[FIXED] Legendary drop bad luck protection system

[Rdtym]

I've reported this a long time ago, also I have some info regarding drop rates and other stuff https://forum.wow-freakz.com/Legendary-drop-system-t460178.html .

[Enryah]

WARNING: Lots of Math in this post
I have read some blue posts about this and this a rough outline of the math behind it. (Combinatorics)

Shocker wrote:

It's not that we don't want to implement this system, but we don't have any info on how exactly it should work, how much does the chance get increased. And guessing would be bad

If we know how it works, we don't need to guess! A good measure for the frequency of the drops is the expected waiting "time" for a drop, in this case how much legendary-eligible stuff you have to do to get your first/next legendary drop. If you want to skip the math, go to the TL;DR at the bottom.

Say, legendary drop chance is at p=0.0001=0.01% probability (probably lower and varies for rare/world boss/wq/emissary/dungeon boss).
Every time you don't get a drop, the probability of getting a drop will increase (add 0.01% for every time it doesn't drop). Your drop chance after x missed drops will scale up to x*p.
In the worst case, you would have to wait x=10000 times to get the legendary (at x=10000 the drop chance becomes 10000*0.01%=100%).

I want to calculate the expected wait time for a legendary here, which can be adjusted with the initial drop chance p and thus the upper bound n=1/p.
Expectation = sum [x*(drop chance at x times)]
where the sum goes from 1 to the upper bound n.

For the drop to occur first at time x, it has to not drop at times x-1, ..., 1 and drop at time x:
drop chance at x = xp
chance to not drop at x = 1-xp
chance to not drop at x-1, ..., 1 = (1-(x-1)p) * ... * (1-p)
=> chance for first drop at x = (1-(x-1)p) * ... * (1-p) * xp

I was too lazy/stupid too calculate this analytically, so i wrote this Matlab script to do it for me:

Code:

n=10000; p=1/n; exp=0; drop_now=p; no_drop_before=1; times = 1; while drop_now<=1     exp         = exp + times * drop_now * no_drop_before;     % add to expectation        no_drop_before = no_drop_before * (1-drop_now);            % still no drop chance     drop_now    = drop_now + p;                                % increase drop chance     times = times + 1;                                         % count up end exp

This code (which can be easily translated to other programming languages) will output the expected times you have to kill a boss/do a wq/etc.. to get your first/next legendary with initial drop chance p.
If you want to increase the "waiting time" for the legendary, you can lower the drop chance p and vice versa.
The personal legendary loot chance would have to be increased by p for every time there is no legendary drop (on legendary-eligible content).

For each character it would look like this on a possible legendary drop:
if (no legy)
increase personal legy chance by this boss' / wq's / etc's legy drop chance
else
reset personal legy chance to initial chance p

If drop chances are too high, you can make the drop chance increase by half of the boss drop chance or less.

TL;DR: Waiting time for legendary drop can be controlled by drop chance if you use a simple pseudo-RNG system like this.
It's up to Shocker how many legendaries he wants to give to the players and not too hard to implement (although some testing would be advised).
@Shocker: It doesn't have to be 100% blizzlike, just create something on your own that does the job!

[Pinocchio Evreiesc]

Enryah wrote:

WARNING: Lots of Math in this post big trump wall

Sounds plausible, although if there are any plans of future updates for 7.2.5 here on freakz, we need this system to be adaptable for separate bad luck protection for each spec as implemented by blizzard recently. Basically on retail now each spec has its *own* chance that gets modified separately whenever you play that specific spec, and getting a legendary on one spec will not reset the drop chance modifier for the others.

[Enryah]

extending this to several specs should be a small matter, once you have it set up for the character
you just have up to 3 (depending on class) extra variables where you save the current legy drop chance for each spec.
at every encounter, you update the correct variable depending on loot spec.

[Pinocchio Evreiesc]

Enryah wrote:

extending this to several specs should be a small matter, once you have it set up for the character you just have up to 3 (depending on class) extra variables where you save the current legy drop chance for each spec. at every encounter, you update the correct variable depending on loot spec.

Sounds like a plan.

[Jot]

Pinocchio Evreiesc wrote:

Enryah wrote: extending this to several specs should be a small matter, once you have it set up for the character you just have up to 3 (depending on class) extra variables where you save the current legy drop chance for each spec. at every encounter, you update the correct variable depending on loot spec. Sounds like a plan.

Don't get so optimistic all of a sudden. They have not even implemented any form of BLP. This with the fact that Blizzard probably has all the algorithms expunged earlier in some form online. We need the devs to be more proactive with this kind of mechanic before releasing new content. Until they have set a goal for releasing this, I would be as hopeful as you are entertaining we should get.

[Evydence]

Enryah wrote:

WARNING: Lots of Math in this post I have read some blue posts about this and this a rough outline of the math behind it. (Combinatorics) Shocker wrote: It's not that we don't want to implement this system, but we don't have any info on how exactly it should work, how much does the chance get increased. And guessing would be bad If we know how it works, we don't need to guess! A good measure for the frequency of the drops is the expected waiting "time" for a drop, in this case how much legendary-eligible stuff you have to do to get your first/next legendary drop. If you want to skip the math, go to the TL;DR at the bottom. Say, legendary drop chance is at p=0.0001=0.01% probability (probably lower and varies for rare/world boss/wq/emissary/dungeon boss). Every time you don't get a drop, the probability of getting a drop will increase (add 0.01% for every time it doesn't drop). Your drop chance after x missed drops will scale up to x*p. In the worst case, you would have to wait x=10000 times to get the legendary (at x=10000 the drop chance becomes 10000*0.01%=100%). I want to calculate the expected wait time for a legendary here, which can be adjusted with the initial drop chance p and thus the upper bound n=1/p. Expectation = sum [x*(drop chance at x times)] where the sum goes from 1 to the upper bound n. For the drop to occur first at time x, it has to not drop at times x-1, ..., 1 and drop at time x: drop chance at x = xp chance to not drop at x = 1-xp chance to not drop at x-1, ..., 1 = (1-(x-1)p) * ... * (1-p) => chance for first drop at x = (1-(x-1)p) * ... * (1-p) * xp I was too lazy/stupid too calculate this analytically, so i wrote this Matlab script to do it for me: Code: n=10000; p=1/n; exp=0; drop_now=p; no_drop_before=1; times = 1; while drop_now<=1     exp         = exp + times * drop_now * no_drop_before;     % add to expectation        no_drop_before = no_drop_before * (1-drop_now);            % still no drop chance     drop_now    = drop_now + p;                                % increase drop chance     times = times + 1;                                         % count up end exp This code (which can be easily translated to other programming languages) will output the expected times you have to kill a boss/do a wq/etc.. to get your first/next legendary with initial drop chance p. If you want to increase the "waiting time" for the legendary, you can lower the drop chance p and vice versa. The personal legendary loot chance would have to be increased by p for every time there is no legendary drop (on legendary-eligible content). For each character it would look like this on a possible legendary drop: if (no legy) increase personal legy chance by this boss' / wq's / etc's legy drop chance else reset personal legy chance to initial chance p If drop chances are too high, you can make the drop chance increase by half of the boss drop chance or less. TL;DR: Waiting time for legendary drop can be controlled by drop chance if you use a simple pseudo-RNG system like this. It's up to Shocker how many legendaries he wants to give to the players and not too hard to implement (although some testing would be advised). @Shocker: It doesn't have to be 100% blizzlike, just create something on your own that does the job!

^ and this http://www.wowhead.com/news=257898/legendary-items-soft-cap-removed-bad-luck-protection-beyond-four-legendaries

After you get 4 legendaries "bad luck protection" will no longer work for you.

@Shocker




If you gonna hit the king you're better kill the king

[MrKrisSatan]

I'd like to see some kind of protection implemented even if its just a 1% increase to legendary chance every emissary chance you open and then it resets when you receive one, its not a perfect solution but it's better than nothing for those of us with bad luck

[Pinocchio Evreiesc]

@Evydence @Shocker

Please read that article you linked more carefuly. Prior to 7.1.5 (and the introduction of more legendaries) there was indeed a soft cap of 4 legendaries after which bad luck protection no longer applied. But if you scroll down some more it says:

Quote:

So we removed that soft cap just over a week ago. "Bad luck protection" now applies indefinitely. ... and we'll continue to adjust the effectiveness of the outlier legendaries (coming up in patch 7.1.5) with the goal of keeping them exciting but not gamebreaking.

If you make the system to not work if you already have 4 legendaries it will be wrong. That feature was lifted before 7.1.5 hit on retail. Are we playing on 7.1 or 7.1.5?

[Enryah]

MrKrisSatan wrote:

I'd like to see some kind of protection implemented even if its just a 1% increase to legendary chance every emissary chance you open and then it resets when you receive one, its not a perfect solution but it's better than nothing for those of us with bad luck

1% increase is actually a lot (way too much). and the system has to be reset to the initial drop chance after every legendary drop, otherwise it would scale up too much and legendaries would be too common. The system discribed ITT is pretty much exactly the same as the one on retail.

@Evydence very helpful post +1

[Shocker]

I made an implementation, taken some of the posts here in consideration. The algorithm is quite complex, but long story short: for a casual+ player which does daily farming (dungeons, raids, emissary, rares killing and/or pvp/bgs) he will have a GUARANTEED drop in 1-2 weeks (he can also have a drop earlier if he's lucky obviously), depending on how much does he farm. If he farms less then the expected average, it will take longer. But the system is there, he will eventually have 100% drop chance. Will post more info on site once it's live (after restart)

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