10 years ago

Why Drop Rates Seem So Low and Cruel – Math and Psychology

Introduction
We’ve all experienced it: you sim 6 nodes to get a shard and none drop. Or you buy a 120 energy refill and try 15 times to get a purple bit and get none of them. And it always seems to happen at the worst time, such as when you only need one more item. It’s infuriating, and it makes it seem like the game is bugged, or even nefariously programmed against your interests.
The CG developers have denied any sort of manipulation of the odds. And when I look at numbers over a long time I believe them. So what’s really going on here? A combination of phenomena: random numbers are weird; probability is hard to understand; and people’s perceptions are colored by biases they often don’t realize they even have.
I hope the following helps some of you understand what’s going on here. Please don’t view this as me lecturing from on high, incidentally, because I’ve fallen prey to all of these things myself.

Random Numbers are Weird
People do not understand random numbers. In fact, people are so bad at understanding them that humans cannot generate truly random numbers. (Try it yourself: attempt to come up with a list of 10 random numbers between 1 and 10. You will find that after the first couple, you will be thinking about what number should come next. You will be influenced by what the previous numbers were. The results will not be random. In particular, humans will tend to “distribute” the numbers to something that seems random, fearing that duplicates are not “random enough”. As an example, I just used a computer to randomly generated these numbers: 1, 1, 2, 4, 3, 3, 4, 5, 8, 4, 3, 1. No human would generate a sequence like this because there are so many duplicated numbers, and all but 1 is 5 or below, so it seems “unrandom”.)
A major confusion comes in the form of believing that if a random chance has a particular value that this means you should always, or usually, get the stated percentage. So if there’s 1/3 chance of a shard dropping from a hard mission, simming it 3 times should always or usually give 1 shard.
The truth is that random numbers are unpredictable and do not tend to follow consistent patterns (see the example 10 numbers above). Long stretches of uneven results are not only normal, they are expected. In the case of a 1/3 chance of a shard and 3 hard missions, the chances of getting exactly 1 shard are actually less than 50%. More than 50% of the time, you will get some other value (0, 2 or 3).
Streaks are also entirely normal with random numbers. This is what makes people think that there are bugs, or the game is cheating against them. Here’s an example. Yesterday I decided to keep track of enemies in GW/Arena when Old Daka was on the team to see how often enemies self-revived. The nominal odds of this are 10%. At one point, I experienced a streak where there were 7 self-revives out of 25 kills in only 5 games. That’s 28%, almost triple the expected number! But then later on, I had another streak where there were only 2 self-revives out of 43 kills, which is less than half the expected value. These streaks are entirely normal.

feedback

57 Replies

Qeltarr
10 years ago
People Do Not Understand Probabilities
One of the reasons why games like this exist, and why lotteries and casinos make a fortune, is that probability is hard to understand. People tend to make assumptions about odds that are false. They also tend to believe they have a better chance at a good outcome than they do.
Lotteries are an easy example. Have you ever noticed that the Powerball numbers always seem to be random, unrelated numbers? For example, they are usually something like 5, 17, 32, 39, 61 and 70. When is the last time you saw a lottery where the winning numbers were 1, 2, 3, 4, 5 and 6? If this ever happened, it would make the news, people would scream and claim that the game was rigged. In reality though, that result is just as likely as any other. Think about how many times you have seen lottery numbers and how you probably never have seen a regular pattern like that (or 1, 3, 5, 7, 9, 11, etc.) That gives you an idea of just how unlikely it is that you will ever strike it rich.
People also again expect to see odds “even out” over time, which doesn’t always happen. Each random occurrence is independent of the others, and the cosmos is not keeping track. While over a long time the average will tend to converge to the probability rate, this is because the numbers get very large so differences become less important in percentage terms. It doesn’t mean that after a long stretch of misses on a sim that you are “due” to get shard drops. This is called the Gambler’s Fallacy, and has made many people walk out of a casino with their pockets empty and a sour look on their faces.
Let’s think about those hard missions again. You have probably simmed a hard mission 3 times and gotten 0 shards and felt frustrated. And then said to yourself: “How come I get 0 so often and never seem to get 3? I should be getting 3 sometimes to offset all these 0s!” I’ve been there. Would you be surprised to learn that, if the chance is really 1/3, the odds of getting a 0 result are 8 times higher than getting a 3 result? That’s how the math works out. In fact, with a 1/3 chance, you should get 0/3 almost 30% of the time. That’s why it happens so often.
(Full odds assuming 1/3 chance: 0/3 result 8/27 times; 1/3 result 12/27; 2/3 result 6/27; 3/3 result 1/27).
What about double-simming two hard nodes, so 6 tries? Assuming 1/3 chance, you should get 6/6 only 1 out of 729 tries. The game’s only been open for something like 45 days, so if 6/6 has never happened to you, that’s why: the odds say it shouldn’t. But the odds of getting 0/6 are only 1 in 11, or 64x as often as a 6/6 result. So you should have had this happen, on average, at least once every two weeks. That’s why it seems like the game isn’t being fair.. it’s just the math not being fair.
Now this assumes a 1/3 chance of a drop. If it is lower, as I suspect, things get even worse. If the odds are 1/4 to get a drop, then your chances of going 0/3 increase from 32% to 43%. Your odds of going 3/3 decrease from 3.7% all the way to 1.6%.
If the odds of a purple item dropping are 15%, then if you sim 15 times, you should go 0/15 8.7% of the time, or about once every 12 refills. If you refill 3 times per day, you should expect to get 0/15 every few days.
Qeltarr
10 years ago
Confirmation Bias
This is a scientific term that describes the tendency of people to assign more weight to outcomes that match their preconceived notions than outcomes that contradict them. Simply put, when something happens that matches what we expect, we notice it and tend to use it to confirm our beliefs. When something happens that doesn’t match what we expect, we tend to either not notice it, or disregard it as being “atypical” or otherwise not relevant.
For example, I’ve read several comments over the last few days that “drop rates have been reduced since the update”. This is possible, but I doubt it. I don’t notice any difference. But if you are convinced that this is the case, you will tend to notice cold streaks much more than hot streaks and believe that this is proof that your theory is correct. This isn’t malicious, it’s just how most people work.
This sort of thing also leads to superstitions that get passed around, usually when something happens out of coincidence but a person finds a pattern that they believe explains it. For example, yesterday I saw someone say that if he is having a cold streak trying to farm a purple gear item, he goes and does something else and then comes back and has better luck. No programmer would write code that works in this way, so this is purely psychological. (It’s actually good advice, but not because it actually works, but rather because it encourages you to cool down rather than getting aggravated, so you view things more clearly.)
Another example: when I was having trouble getting Dooku shards someone suggested to me that I not do Dooku first but rather some other character I cared less about, and come back and do Dooku later, because he had better luck this way. I tried it, and it made no difference at all. Again, I highly doubt the developers bothered to tweak the odds based on what order you sim missions. It’s just a cognitive bias he developed because he had better luck doing Dooku later in the day a couple of times.
Qeltarr
10 years ago
“Red Light Syndrome”
We tend to notice things more when they are unusual, when they are annoying, and when they happen at what seems like a bad time.
Ever tried to drive somewhere and you hit every red light? Ever noticed that this always seems to happen when you are running late or in a hurry? Of course the traffic lights don’t know anything about your schedule. You just notice the red lights more when you hit a lot of them, and especially when you are in a hurry. I’ve actually tried to look at this phenomenon and noticed that sometimes I actually hit all the green lights. But I have to pay attention to notice them. When I hit all the red lights I need no effort to notice it.
This happens in games as well. You notice the 0/6 because it irritates you; you notice the 4/6 much less because it’s a good outcome (and also because you “expect it” since you are “overdue” from having so many 0/6 results).
I have in the past remarked that I never seem to get 3/3 from hard missions. Yesterday I paid close attention and it happened to me 3 times, on different characters. But I probably would have glossed over it if I hadn’t deliberately been paying attention.
The “in a hurry” part comes in with a game when you are trying to get that last shard or item drop. You have 79/80 shards and you sim 10 times and get 0 drops. Clearly the game must be deliberately torturing you by lowering the odds! It’s not true. I’ve actually examined this and found no difference in drop rates as I approach an unlock point. It just seems this way because you are paying much more attention to shard #80 than, say, shard #17.
So, no, the game is not trying to prevent you from getting that character you want. You are just noticing every failed attempt because it's important to you.
The same thing happens when you are running low on a resource. Say you only have enough energy for 4 tries at something.. you'll notice if you fail at those 4 much more than 4 tries first thing after a refresh.
maxfifafan
10 years ago
Wow that's a lot to take in
Very good, constructive post tho!
Good job OP
JohnSalera
EA Staff (Retired)
10 years ago
Holy cats! Awesome work, @Qeltar!

Stickied this for future reference.
roshandita
10 years ago
tldr;

Drop rates sucking have nothing to do with biases and everything to do with what the developers set those drop rates at.
cptkloss
10 years ago
"stupidfatfool;58395" wrote:
tldr;

Drop rates sucking have nothing to do with biases and everything to do with what the developers set those drop rates at.

yep...not sure why this long epistle...

"If the odds of a purple item dropping are 15%" meaning true cost of 1 purple is 40 energy or so...
with upgrades that cost 50 energy or 2000 energy, or a week give or take (excluding refills) you can clearly see it's just an artificial way of obfuscating the lack of content. No apologetics will hide this...
Qeltarr
10 years ago
I said right at the beginning that I have been led astray by these things myself and wasn't claiming otherwise. So it wasn't really necessary to dig up old posts of mine to make me look bad. I wrote this essay at least as much based on observations of my own behavior as that of others.

I do thank you for the kind words on this post.
cosmicturtle333
10 years ago
YAY! Now I have a link to spam at people when they complain about drop-rates.
secondclaw1
10 years ago
Thanks for the writeup