The Elder Scrolls Online: Math of RNG, Problems & Suggestions

I know there are tons of threads about it allready, 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 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
Number of MSA weapons:
– 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

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: 1/288Looking for a specific MSA weapon with a specific trait. Probability: 1/96
3. Specific MSA weapon with a specific trait. Probability: 1/96
4. Specific MSA weapon with a specific trait, only 3 traits each. Probability: 1/36

(*): shoulder example with only 6 traits, considering training and prosperous would be removed.

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.

Plooting the results:

Math of RNG, Problems & Suggestions

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.
5. The comparison for the MSA weapons is pretty extreme. After 150 runs you now have a 80% chance to have the desired weapon with the perfect trait. Before the addition of traits you would have had a 98.5% chance.
6. Since we are talking about exponential functions converging to 1 there is only a 100% chance after infinite runs.

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 (shoulders only):
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.

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