a Garr binding. We started MC raiding around October/September 2012, and then theres ~10 months of nost being down.

Bitch pls.

Rik is bad luck.

[Storfan 24]

15 hours ago, Netherfrost said:

Dreamstate has never completed a full TF in the whole lifespan, of the vanilla servers we've played on, in neither Nost/anathema NOR Emerald Dream (ED release -> ~AQ release where we made the transition), spreading our tanks on up to 3-4 different MC runs, and when not, typically split raiding. The only exception being tanks we recruited who already had a Garr binding. We started MC raiding around October/September 2012, and then theres ~10 months of nost being down.

Bitch pls.

In Endurance on ED we had 11, (yes, ELEVEN!) Garr bindings and not a single Geddon binding. Here on Nost we had 2 Garr bindings and 0 Geddon in the short timeframe we raided here.

Sometimes I wonder if we angered some GM in ED who also started as a GM on Nost, only to forever pester us with Garr bindings:D

[killerduki 54]

I think someone didn't took Balar so serious :)

1- 1st run The Blooders = Garr Binding drop , 3rd run The Blooders = Baron Gheddon binding drop. (Conspiracy theory).

2- Legendary Items according to archives i read are "chance to drop per world wide server kills" , not "chance to drop per the same raid" (unless this server have it differently modified).

3- http://ah-web.at/mobs.php This is the Link Blizzard used for "Droprate" and how it work.

Enjoy.

/Kind regards Killerduki

[mytchi3 1]

1 hour ago, killerduki said:

I think someone didn't took Balar so serious :)

1- 1st run The Blooders = Garr Binding drop , 3rd run The Blooders = Baron Gheddon binding drop. (Conspiracy theory).

2- Legendary Items according to archives i read are "chance to drop per world wide server kills" , not "chance to drop per the same raid" (unless this server have it differently modified).

3- http://ah-web.at/mobs.php This is the Link Blizzard used for "Droprate" and how it work.

Enjoy.

/Kind regards Killerduki

Gave it to paladin :D HAHAHAAAAAAAAAAAAAA  HAAAAAAAAAAAAAA 34g GfuckinG. GAVE first TF to paladin tank :D

Will spend next 2 years gathering gold at this rate

[Alyndra 3]

2 hours ago, mytchi3 said:

Gave it to paladin :D HAHAHAAAAAAAAAAAAAA  HAAAAAAAAAAAAAA 34g GfuckinG. GAVE first TF to paladin tank :D

Will spend next 2 years gathering gold at this rate

with their luck they will get an ingot every time, if they ever manage to kill golemag. then he will have it in a few weeks (+10 years prgression)

[Balar 0]

4 hours ago, mytchi3 said:

Gave it to paladin :D HAHAHAAAAAAAAAAAAAA  HAAAAAAAAAAAAAA 34g GfuckinG. GAVE first TF to paladin tank :D

Will spend next 2 years gathering gold at this rate

Like I said...it's ok to be salty.

[killerduki 54]

7 hours ago, mytchi3 said:

Gave it to paladin :D HAHAHAAAAAAAAAAAAAA  HAAAAAAAAAAAAAA 34g GfuckinG. GAVE first TF to paladin tank :D

Will spend next 2 years gathering gold at this rate

You mean this ?

Or This

Or maybe this

Or perhaps this?

3 hours ago, Balar said:

Like I said...it's ok to be salty.

I love you man <3

/Kind regards Killerduki

[mytchi3 1]

22 hours ago, killerduki said:

You mean this ?

Or This

Or maybe this

Or perhaps this?

I love you man <3

/Kind regards Killerduki

Mah that there you just posted is all vendor trash.

Where are flasks, resistance pots, elixirs, nexus crystal, ZG ENCHANTS AND FLASKS? You are a meme

[Theloras 108]

3 minutes ago, mytchi3 said:

Mah nigga that there you just posted is all vendor trash.

Where are flasks, resistance pots, elixirs, nexus crystal, ZG ENCHANTS AND FLASKS? You are a meme

Maybe, but he's now a meme with a Thunderfury, Blessed Blade of the Windseeker

[killerduki 54]

1 hour ago, mytchi3 said:

Mah nigga that there you just posted is all vendor trash.

Where are flasks, resistance pots, elixirs, nexus crystal, ZG ENCHANTS AND FLASKS? You are a meme

/Kind regards Killerduki

[Storfan 24]

On 2017-05-13 at 10:45 AM, killerduki said:

I think someone didn't took Balar so serious :)

1- 1st run The Blooders = Garr Binding drop , 3rd run The Blooders = Baron Gheddon binding drop. (Conspiracy theory).

2- Legendary Items according to archives i read are "chance to drop per world wide server kills" , not "chance to drop per the same raid" (unless this server have it differently modified).

3- http://ah-web.at/mobs.php This is the Link Blizzard used for "Droprate" and how it work.

Enjoy.

/Kind regards Killerduki

As a garr-binding holder and warrior this TRIGGERS ME TO NO END!

A PALADIN....

EDIT: Your guilds warrior MT gotta be the biggest cuck of all time for letting a paladin take the bindings. Man I feel sorry for him.