Calculating the chance on a perfect q9 20/20 machting attributes Wand

Jodel_GW · May 12, 2020 at 12:19 AM

LETS DO SOME METH …. ehm …. i mean MATH!!!

I was wondering what the chance on a perfect q9 Wand with matching attributes is. Let's start with some Basics:

1) I will not make a 100% correct calculation as i am not a 100% into min-max values for each possbile mod on a gold max damage wand. We know that 15% HSR "attribute" is possible on blue wands but for gold ones the min is 18% i think.

2) Wands can come in single mod or dual mod. Single mods come either with the "inscription" or the wand wrapping (if we translate that from NF/EotN).

3) There are just two different wand wrapping mods (HSR of spells and HSR of specific attribute)

3.1) HSR of spells can come in 8,9 and 10% --> 3 different possibilities

3.2) HSR of specific attribute can come in 18, 19 and 20% --> 3 different possibilities

3.3) HSR of atribute can come in 21 different attributes --> 21 different possibilities

4) There are some different wand "inscriptions" (5^50, 5^ench, 5^hex, hct spells, hct "attribute", more?)

4.1) i am somehow sure all wand "inscriptions" with 5^50, 5^ench and 5^hex have a range of 4..5 on gold max wands. --> total of 6 different inscription possibilities

4.2) HCT of spells can come in 8, 9 and 10% --> 3 different possibilities

4.3) HCT of attribute can come in 18, 19 and 20% --> 3 different possibilities

4.4) HCT of attribute can come in 21 different attributes --> 21 different possibilities

5) Dual mod wands have a total chance of all "inscription" single mod wand * wand wrapping single mod wands --> total of 3*3*21*6*3*3*21 different dual mod possibilities

6) at the Moment we have the chance of 5 different requirements (9 - 13) --> total of 5 different requirement possibilities

7) a wand can come in 21 different attributes --> total of 21 different attribute possibilities

Now we take our calculator: canche of a q9 20/20 matching attribute wand is 1 in (3*3*21*6*3*3*21)²*5*21

= 1 in 4.800.000.000.000

PS: i know i had some alcohol and it's almost half past 12 in central europe. Please confirm or decline this number! I know i did not take into consideration that a q9 ES wand with 20/20 fire is also called a matching attribute wand. but this will not significantly change our number here!

PyroLobster · May 12, 2020 at 5:18 AM

I've tried to do similar calculations before mostly for shields, and did staffs once. It's crazy. Couple things in ur numbers:

1. Unless I've gone completely mad isn't an 8% and 18% on a gold wand prenerf? Please somebody call me mad if I am

2. Didn't see a mention of 15-1 and 14-1 mods as possibles

The final value gives you total possible combinations but when you make it into a ratio of 1:xxxx its using the assumption that all variables have an equal chance. We all know that chance of 2 mods is lower than 1 so there is a problem with weighting of variables just from that. So its not exactly accurate to represent them in this way. Taking it a step further I've always believed that different mods have a different drop chance. There is some mods (and mod combos) that from 15 years of observation just seem to be rarer than others and even a difference because of skin. There no way to account for these kinda discrepancies so targeting 1 combination might be even worse that the number your calculation gives lol. Total speculation, can't confirm without anet showing a drop table and the code behind it but its an assumption I've always held. Anybody else think this way?

All that withstanding I like the way ur mind works

Red Fireball · May 12, 2020 at 7:49 AM

fun one - I also did that at some point with pleikki I think...

Few things that are off:

You calculate in the different attributes part three times - that means you calculate the chance for a wand of a specific attribute (not just getting any q9 20/20 as title suggests.

You say there's 21 possibilities for attr on hct and hsr. Now only 18attr can drop as hsr/hct (estor, sr, fc can't) Furthermore that only applies to multiprofession wands - getting a matching fire wand would be significantly easier since only ele-attributes could come.

You say there are 21 possibilities for the req - that's only 14 for multi profession wands (if I counted properly)

As pyro said 8% and 18% aren't within the available range on todays drop.

Os wands do not necessarily have an "insc" + a "wrap" - doesn't mean any combination is possible, but more than you respect this way. On shields I'm far more into what is and is not a possible combination.

And finally as pyro stated: number of possibilities does by far not say anything considering rarity or rate! Think of os swords - following the logic there's 12 (including nomod) possibilities and you'd deduce a 1:12 ratio for a 15/-1healthreg one - which is by far off.

Long story short - fun project for sure but off on a few assumptions. Just properly deducing all the possibilities is something I would be unable to do since I do not know which combinations of mods are possible. Then deducing the chance is something which is again far off my capabilities - as said: different mods may carry different chances.

Fun idea we followed back then: what about foci? There are all the armor mods, all the +1 attr mods and so on. Compared to all the possibilities on there wand seem easy to get as matching

Jodel_GW · May 12, 2020 at 7:56 AM

PyroLobster thanks for your answer. It could be that 8% and 18% are prenerf. Let's wait for confirmation here.

Yes, i forgot the 14/1 and 15/1. Will add this later.

I will not take the chance of a specific mod into consideration. I do also think that HCT/HSR “attribute“ has a lower chance to drop compared to HCT/HSR spells. But we don't know anything about these chances. Thus, i will asume that every mod has the same drop rate.

I am also not taking into consideration that a specific skin does not come in all attribute combinations. But i do also not taking specific skins into consideration. I was just calculating it for a random skin.

PyroLobster · May 12, 2020 at 8:30 AM

I was 99.9% sure 8% and 18% are prenef and as Red confirms then I'm 100%. A madlad calculation would be what were all the prenerf possibles.

I can say with certainty 16% was possible cause its on my fav wand in the game:

I don't recall seeing a 15% but have a feeling it was possible? perhaps even 14%? I know min on shield was 6vs so was 6% min for wand mods also? Red Fireball Pleikki will likely have that answer. prenerf caster stuff is not my area of expertise so will have to defer to somebody else on that. + all the lower bounds of other mods need to be figured out. If we could get clarification on that could run numbers for total possibles prenerf vs postnerf. What a giant nerdy waste of time that would be haha. Lets do it

Jodel_GW · May 12, 2020 at 2:48 PM

Quote from PyroLobster

I was 99.9% sure 8% and 18% are prenef and as Red confirms then I'm 100%. A madlad calculation would be what were all the prenerf possibles.
I can say with certainty 16% was possible cause its on my fav wand in the game:
I don't recall seeing a 15% but have a feeling it was possible? perhaps even 14%? I know min on shield was 6vs so was 6% min for wand mods also? Red Fireball Pleikki will likely have that answer. prenerf caster stuff is not my area of expertise so will have to defer to somebody else on that. + all the lower bounds of other mods need to be figured out. If we could get clarification on that could run numbers for total possibles prenerf vs postnerf. What a giant nerdy waste of time that would be haha. Lets do it

That wand is pure love. Thanks for showing us!

Ye, i sometimes feel a bit bored and then thinks like that come into my mind. I don't know why i am doing this cause i have a full time job + family. But when i have such an idea i HAVE to do it.

BTW: we know dual inscription shields exist like +10vsFire -3whileHex. Is this also possible for wands? Like 5^50 & HCT spells 10%?

Pleikki · May 12, 2020 at 3:31 PM

Well yeah i have atleast this wand

And this staff:

So i can confirm 15% possible, i cant confirm that its lowest tho (somehow i have some vague memory of even lower but cant say for sure)

But yeah, we did someting like that with red few years back, and multiprof offhands (paper fan example) has ALOT more possible combinations then wands even

But ye otherwise i agree whats stated above (19-20% only drops now etc)

And yeah you can get 5^50 10hct etc "dual inscriptions" same way as shiels and offhands

Invokeur · May 12, 2020 at 3:57 PM

Quote from Pleikki

But yeah, we did someting like that with red few years back, and multiprof offhands (paper fan example) has ALOT more possible combinations then wands even

About that ; I cannot recall seeing any multiprof offhand with mixed profession bonus, do you have anything in your gear like this ? (i.e. fast cast fans come with mes-only bonuses...)

I'm probably wrong and kinda lucky but out of ~40 I identified I cannot remember of one mixed

Pleikki · May 12, 2020 at 4:05 PM

I know i dont have anything like that right now, and i know that prenerf even single prof items could have mixed mods!

https://archive.guildwarslegacy.com/08/08%20Price%…20Q.Q).001.html

I somehow think they could drop mixed, but ye dont have any to prove it and might be just bad memory so guess well need to find out

Oofus · May 12, 2020 at 5:47 PM

As a mathematics teacher I applaud the enthusiasm shown for a good probabilities exercise. As a 20/20 enthusiast I respect the interest in the subject matter. But as a programmer I can tell you from experience this isn’t as simple as drawing up a pool of drop possibilities, it’s not just math at work here. The odds are artificially manufactured. There is no body of mods floating around in the ether, containing more 10% mods than 20% mods, that we pick from.

I say this because we know, for example, that two Recharge mods cannot drop on one wand, AND we know, anecdotally, that 20/20 is far more rare than 20/10 and far, far more rare than any 20/+5. So we can easily assume that mods are artificially limited with assigned probability parameters of some sort. Otherwise the odds would be exactly the same for any wand combo to drop, 10/+5 would have the exact same chance to drop as 20/20 or any other combo including single mod. They are not.

One of several things we don’t know is what those artificial parameters are, how mods are applied to items from a programming perspective. We don’t know if there are virtual “slots” in a wand to be “filled”, or if there is simply a max number of possible mods(2) with a series of if/then conditions applied, or some other creative method employed by the devs. We just don’t know, and it is important information for this question that us mere mortal end-users aren’t privy to.

If we knew those parameters we might apply a series of Conditional Probability(B|A) formulas to determine the actual chances of drops. But without that understanding we’re just blind and any results would be ...well... wrong.

Surge goes pre · May 15, 2020 at 9:58 PM

I do not think that every type of mod (HSR vs +energy) and mod strength (19 vs 20, 10 vs 9) are equally likely. Probably not even close.

Oofus · May 18, 2020 at 12:45 AM

Did some quick maths over coffee this morning.

Unless I missed something, just for an old-school, core skin Fire Wand, gold, max damage, of any req(9-13), where the order of the mods on the wand do not matter, there are

346 mod possibilities. This includes imperfect mods and single mod wands.

If you include req(9-13) in the mix, the possible drops increases to

1,730.

If the order the mods appear on the wand matters to you, then there are a whopping

3,310 possible drops from just the one skin alone.

Jodel_GW · May 18, 2020 at 10:09 AM

Quote from Oofus

Did some quick maths over coffee this morning.
Unless I missed something, just for an old-school, core skin Fire Wand, gold, max damage, of any req(9-13), where the order of the mods on the wand do not matter, there are
346 mod possibilities. This includes imperfect mods and single mod wands.

If you include req(9-13) in the mix, the possible drops increases to
1,730.
If the order the mods appear on the wand matters to you, then there are a whopping
3,310 possible drops from just the one skin alone.

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You totally forgot the chance of beeing mixed attributes here. So you assume that fire wand ALWAYS comes in Fire HCT/HSR but it doesn't.

Oofus · May 18, 2020 at 1:08 PM

Quote from Jodel_GW

You totally forgot the chance of beeing mixed attributes here. So you assume that fire wand ALWAYS comes in Fire HCT/HSR but it doesn't.

No, I did not. That’s why the number is so large, it includes possibilities like 20% recharge of Air/20% casting of Water, or any other combination of the 4 possible Elemental attributes which can drop on a Fire Wand.

MawKaw · May 19, 2020 at 12:21 AM

Talking about this, a guildi got that wand and sold it to me lol ! The skin is amazing for a necro !

Oldschool Cool · May 30, 2020 at 10:56 PM

Maybe you guys can help me out. Along the years I have collected more than 50 gorgeous triple prof wands, as in wands with a req in prof A, HSR in prof B and HCT in prof C.

My end goal would be to have all the available triple prof combo that can drop for the faction multi-prof wands (Celestial, Jade, Amber, Zodiac, Plagueborn etc…)

Considering that :

* There are 14 possible req attributes for the faction multi-prof wands (2 for Monk/Mesmer, 3 for Necro/Ritu, and 4 for Ele)

* There are 18 possible attributes for HCT and HSR (4 for Monk/Ritu/Ele, and 3 for Necro/Mesmer)

* I do NOT distinguish between the req, HSR or HCT. For example : Req Blood/HSR Fire/HCT Domi = Req Blood/HSR Domi/HCT Fire = Req Fire/HSR Blood/HCT Domi etc...

I calculated there are : 351 possibilities. I haven't done probability calculus in a very very long time, so if someone can double check my maths I would very much appreciate it.

Btw, I will shamelessly link my WTB thread, if you want to give a new home to your triple prof wands

Oofus · June 20, 2020 at 6:42 PM

Quote from Oldschool Cool

Maybe you guys can help me out. Along the years I have collected more than 50 gorgeous triple prof wands, as in wands with a req in prof A, HSR in prof B and HCT in prof C.
My end goal would be to have all the available triple prof combo that can drop for the faction multi-prof wands (Celestial, Jade, Amber, Zodiac, Plagueborn etc…)
Considering that :
* There are 14 possible req attributes for the faction multi-prof wands (2 for Monk/Mesmer, 3 for Necro/Ritu, and 4 for Ele)
* There are 18 possible attributes for HCT and HSR (4 for Monk/Ritu/Ele, and 3 for Necro/Mesmer)
* I do NOT distinguish between the req, HSR or HCT. For example : Req Blood/HSR Fire/HCT Domi = Req Blood/HSR Domi/HCT Fire = Req Fire/HSR Blood/HCT Domi etc...
I calculated there are : 351 possibilities. I haven't done probability calculus in a very very long time, so if someone can double check my maths I would very much appreciate it.
Btw, I will shamelessly link my WTB thread, if you want to give a new home to your triple prof wands

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Hmm, I tally 458. Probably not what you wanted to hear.

FYI my bag tallies were; 292, 120, 36, 8, 2

Evelynn Roscoe September 30, 2021 at 3:56 PM