Bow Down to the RNG!

How RNG REALLY Works...

By: Brian Randich

a/k/a Brian_R

Brian has come out of his corner and decided to write his first article!  Now with 120% of your daily value of math!  Okay, so it’s more like 500%.  But, perhaps, you will learn something about basic statistics which you can apply to other things in life.  Like video games, which is probably the last place anyone thought they would ever use something they learned in school.  But that’s what I do:  I destroy your dreams and tin foil hat conspiracies with math and science!!  Since I already destroyed “109’s are doing more damage this week than last week,” it’s time to tackle the second popular conspiracy theory:  rolling for rogue crews.

Over on another "blog", a player did some simple experiments with rolling rogue crews to observe an approximation of how often they would come up.  The key word is approximation.  Every roll is different, and every roll is independent of the other rolls.  The second part is key, and is called the “Law of Independent Trials.”  You can roll a die 20 times and get no 6’s, but the odds of a 6 coming up the 21st time are exactly the same as the first 20 (unless you have a loaded die, but that’s cheating.  No cheating.  Bad!)  Also, yes, the crew you get always lands RIGHT BETWEEN THE TWO CREWS YOU WANTED OMG!  That is a psychological ploy to make it more attractive to keep rolling since you were SO CLOSE to that Grease Monkeys crew.  In practice, that rarely matters, as you’re going to keep rolling until you get what you want or run out of uranium anyway.

My major issues with the article (other than the simple failure of basic math, as 170+226+391+403=1,190, rather than the stated 1,447) are 1. the attempt to take this or any sample as gospel and 2. some faulty conclusions.  The Law of Large Numbers states that the average of the results obtained from a large number of trials should be close to the expected value, and will tend to become closer as more trials are performed.  If you flip a coin one time, or ten times, or a hundred times, you could get landing on heads every time, or at least far more than half.  Do 1,000, 10,000, or even more, and you are likely to come out closer to an even split of heads and tails.  Even a sample like this, over 1,000 rolls, can hardly begin to determine the actual probabilities (including the Disciples of Skullduggery crew, but more on that later).

Now we tangent to talk about the binomial distribution, as it’s going to be very helpful here and can also help determine the minimum amount of evade needed to avoid a certain number of missiles given their chance to hit, which needs their accuracy and your evade to calculate chance to hit, the number of missiles, and the number of hits, or how to avoid a shockwave building up on your Prides.  The binomial distribution is a way of computing the chance of getting exactly k successes in n trials with a probability of success p.  It looks like this:

Why does this matter?  We can use this to determine just how likely some of the rolls in this sample are.  

In the overall sample, a Bullseye Brigade was only found 3 times.  Even counting this against their own total, this has a 22.43% chance of happening, based on the above equation.  Small chance, isn’t it?

In addition, since you can store enough uranium to do 409 rolls, let’s do the math that you’ll get a Bullseye Brigade crew in a full stock of uranium, assuming the odds of 3/1447 (0.21%) to get one are correct:

P(getting at least one BB) = 1-P(getting no BB’s) = 1-binompdf(409,3/1447,0) = 0.5721

You have a 57.2% chance of getting a BB crew when you roll a full WH of uranium, if their math is right.  If you believe the math is right, your chances of getting some of the rarer crews are just that:  rare.  Nobody wants to sit there and roll nearly two full stores of uranium for a reasonable chance at one rare crew.  If you go with the Law of Large Numbers instead, you do not put faith in this math as a representation of the actual chances.  

My other main concern is with some of the conclusions.  From said article:

“Here are the averages that matter:

• 37% for rolling a Common Crew 
• 61% for rolling an Uncommon Crew
• 1.5% for rolling a Rare Crew 
• .41% for rolling a Legendary Crew”

Not exactly 100% due to rounding, but that happens sometimes, no big deal.  Combine this with the following statement, and we have a problem.

“But the biggest shock from it all?

• The average chance of rolling a common crew is higher than an uncommon crew.”

That is not a shock.  That is how English works.  It should be more likely to roll a common crew than an uncommon crew, even across particular types of crews.  It is also a bit misleading when paired with the above statistics, but is explained more clearly when comparing common crew rolls to uncommon crew rolls.  Again, this is how things should be.  A particular common crew, if not most common crews, should come up more frequently than most, if not all, uncommon crews.  The weighting is supposed to be somewhat in favor of the player because they are spending more uranium, but descriptions from Kixeye are often vague.

“Gearheads isn't the most common crew either, it’s Lucky Bastards at 5.6%, more than any uncommon crew. Which, isn't right at all.” 

While that does fit most of our subjective experiences, it also makes sense that a common crew is the most common to roll of any variety of crew.  I’m more surprised that in that sample, they rolled about 1.65 uncommon crews for every common crew.  

The complaints about Disciples of Skullduggery (DOS) have mostly died down.  But why?  Surely any player that rolled one would brag about it online, right?  Maybe not.  From the field of psychology, “herd mentality” refers to how people are influenced by those around them to adopt certain behaviors.  Basically, peer pressure.  (Don’t do drugs, kids!)  Even a generous estimate of one-third of the total players that are playing BP and frequently roll for crews are on any given facebook page to brag about it mean that if a DOS crew is rolled, it goes unreported two-thirds of the time.  If the person can report it, they may not, because the internet would likely spot hateful, jealous comments at them for their good fortune, and ain’t nobody got time for that negativity!  In addition, confirmation bias states that people would seek out opinions or ideas that match their own.  A big mass of comments on a post that are little more than “I agree” is a great example, and one a lot of people reading this have already seen.  Also, in general, people tend to exaggerate their misfortunes, either unintentionally or intentionally, in order to gain sympathy on the internet, which is not the place one should go for sympathy.  Even if one DOS crew was rolled in that entire sample, the odds of NOT getting one if you tried that number of rolls for yourself are still 36.8%.  Is rolling a DOS hard?  Yes, and it should be.  But I do not yet believe it impossible.  

So, there you have it!  Rolling for a specific crew takes a long time and a lot of uranium.  But you knew that already, right?  Sometimes it takes three full stores of uranium and you don’t get a crew you want, and sometimes it happens on the first roll.  It all averages out in the long run, although even a lifetime may not match up with the specific probabilities crews are assigned.  But with the Tideseeker and 100 and 200 elites to get the sector to orange easily and Ironclads to do DUBs, uranium is a lot easier to get.  Tideseekers do Reaver armadas on auto.  So get your uranium and keep rolling, you might find what you need sooner than you think.