W.A.R.B.I.S. Armour - Too Long To Get With Current Blueprints Drops

[Wumpair]

Beta thoughts and introduction:

I would like to start by saying that I am enjoying this beta a lot! It is truly spectacular work, good job Klei!

Nevertheless, there are some things that need tweaking; that is what betas are for essentially.

I've seen people complain that waiting one in-game year to get one of the three new boss items is too slow (I second that, btw); but I haven't seen people talking about the W.A.R.B.I.S. armour that much, so I thought to throw my hat into the ring. 

About me: Aside from DST, I love mathematics! In fact, I am currently in my 2nd year pursuing a degree in statistics. And I see a problem with the way you obtain the new W.A.R.B.I.S. armour.

How do you obtain the W.A.R.B.I.S. armour?

• Once the rifts on the surface are active, Wagstaff can spawn around the player from time to time running in a direction.

• Following Wagstaff can lead you to a setpiece with 3 structures.

• Breaking each structure can give you 1-2 scrap metal (needed for the armour) and a 20% chance to get a blueprint to learn the new armour.

You need 3 blueprints to get the entire armour set: The body, the head, and the repair kit.

And this is a problem, a 20% chance for getting a blueprint is too low, which results in having to repeat this mini-game too many times. How many? Well, for that, we need the power of Probability!!!

Mini-lesson on statistics and probability:

In math, there are some probabilities we can calculate theoretically using certain distributions. Like throwing a "fair" coin, you can get either heads or tails each with a 50% chance; and counting how many heads you get if you throw the coin N number of times (e.g.. 100) is called a Binomial distribution. For these theoretical distributions, we have formulas, you just need to know certain parameters like the probability of getting heads or the number of throws.

We focus now on the "Negative Binomial"; it counts the number of times you lose, before winning "r" times. We need to assume that the probability of winning is identical (p) and the cases are independent from each other.

This is exactly what we need if we want to know the probability for the variable "X"="Getting 3 W.A.R.B.I.S. blueprints from the new structure, after not getting it r number of times"

X follows a Negative Binomial distribution, with parameters r=3 and p=0.2 (chance of getting the blueprint).

Side note: I am not considering that you could get the same blueprint (e.g. Head, Head, Body), although from my testing it can definitely happen! For now, let's consider that you get what you want without repetitions; further down is an experiment in game, with results of what happens in reality.

Using the formula of the Negative Binomial we can calculate the different probabilities (If you would like to know from where it comes, you could start with the Wikipedia article: https://en.wikipedia.org/wiki/Negative_binomial_distribution)

The theoretical chance of getting blueprints:

Probability of losing k times, before getting r wins:

Spoiler

We could start putting numbers at random, but let's be systematic and consider how many structures you will have to break regardless, just to be able to craft the new armour.

Each part costs 8 scrap metal, and I assume you would like a couple of repair kits, let's say at least 2. That means that you need around 18 scraps.

If each structure gives 1-2 scraps when broken, in the best case scenario you would need to break 9 structures, in the worst case 18; assuming you have "average" luck, you need to break around 13-14 structures. Since the structures come in sets of 3, let's say you have to break around 15.

So, what would be the probability of getting the blueprints after breaking 15 structures or less (a.k.a. doing the event 5 times!)? Well, 3 structures would need to contain the blueprint, which leaves us with k=15-3=12 that don't. Putting the numbers in the formula we get, drum roll please.... 60.20% 

This is too low, it basically means that by the time you get the scrap you need to make the armour (After doing the event a grand total of 5 times), you may not even have all of the blueprints yet and won't be able to make it!

And if you consider the fact that DSTogether and multiple people would like to have the blueprint, this process becomes quickly tedious.

This is too low, it basically means that by the time you get the scrap you need to make the armour (After doing the event a grand total of 5 times), you may not even have all of the blueprints yet and won't be able to make it!

And if you consider the fact that DSTogether is a multiplayer game, and if multiple people would like to have the blueprint, this process becomes quickly tedious.

Experimental probability:

A beta is a beta for a reason, so we can try to how things are in the actual game, not just theoretically.

As a man of science, I ran an experiment (A small one, but practical and repeatable).

I counted the number of times I would have to do the new "event" to get all 3 blueprints, and how much scrap I would end up having by the end of it; repeating it 10 times.

For each sample I generated a new world, and I counted both the time it took me to get 3 random blueprints (Events_For_Any_Blup) with the respective junk gained (Junk_Any_Blup), as well as the time to get the three blueprints you need (Events_For_Needed_Blup) with the junk gained (Junk_Needed_Blup).

The table below shows the results.

As you can see, on average you have to do 5.3 (6) events to get 3 random blueprints, and by that time you get around 18 scrap. These numbers are really close to the theoretical value we calculated earlier; and I feel like doing the event 6 times is already too much.

But it gets even worse, cause in reality we can get duplicate blueprints. It actually takes around 8 events to get all 3 blueprints, and you get so much scrap you don't even have a use for them anymore.

Sure, sometimes you "get lucky", and only have to do the event 4 times, like in sample #8. But as you can see in sample #9, you can be "unlucky" and have to do 18 events!

Now consider the fact that the structures have a re-spawn timer and that you have to run around the world to find them. And then go back to the idea that the game is multiplayer.

Repeating the "event" so many times is too much; it would be much more fun to be able to craft the armour once you have enough materials, and not make it so rng based. Running around the entire map is not exactly the most fun exercise.

What can be done? (Ideas)

1. Increase the chance of getting a blueprint. If you at least change the probability to 30% from the original 20%; suddenly the chance of getting 3 blueprints in 5 events or less is 87.32% instead of 60.20%. Definitely better, but you still could get repeated blueprints.

2. Make it so you get all 3 blueprints at once instead of one at a time. Then we would have a 94.50% of getting all the blueprints in 5 events or less. You still need the scrap to make the armour, so you would repeat the event regardless, so it wouldn't be "OP" to gain all the blueprints at once.

3. Make it so you can deconstruct the structures with a green-staff, guaranteeing a 100% drop rate of a blueprint if you do it this way. (This content is late game regardless, so this is “not-too-expesive” in my opinion)

Thank You!

And with that, I leave this thread to the mercy of the forums. As a statistician, I think 60.20% for doing an event 5 times is too low; I sure know that if it stays that way, I won't bother going after the armour myself, as it isn't worth the time invested.

One more time, incredible beta Klei! 

[ZeRoboButler]

wow, best explanation I've seen in a while, I would love to see any of the the three solutions to be put into action. (the decon-staff is my favorite)