Hello,
I know there are tons of threads about it already, but I would like to discuss the problems of RNG by taking a look at the underlying math. I will present some calculations and examples to display the problems and discuss some possible solutions.
TL;DR can be found in the end.
To be honest I'm one of the players who have no luck at all when it comes to drops (Looking for a SPC sash in divines and Scathing Mage gloves since IC launch, took uncounted runs to get the desired helmets, ...) and I find it extremely demotivating to know that there is no guaranteed drop after N runs (aka token system).
Ok so lets do the math. Basically RNG can be treated as an urn problem (
https://en.wikipedia.org/wiki/Urn_problem) with replacement. The number of keys /MSA runs corresponds to draws. If we consider only two possible outcomes (get item, don't get item) the problem is described by a binomial distribution.
In order to calculate the probabilities for the outcomes we need to determine the number of possible items:
Number of different sholder pieces in undaunted chests:
- 12 sets, 8 traits, 3 weights (light, medium, heavy): 288
- 12 sets, 6 traits (removing training, prosperous), 3 weights: 216
[outdated]
Probability for MSA weapons:
According to
@Meld777,
@kasa-obake and
@Alanar MSA weapons seem to drop in 6 categories: Bow, Resto, Destro, 2H, 1H&S, Dagger/Axe with equal probability and 8 traits each.
Bow, Resto, 1H&S, any 2H, any destro, any dual wield: 1/48
Dagger, Axe: 1/96
Specific Destro, 2H: 1/144
[outdated end]
I don't know the exact new probabilities for each weapons after the changes made in homestead (?), but they should be somewhere in the range of 1/96 if we assume equal probabilities for all weapons and traits (12 MSA weapons (4xStaff, Bow, Dagger, 2x(Sword, Mace, Axe))). It corresponds to the Dagger/Axe line in the plot below.
old assumptions:
- 12 MSA weapons (4xStaff, Bow, Dagger, 2x(Sword, Mace, Axe)), 8 traits (?): 96
- 12 MSA weapons (4xStaff, Bow, Dagger, 2x(Sword, Mace, Axe)), 3 traits (like it once used to be): 36
Data
Thanks to
@kasa-obake we have some data of the MSA drops to back up the assumtions made above. Original thread can be found here (
Link). Approximately 1.5k observations lead to the following results:
If we group the drops in the categories defined above we get:
2H 14,5%
Destro 14,8%
1H&S 15,2%
Dual 17,3%
Bow 17,5%
Resto 20,7%
Compared to the expected 1/6 = 16,7% we get a variance of 0,047% and a standard deviation of 2,17%, which is ok for the sample size we are looking at.
Dungeons:
- Monster mask: 8 traits, 3 weights: 24
- Set weapon: 3 sets, 8 traits, 13 weapons (4xStaff, Bow, Dagger, 2x(Sword, Mace, Axe), shield): 312
(assuming a x dropchance for weapons instead of jewelery this number increases by 1/x, so for 50% by a factor of 2)
Calculation:
The Probability to have the desired item after N draws (e.g. keys/runs) is given by:
1-(1-P)^N
so we first calculate the probability of not getting the item (1-P). The probability of not getting the item N times in a row is given by (1-P)^N. And to get the probability to get the item we take the opposite event: 1-(1-P)^N.
Undaunted shoulders:
Examples:
1. Undaunted shoulder with a specific trait, any weight (light, medium, OR heavy). Probability: 3/288 = 1/96
2. Undaunted shoulder with a specific trait and a specific weight (some stamina best in slots). Probability: 1/288
(*): shoulder example with only 6 traits, considering training and prosperous would be removed.
Results undaunted shoulders:
Interpretation:
1. As stated above getting a shoulder with a specific trait but any weight is the same as getting a specific MSA weapon, so they share a line.
2. After 300 keys you have a 95% chance to get the shoulder in the desired trait but any weight (I belong to the 5% who don't have it, e.g. Grothdarr in divines).
3. If you are looking for a specific shoulder trait and weight there is only a 65% chance to have it after 300 runs. That means that 1/3 of the players wont have it after 300 runs. Even after 500 keys 18.4% won't have this item. A guildmate of mine is above 400 keys now without a medium Krahg's.
4. Removing training and prosperous from the loot table would help to improve the situation (green lines), but there would still be 10% of the players without the desired shoulder after 500 keys.
6. Since we are talking about exponential functions converging to 1 there is only a 100% chance after infinite runs.
MSA & DSA weapons:
I assumed the same drop behavior for DSA weapons as for MSA weapons, but considered group trading in the DSA case to show it's benefits.
Results MSA&DSA:
Interpretation:
If we would assume that we don't have categories for the drops, so that a specific destro staff (e.g. fire staff) drops with the same probability, then every weapon would drop according to the "Dagger, Axe" line. The split in categories helps people who search for a bow, resto staff, 2H or 1H&S, but hurts people searching for a specific destro staff.
In order to show how the addition of traits changed the drop chances I also added the specific destro example with 3 instead of 8 traits. The change is huge going down from a 85% chance to a 50% after 100 runs.
You can also see that limited trading within a group heavily increases the drop chances for specific items.
Dungeon sets:
To demonstrate the effects of limited trading within a group I will present more examples with dungeon drops:
1. monster mask, specific trait, any weight, no group trading ("solo")
2. monster mask, specific trait, any weight, 4 man group
3. monster mask, specific trait, specific weight, no group trading ("solo")
4. monster mask, specific trait, specific weight, 4 man group
5. set weapon, 4 man group (assuming 50% dropchance for weapons)
6. set weapon, 12 man raid (assuming 50% dropchance for weapons)
Results monster masks and dungeon sets:
Interpretation:
One can clearly see the benefits of trading even if it's only within a small group. Mathematically one run with a group is the same as 4 runs solo/without trading, therefore adding a factor 4 in the exponent, so that the curve converges a lot faster.
Farming set weapons is a real pain, since there are so many options with 3 different sets and jewelery. Even with group trading the chance to have a weapon in the desired trait after 100 runs is below 50%. For raid groups the chances are better if they are trying to get a weapon for one player. Getting 2 weapons like dual wield swords extended the capability of Excel, but its much lower than the probability for one weapon.
So what is the problem?
For MSA it is pretty clear that the addition of traits made the grind a lot worse and with runs taking about 40-60 mins it's not very efficient to farm.
For the undaunted shoulders the problem is clearly the number of shoulders and traits. Splitting the shoulders in 3 chests allready helped a lot and was a good move, but the number of unused traits is still negatively influencing the drop chances.
The attempt to make every trait usefull and the trait rebalancing failed otherwise there would be no discussion here. The difference between a divines shoulder wearing TBS (+0.9% crit & crit dmg, Thief & Shadow mundus) compared to infused (+100? magicka) is huge.
Solutions:
1. Remove unused traits:
Check the data, see what traits are really used and remove the unused ones. If you don't want to remove them, modify the drop chances. Instead of a uniform distribution of traits go for higher chances depending on the item aka smart loot (offensive weapons: sharpened, precise, nirn; Offensive shoulders: divines, impenetrable, (infused), defensive shoulders: divines, impenetrable, reinforced, sturdy, ...). Check your data or ask your players! We know what pieces we want and in what trait.
2. Remove bind on pickup restriction:
I don't want the BOP restriction removed from the MSA weapons, since MSA is an achievement and it should be rewarded exclusively.
For the shoulders everyone can farm keys on normal modes, so they are not as exclusive as MSA weapons.
Why would it help?
Assuming the shoulders drop with equal probability and every player on the server used 288 keys there will be approximately one shoulder of every trait and weight per player, but there are variations for every player according to the probabilities calculated above. Allowing the players to trade enables the 35% who don't have a specific shoulder in a specific trait at this point to buy or trade the desired one, because not having the one you want means you have more of the others (in my case 4 Illambris in divines but no Grothdarr).
What is the downside?
People will get their gear faster, or could get it even without doing dailies at all. If people have what they want they might stop doing the undaunted dailies, on the other hand there will be people trying to get good shoulders in order to sell them.
I think at the moment we are at a point where people stop doing the dailies or even playing because of the frustration about bad rng, so we have to find a middle way.
3. A token system:
Being able to trade an specific amount of undaunted keys for an item would help.
4. Improving the Cyrodiil vendor:
Including divines instead of infused on the shoulder pieces and presenting multiple different sets per weekend would also be a solution.
I personally would like to see a combination of both solutions, removing some traits or adjusting the drop rates (reinforced only on heavy shoulders, well-fitted only on medium, etc.) and making shoulders BOE. I think the game's economy could need some more high value armor pieces and after a time the prices will go down anyways making it easier for new players to buy some gear and having a better start into the end game.
I hope I could display the problems well and contribute to the discussion, leading to changes and a better playing experience for everyone.
Thanks for reading.
Gil-Galad
@ZOS_GinaBruno,
@ZOS_KaiSchober,
@ZOS_RichLambert: I would love to get some feedback if you read this thread and if you are discussing to change the RNG system.
TL;DR:
The chances of not getting a desired item after 200+ runs/keys is pretty high, due to a high amount of useless traits. Removing traits or reducing the drop chances for unused traits would help a bit but don't solve the problem completey. BOE instead of BOP would be a good solution for undaunted shoulder pieces.
Edit 30.11.2016, 22:50:
Added monster masks and dungeon set weapons.
Edit 01.12.2016, 12:05:
Added a section especially for MSA & DSA weapons. Added spoilers for better overview.
Edit 03.12.2016, 19:55:
Added data and charts from
@kasa-obake to back up the assumption about the MSA weapon drop distribution.