Like most MMO's, Elder Scrolls online uses a lot of RNG for everything from combat to loot mechanics and soon maybe even monetization! But just what can RNG do for you? Well, that depends on exactly how "random" your tables are! Let's look at some common examples.
Everyone knows about the flip of a fair coin. On average you'll get 50% heads and 50% tails. And everyone knows about the roll of a fair die. 1/6 times you roll it you'll get some given number, 1/2 of the time you'll get an even number, and 1/2 of the time you'll get an odd number. But what about something more complex, like the amount of gold looted from an enemy or your chance at a Light Infused Molag Kena helm? Read further to find out!
Let's start with gold, because who doesn't love those shiny little devils? Gold drives the in-game economy and keeps our gear in good repair! But how often will you get it, and how much will you get WHEN you get it? Let's take a look at a sample loot table. Note that this isn't a real loot table from the game, it is an artificial one made to enhance understanding!
As you can see, there's a 2/3 chance that you'll get gold (4 out of the 6 entries have gold), but what's with the range on the entry? More random numbers! Under this model, 1/6 of the time you'll get 1-2 gold, 1/6 of the time you'll get 2-3 gold, and so on. This model can easily scale up based on player level by simply adding a level-based multiplier to the expression, so at level 50 it could become 50-100 gold 1/6 of the time, and 100-150 gold 1/6 of the time, etc. How-forward thinking!
"But wait!", you might say, "I remember combinatorics and statistics from high school, and I'm pretty sure those empty slots means that there's a chance you'll NEVER get gold!" Well, you are correct. But also wrong
!! This is because you can tweak and RNG-based loot system to be slightly more fair while still maintaining a semblance of risk. For example, you can put a cap on the number of consecutive instances of not getting loot. You just increment a counter, and when you hit a certain number of enemies that didn't drop loot, you reduce your loot table to only contain actual instances of loot. Simple and very helpful!
If you don't do this, you are leaving yourself open to some very naughty happenings. As stated previously, there are circumstances where empty slots in your loot table will almost guarantee that as your playerbase increases, some people just won't ever get loot. It becomes more and more unlikely, but for a game like ESO with 7 million players, it can happen! Let's examine that by modeling the way Undaunted set helmets drop.
Currently (but soon to change!!) fighting certain dungeon bosses has a chance to drop a helmet from the undaunted set. The key phrase here is "a chance to drop". Let's say, as an example, that your boss monster drops a helm 1/4 of the time. You want to find out what your chances are for getting a helm by running the dungeon a certain number of times. This is very complicated math!! I won't try to make you understand it, but for fun it looks something like this!
Wow, what a mouthful! Of course, we don't actually need to do that. By being clever kittens, we can instead choose to figure out what your chances are for receiving nothing after a certain number of dungeon runs, and then take the compliment of that chance to obtain the chance of obtaining a helm!
That little bit at the end there means we can skip aaaaall that math and go straight for something easy that you can plug into the simplest of calculators! Take THAT, Texas Instruments! All you need to do is figure out the drop rate for a helm (25% in our example, or 0.25), subtract it from 1, and raise it to the power of the number of attempts, then subtract that from 1 again! So if we're running the dungeon 50 times, that's just 1 - 0.75^50, which is 0.99999943367. Great odds!!
Hmmm... something's wrong, though. We have 7 million players in our game, and climbing! If we multiply that by 7 million we should get the average number of people out of our 7 million who will obtain a helm after 50 runs. Uh oh! Only 6999996!! On average we're still leaving 4 people out if they all run the dungeon 50 times. Better luck next time, kids! I hope the meta doesn't change as soon as they finally get one.
But surely those 4 people just need to run a few more dungeons to be sure that they get the helm they want, right? Let's find out together! If they run 60 dungeons then on average 6999999 players will get the helm. Wow, already knocked 3 out of 4 off, surely just a few more will do it! At 70 dungeons it goes up to... 6999999 again. Hmm. 80? No, still 6999999. 100? No, still 6999999. A thousand? No. A million?? No!! Surely there must be some
number that will do it, though, right? Well, no. Mathematically, you will never be sure! The chances of getting nothing get smaller and smaller the more you do it, but it is never guaranteed. And with 7 million players (and growing), it becomes much more likely that at least one person will lose out, no matter what you do or how often you run.
Adjusting the drop chance won't do it, either. As long as there is a chance for nothing, there is an chance for infinitely nothing.
That's one reason why the upcoming changes to Undaunted helms are so great!! By guaranteeing a Monster Mask reward for Veteran Dungeons, they've ensured that ALL players will get something good, no matter how bad your luck is! Of course, it's not all sunshine and rainbows. the armor type and trait are still random, after all. Thus, if someone needs something more specific than "a Monster Mask", we are back to guaranteeing that someone comes away upset. We simply redo the equation so that we only count the one trait/weight combo as "something" and everything else as "nothing". Still, most builds have at least a little leeway for trait/weight combos, as the most powerful feature of the sets tend to be the set bonuses, so even if you run the risk of never getting true Best In Slot for your build, you will no longer run the risk of getting truly "nothing".
As we've seen, a player's perception of what is valuable/useless can skew how we compute probabilities using our loot tables. For some, getting a Light Divines Molag Kena helm is just not enough, so we have to cross even that rare drop off their loot table when evaluating for the probability of getting "something" versus "nothing". This same principle affects RNG across all aspects of the game, including the ne Crown Crates!
As surely everyone's seen by now, Crown Crates are coming to the Crown Store. These items will always contain some amount of random consumables, and also have a chance to contain costumes, pets, and mounts! Pretty exciting for people who love random consumables, but maybe not for everybody. If you like random consumables, the probability of getting something you want in the crate is 100%! Congratulations!! If not, however, we have more math to do.
Let us consider the case of someone only wanting the rare mounts that will drop. Let us first consider the subset of this case where somebody only want one mount out of all the mounts that have a chance to drop. For this player, we can simply take the drop rate of the mount, subtract it from one, and raise it to the power of how many Crown Crates that player is willing to buy. Of course, we don't have the actual drop rates, so we'll work with some sample values instead! As for how many Crown Crates someone is willing or able to buy, we'll use another example!
Here is my current Crown balance. Gee willickers, what a haul! With this balance, I could buy 80 Crown Crates. Let's assume I spend all of my Crowns on Crown Crates for the sake of science! What a noble sacrifice, brings a tear to the eye and everything. Let's start with a 5% drop chance and go from there! Remember, we're calculating the odds of getting "nothing" since it's an easier computation. (1 - 0.05) to the 80th power is... 1.7%! Not bad, not bad, it's almost certain that we'll get it. But as we saw before, it is not certain, so the more number of people buying Crown Crates with this drop %, the more people who will walk away disappointed. If we round down that's only 1 player out of 100, but remember, 7 million players. That's quite a few individuals!! Let us also not forget that not many people will be able to buy 80 Crown Crates, and the fewer you buy the worse your chances will be.
Now, 5% drop rate seems pretty good, it might even be the actual drop rate for some of the discontinued mounts like the Polar Bear or the Clouded Senche, but what about the reaaaally
rare mounts that have yet to be revealed? Let's assume a 1% drop chance. It's not stupidly rare, but it's far outside most peoples' playgrade. 80 Crown Crates, here we come!! (1 - 0.01) to the 80th power is... 44.8%!! Wait, WHAT?? But with a 5% drop rate it was only a 1.7% chance of failure, how did it grow so fast?? Well, that's a long and complicated mathematical discussion, but it serves to illustrate the point.
"Well, maybe you need to buy the full 100 Crown Crates, right?" you ask, plaintively. "I mean if it's a 1% drop chance then surely at 100 Crown Crates you'll get it down to only a 1% chance of failure!" Oh, you poor sweet dear. (1 - 0.01) to the 100th power is still a 36.6% chance of failure. "YO, BUT HOW MANY FOR 1%??" you ask, eyes wide in terror. 458.2, and since we can't buy partial Crown Crates we round this up to 459. And again, this is still leaving you with the same chance of failure as all of those individual Crown Crates had to drop the mount to begin with. Better luck next time!!
Obviously, however, some folks are going to want more than just the one mount! And also we don't know the drop rates so it might not be as bad as all that! It could also be worse than all that, I'm not going to sugarcoat the science or the uncertainty, but there is definitely more wiggle room than the 1% scenario. If, for instance, someone wants more than one thing from the Crown Crates, you can add up all the drop percentages to get your overall chance for failure. Let's look at an example.
If you want one mount that drops 5% of the time, another mount that drops 10% of the time, and a mount that drops 20% of the time, then technically you will get "something" at a 35% drop chance! If you buy 80 Crown Crates, that's (1 - 0.35) to the 80th power, which is a number so close to zero that you won't even recognize the notation for it unless you remember all of your highschool math. Naturally, it's not so low that there won't be, on average, someone who still fails despite the high drop chance, but it will happen very rarely. Maybe you don't want to buy 80 Crown Crates, though? Let's try just 40. Nope, still too close to zero to be worth mentioning! How about 20 Crown Crates? AHA!! EXPOSED! Oh, wait, that's 0.01% chance of failure. It's still going to be terrible for somebody
, but it's very unlikely. Even by buying only 10 Crown Crates, you come out with only a 1.3% chance of getting nothing. So clearly the more things you actually want in the store and the better the drop chance of the individual items, the more likely your gamble will pay off.
Don't forget about Crown Gems! You can calculate your chance of getting Crown Gems if you know the drop rates of items already in your Collections UI. Then you can just plug that into the formula and find out your chance of failure to get Crown Gems (or, again, just subtract that from 100 to get your % chance of getting Crown Gems). If you consider Crown Gems to also be "something" instead of "nothing" you can even add it to your previous calculation regarding your overall chance of getting at least something you want, be it a mount, costume, pet, or Crown Gems.
Now, for some risk-averse players like myself, these RNG systems are all pretty scary and undesirable. ZOS has made great strides to modify the RNG so that as you complete the content you are more likely to be rewarded with something at least close to what you want, like the changes to Undaunted Helm drops. There's still some chance for a much narrower type of failure, but it is much better than a real chance of complete failure. This makes completing both new and old content much more rewarding from a progression standpoint, on top of the already thrilling feat of victorious combat. Other systems, which still offer a chance for what could be considered "complete failure", are less impressive. But at least now you can make a more informed decision while you interface with the various RNG systems in the game.
Here's that formula again, for anyone interested.
Also please don't just talk about the Crown Crates, I don't want this thread closed down for "duplication", lol. Mention the other systems as well!