RNG and drop chance is one of the most misunderstood and also frustrating topics for players in Warframe. This not only because of the maths involved but because of many half-truths found on the Warframe subreddit and in the official Warframe forums. Players tend to confuse the drop chance which belongs to probability with school-taught use of percent in calculus. Let’s look a bit deeper into this topic. If you prefer a video instead you can head to the video at the end of the article.
What RNG means
RNG stands for random number generation and simply describes a tiny piece of software tossing the coin or rolling the dice for you. There is nothing fancy about this and in most programming languages it is just one line of code that decides about your luck.
This is how a success drop is calculated in the programming language Java:
In Warframe this kind RNG is used after every enemy encounter, after every boss fight or fissure run, to name just a few.
RNG in drop tables
Whenever a drop in Warframe can happen it follows defined drop tables. Drop tables mostly have multiple items that can drop. The common drops will mostly likely happen all the time. The uncommon drops occasionally and the rare drops will happen only after many repetions or a long time of playing.
Take for example Arbitrations rotation A where the rare drop is the Adaptation mod. You get this drop only after many many missions whereas the common drop of 1300 Endo will happen most of the time.
Warframe’s drop tables are public and can be accessed by everybody who interested at this link.
Most things that can drop will be in this drop table. Just use CTRL+F to search in the site. They contain the drop chance in percent that give you an overall “feeling” of what common, uncommon or rare means. To really understand and appreciate those numbers we have to do some more exploration of the maths involved.
Down the rabbit hole of probability
As said before RNG means that a piece of software is rolling the dice for you. Given that noone has manipulated the RNG software this digital dice rolling represents a perfect die that is rolled by a perfect hand on a perfect table. And thus the results of each roling are bound by the rules of probability.
Here are the most important facts about probability using the die example:
- Each time you roll the dice your dop chance stays the same. If you want to roll a 6 there is a 1 in 6 chance each time the die is rolled.
- 1 in 6 can be written as a fraction 1/6. That fraction is 0.1667 which is in turn 16.67%. A 16.67% drop chance is just for the definition and has nothing to do with how probability actually works.
- 1 in 6 is an average if you repeat something long enough. Long enough means thousands of times. You can test it for yourself with a die and roll it 6 times and will most likely not get each number once.
- There is absolutely no pattern when the number 6 will appear when you roll the dice.
If there was a pattern that could be calculated we would not have a gambling industry that makes decent money from people being unlucky. If someone thinks there is pattern that person has fallen for what is known as as Gambler’s Fallacy.
Combination to spice up probability
That last paragraph might have struck you because when playing games with dice you intuitively know that a 6 will appear after having rolled that die 20 times without a 6. You are totally right and it does not violate the rule of no pattern. A pattern would be something you can calculate and make exact predictions.
What you and me experience when rolling a die repeatedly without getting a 6 for a long time is called: Decreasing the probability of being unlucky. In math terms this is called combination and we can calculate it. But – a big but – there is a limit to that calculation because probability will never allow us to make a 100% probability prediction. A 100% prediction would be a pattern and we do not have a pattern.
So we can calculate how the probability that something will happen increases over time but at the same time have no clear pattern. That is confusing but that is at the heart of it. And it is at the heart of it because it is probability.
To bring out the die example. After 25 dice rolls you and the vast majority of all human on this planet beings should have seen a 6 at least once. But it is perfectly possible to not see a 6 after after 100 rolls for hand full of people on this planet.
Using combination and understand its meaning
We can and will use combination to calculate the probability of getting an item with a defined drop chance through repeated runs. The results of combination is a good indicator of what to expect. But let us not forget, it is just an indicator and not a reliable number.
This is the formula that is used to calculate the probability of not failing after X runs:
1 – ((1-dropChance/ 1)^numberOfRuns)
The result of the above formula will always be followed by “chance of getting the item at least once”. Thus indicating you could have gotten the drop even earlier.
By turning the formula upside down – using logarithmic calculations – we can make a statement about the number of runs it will take you to have 90% or 99% probability. The 90% probability is what in most video games is considered the expected number of runs you have to do to get an item at least once. The 99% probability is what in most video games is considered as almost guaranteed number.
If we take the Heavy Caliber mod as an example. It has a 4.35% drop chance upon open an Orokin Vault. You have to do 52 runs to have a 90% probability to have at least one drop of Heavy Caliber. That is the expected number of runs. But you have to do 104 runs to get to a 99% probability to get at least one drop. So, 104 runs to have nearly guaranteed drop.
Can you still not get the item after you repeated the number of runs that are calculated with 99% probability? Sadly yes and it is called bad luck. But it will happen very very rarely.
Just use my dropchance calculator
I build a drop chance calculator that will do all the math for you. You just enter the drop chance and it will tell you how many runs you have to expect and how many you might have to endure for nearly guaranteed.
You enter the drop chance, hit the calculate button and it will give you the result. This will help you to make an educated guess how much time you have to invest.
Drop chance in percent works differently than your everyday percentage calculation and that is what people get confused about. Drop chance percent should be understood in the context of doing thousands of repetitions.
A 10% drop chance does not mean after 9 runs it should drop. A 10% drop chance mean that after a thousand runs around 10% will have given the drop without knowing the time of the drop. That could mean you do not see a drop for 100 runs and after that 10 times in a row.
Use the drop calculator to get a feeling of the expected and nearly guaranteed drop to understand the number of runs that is required.