Mathematical analysis of the new loadout crafting system


(ArsonistCow) #1

These numbers are still subject to change (it’s a beta after all)

TL;DR:

[list][*] Cost of all rarities reduced by 12 to 22%; Cobalt -12%, Gold -14%, Silver -20%, Bronze -22%, Iron -17%.

[*] Cost of “trade ins” reduced by 35 to 77%; Cobalt -35%, Gold and Silver -73%, Bronze -77%.

[*] Trade UP value of ALL loadouts is decreased.

[*] Overall RNG increased; Higher drop-rates means higher variance in value of each tier. The old system also allowed you to keep good loadouts that you got in the trade up process toward Cobalt, while the new system doesn’t allow for “partial” upgrades without significantly reducing efficiency.[/list]

[s]What to do before the new system lands:[/s] <-Too late now

[list][*] Trade UP any bad/unused loadouts. (use this guide for reference if you’re unsure)

[*] Don’t trade IN anything.

[*] Don’t buy any cases.

Spreadsheet with all the math and numbers can be found here.
I’m 100% sure the math for the old/current system is correct as that has been verified by several people with several methods of calculation. I’m pretty sure the new calculation is correct too, but more verification is always nice.

Crafting kits: 1 for 0.99$, 5 for 4.49$ (0.898$/kit) and 10 for 7.99$ (0.799$ per kit). Each kit can be used to replace 5,000credits worth of upgrade cost (i.e: 1 for Silver, 5 for Gold, 10 for Cobalt). This translates to a conversion rate of 5051 to 6258 credits per dollar(depending on which pack), compared to the 5005 credits per dollar of purchasing mercs. So if you buy them in packs it’s a slightly more efficient way of spending money than buying mercs, but still less efficient than buying Elite/Expert cases.

Overall I think the new system comes with some great improvements, but also some issues that really should be taken a look at:

Crafting Iron loadouts is pointless (unless you specifically want to avoid a perk). 500 credits is pretty much half the value of an Iron card, so why would you throw away that value by crafting an Iron loadout? If the crafting cost was something like 100 credits you’d only be throwing away ~10% by crafting it. This would make it reasonable to craft Iron loadouts as an intermediary step between Default and Bronze loadouts. And a great thing about the crafting cost of Iron loadouts is that it can be changed without having any effect on the rest of the economy; it’s a super-easy tweak.

While the increased drop-rates are nice (less Lead-poisoning, woop) they also result in more RNG, which I am not a fan of. Same thing with not being able to keep good loadouts in the trade up process; it increases RNG. Sure, this is partially mitigated by the cheaper trade ins, but trade ins are still pretty bad value-wise, and crafting a low rarity card becomes a huge loss if you want to recycle it later for crafting a higher rarity loadout. I think there’s still room for improvement there.


Here’s how I would solve these issues. (+refine a few things)

All rarities divide evenly with each others’ fragment values, to make the crafting process more straightforward.

All rarities except Cobalt recycle for the same number of credits they cost to craft, effectively making their “trade in” costs the same as their crafting credit costs (once again reducing complications).

Cost of Silver, Gold and Cobalt increased by ~10% to compensate for cheaper trade ins (still cheaper than old system).

“Trade in”/crafting cost of Iron reduced to 100, which is roughly the point where it actually becomes a reasonable choice to craft an Iron loadout as a stand-in before you have the resources to make a Bronze loadout.

“Trade in”/crafting cost of Bronze reduced to 500. This will allow people to more easily grab the loadout they want or get rid of unwanted loadouts without significant loss in credit value. Another very helpful change for new players.

“Trade in” cost of Silver and Gold reduced to 5,000 and 25,000. I’ve set these to roughly a third of their overall credit value.

“Trade in” cost of Cobalt reduced to 163k (from 219k); about half the cost of a Cobalt. This doesn’t need to be as low as a third of the total value (like with Silver/Gold) since Cobalt is the end of the line.

Overall these numbers will increase the cost of high rarity loadouts slightly, but decrease the cost of getting a specific loadout across all rarities by making “trade ins” better value. And this decrease in RNG will help combat the increased RNG this new system will have due to higher value-disparity between rarities and the loss of partial upgrades.

Oh, and for anybody curious about what I mean by “soul-crushing” calculations, here’s the full formula for the cost of Cobalt with the old system :smiley:
1000/(((((0.8/3+0.15)/3+0.03)/4+0.015)/4+0.004)/6+0.001) + 0.8/3 * 500 /(((((0.8/3+0.15)/3+0.03)/4+0.015)/4+0.004)/6+0.001) + (0.8/3+0.15)/3 * 1000 /(((((0.8/3+0.15)/3+0.03)/4+0.015)/4+0.004)/6+0.001) + ((0.8/3+0.15)/3+0.03)/4 * 2000 /(((((0.8/3+0.15)/3+0.03)/4+0.015)/4+0.004)/6+0.001) + (((0.8/3+0.15)/3+0.03)/4+0.015)/4 * 4000 /(((((0.8/3+0.15)/3+0.03)/4+0.015)/4+0.004)/6+0.001) + ((((0.8/3+0.15)/3+0.03)/4+0.015)/4+0.004)/6 * 10000 /(((((0.8/3+0.15)/3+0.03)/4+0.015)/4+0.004)/6+0.001)

New formula is a bit better:
(1000 + (0.669 * 15+0.23 * 45+0.075 * 135+0.02 * 540+0.005 * 2150)/20000 * 50000)/((0.669 * 15+0.23 * 45+0.075 * 135+0.02 * 540+0.005 * 2150)/20000 + 0.001)


(FireWorks) #2

Thanks for typing it all down, you just saved me a lot of work :slight_smile:


(bontsa) #3

This should be darn stickied and even represented in DB’s main menu news. Would call it a day with the bloody bwaabwaa whine-with-cheese threads so we could instead have actual discussion about cons/pros and tweak suggestions. Please @Amerika @Ardez @RazielWarmonic @Eox ?


(The_N00Ba) #4

A calm discussion would be wonderful I think. I am not sure about some of the numbers on that sheet though. They don’t match what Exedore posted before. What am I missing?


(DB Genome editor) #5

In short, Exedore’s number are based on getting 100% Lead from cases, while the number above seem to take into account the true average value of a case (the fact that for instance 1 in 1000 will give you a Cobalt to recycle rather than a Lead).


(Eox) #6

I wouldn’t mind to pin that, however I don’t think I am allowed to pin whatever comes through my mind. I’ll ask @RazielWarmonic if it’s worth a pin when she’ll be available first.


(bontsa) #7

I just thought it has enough effort behind it to be worth it (also quite hot topic at the moment) so it was merely my (hasty) opinion, sorry to abuse the call system for such :smile: I was pretty done with lifestuff and salt levels werent exactly helped by the amount of useless bish-bosh on forums about this crafting, I should’ve just stayed away instead of getting ahead of myself pardon me.


(The_N00Ba) #8

Not to sound like I am trying to be elitist or rude in any fashion but I have a bachelors in mathematics and the math used for that spread sheet does not flow well with me. Something feels way off. professionally as a mathematician I can not recommend using it as a piece of evidence until I understand the numbers better. i advise caution for any one who does. :slight_smile:


(AnonOmis1000) #9

inb4 you get shit on by the rest of the community.


(MisterBadmin) #10

I did not do the math, the below are assumptions I’ve made from reading the methodology. Please do correct me if I am wrong.

I believe the calculations assign a value to each level of card, in credits, based on the odds of them dropping from a case, so a weighted average of the values yields the cost of a case, 1000 credits. I think these values are used to fill cost columns.


(The_N00Ba) #11

K I have worked through it. MisterBadmin I agree the weighted average of the values is being used. Unfortunately it appears the chances for cards equal to and above the card rarity you are trading for as still being included in the calculations for the old system. i find that cards equal and above the card rarity you are trading don’t technically add to the cost of the card you are making. Furthermore cards of rarity equal to above the card you are trying to make add no components to make the cards in the old system.

this fact normally would zero out those cards when taking the weighted average to determine the average components needed to make the rarity you are looking for using all “lower” rarity cards as possible sources as the formula tries to do, but it was not included.This extra chance throws off the calculation at the start.

From the weighted average we try to determine the number cases needed to gain all the components to make 1 card. The formula produces a decimal number. This number is off due to the other chances for higher rarity cards still being included. The decimal number unfortunately does not correctly represent the system. The system counts cases using whole numbers not decimals. I think the number needs to be rounded up to the next whole number.

It is sadly assumed that the players will pay 1000 credits a piece to gain these cases. While for some this is definitely the case, the amount of free cases dropped and the cases bought with real money are not even considered, which does influence the cost.

From there, the cost of the transactions is added in but the transactions appear to be considered decimal numbers as well. This again does not reflect the system. Transactions are made only with whole numbers not decimals. This lead me to feel the transactions are fixed numbers.

overall the values on the sheet feel to be higher than they should be due to the observations I have mentioned

Again I am not trying to be rude or put anyone down intentionally. Some thing about this drew my attention. i am glad to can finally say my professional opinion is that this is inaccurate to at least one of the systems it is trying to represent. I personally will not trust this.

cheers :slight_smile:


(Xenithos) #12

[quote=“The_N00B;194067”] SUPER SNIPPING POWERS WERE EXTREMELY SUCCESSFUL!

overall the values on the feel to be higher than they should be due to the observations I have mentioned

Again I am not trying to be rude or put anyone down intentionally. Some thing about this drew my attention. i am glad to can finally say my professional opinion is that this is inaccurate to at least one of the systems it is trying to represent. I personally will not trust this.

cheers :)[/quote]

@The_N00B
Holy crap. The_N00B is NOT a Noob! Quick! Someone grab him and make him intelligify everyone! I want your juicy math-inclined brain functions to be mine! :3


(bontsa) #13

I fell off the wagon, got lost and missed the station about halfway through this thread already yet reading these is fascinating. Kudos!


(Xyfurion) #14

@The_N00B I currently have a migraine. Normally I enjoy these things and understand them well. Right now I feel my head is splitting in half. Jeezuz


(HunterAssassin5) #15

NUMBERS!
https://scontent-kul1-1.xx.fbcdn.net/v/t1.0-9/13654231_1326192664075334_3275563293389544492_n.jpg?oh=d99dd4ef36ca7f8158f8fc72e791bc10&oe=57EBA5E1
STAY AWAAAAAY!!!

in all seriousness tho thanks for doing the math i wont even try to understand, you guys.


(The_N00Ba) #16

@Xyfurion his excel spreadsheet or my explanation. lol :slight_smile:

To better understand his table go here

http://steamcommunity.com/sharedfiles/filedetails/?id=613497039

and look at how he did bronze. honestly I don’t feel the layout of his equation helps explain what he is trying to do. I honestly still do not quite know what they were trying to do. To better understand though multiple the fractions through all the parenthesis. You will then get an equation sort of showing the weighted average of the card types in a case but the cards types are shown as their equivalent value of pieces needed to craft a bronze card.

so 1/9 for a lead. 1/3 for an iron. 1 for .05 is not correct as far as I can tell. it could be 1 for a bronze chance but the idea of the equation is to find cost to make a bronze and getting a bronze in a case does not add to cost. so I am pretty sure .05 should have a 0 by it instead of a 1.

that first equation finds the average number of bronze components gained from each case which is a decimal number. This is then used to find the average number of cases needed to gain enough components to be able to make a bronze.

the next two equations cover the trade u costs. unfortunately they treat the trade ups as decimals even though the system does not use decimals only whole number. meaning trade ups use whole cards not fractions of cards.

it is because of the decimals that extra credits are being added to the cost and why i believe the table does not properly represent the systems as they are designed.

this can be even better understood if you took Calculus and understand how taking integrals work.

given the cost function for trading up. the previous system was taking the integral of the function at specific points.

The excel spreadsheet provided however is adding up everything under the curve, including the cost for fractions of cards that technically do not exist in game.

Extra stuff is being added in basically at least as far as i can tell. :slight_smile:


(ArsonistCow) #17

Oh, didn’t get much action in here so I thought the thread was dead.

[quote=“MisterBadmin;193763”]I believe the calculations assign a value to each level of card, in credits, based on the odds of them dropping from a case, so a weighted average of the values yields the cost of a case, 1000 credits. I think these values are used to fill cost columns.[/quote]Not quite.
I calculate the average credit cost of obtaining each rarity or higher (plus sign. Cobalt is highest possible so that average is for Cobalt alone). The calculations include chance of getting each rarity from a case, fragment gain, trade up/crafting costs and case costs.

Nope. No weighing is done.

Those are not weights, those are chances of getting each rarity. 0.05 is the chance of getting Bronze or higher. 0.03 (AKA 3%) chance of Bronze, plus 0.015 (1.5%) chance of Silver, 0.004 (0.4%) Gold and 0.001 (0.1%) Cobalt equals 0.05 (AKA 5%).

[quote=“The_N00B;194403”]http://steamcommunity.com/sharedfiles/filedetails/?id=613497039

and look at how he did bronze. honestly I don’t feel the layout of his equation helps explain what he is trying to do.[/quote]
Well sorry if it’s not easy to look at, but that’s the most eye-friendly layout I could come up with. If you’d prefer the raw formula (for Cobalt) then it’s listed at the bottom of the post:

And luckily the eye-friendliness of a formula has no impact on its correctness.

Wrong already. The first equation finds average number of cases required to attain said rarity.
Here’s the formula for Bronze+:
1/((0.8/3+0.15)/3 + 0.05)

Explanation:
1/((Chance of Lead/3 + Chance of Iron)/3 + Chance of Bronze or higher) = Average number of cases required

Exactly. Which is why I’m including them as equal to the rarity you are trying to get, because if I don’t it would increase the cost of each rarity with the old system as trading down was impossible.

It adds to the cost of rarities with the new system because not trading down higher rarities gives a lower net-gain of fragments.
And in case it wasn’t obvious already: I can’t compare the two systems if I don’t calculate the same thing for both (“same thing” referring to said rarity or higher).

[quote=“The_N00B;194067”]The system counts cases using whole numbers not decimals. I think the number needs to be rounded up to the next whole number.[/quote]Wait, you have a bachelors degree in math and have trouble understanding an average? O.o
Did you not learn any probability math?

I really shouldn’t have to explain this…

Of course it doesn’t have to be using whole numbers because an average is just that: an average cost. If you buy an infinite number of Bronze+ (or higher) loadouts the average cost per loadout will approach 5278.74493927 credits the longer this simulation keeps running.

You’ve made several more comments on the calculations being wrong based on not understanding what an average is. I will not be addressing these; they are irrelevant as they are based on a faulty premise.

Cases dropped from playing are still worth 1000 credits.
And cases bought with real money are have no relevance to the average CREDIT cost of a rarity. It should go without saying that the credit cost of a loadout is the only thing relevant when somebody is sitting on a mountain of credits looking to buy some new loadouts.

And I’m not trying to be rude or put you down, but you’ve written some highly questionable stuff in here. I would not trust anything you’ve written so far.

Then please do something useful and try calculating the average cost using integrals. Because so far you’ve only posted faulty assumptions. Have fun, I’m not even sure integrals can be used to calculate this…


(ArsonistCow) #18

I added a formula and explanation for the old system in the spreadsheet. (instead of the link)

Holler if there’s some part you don’t understand and I’ll try to explain it.

Edit: oh, and I’m shortening the “*(1/” to just “/(” for “Cases required” to cut out an unnecessary part of the equation. X/Y is the same as X*(1/Y). Sorry if that confused anybody.


(Ardez1) #19

So I didn’t read through every reply(sorry!), but could you explain something to me? How do you believe the RNG has increased with this new system?

Overall RNG increased; Higher drop-rates means higher variance in value of each tier. The old system also allowed you to keep good loadouts that you got in the trade up process toward Cobalt, while the new system doesn’t allow for “partial” upgrades without significantly reducing efficiency.

Higher drop rates from what? Cases? Fragments? I’m afraid I misunderstand what you are trying to say here…

In my mind, RNG is purely based on expected output and doesn’t have any relation to input. Understanding the ‘Higher drop-rates’ bit of your statement would go along way towards helping me figure out what you mean overall.

If we now have the ability to cut 2/3rds of the possible results out that is a massive decrease in RNG for me, where before we had zero choice in the matter and there was a possibility of getting any loadout in the pool…

I’m going to break this next part into bite sized chunks so I can try to understand it better.

While the increased drop-rates are nice (less Lead-poisoning, woop) they also result in more RNG, which I am not a fan of.
I wish I knew what you meant by increased drop-rates. Drop rates are generally used to determine how often a particular item drops. In this case it is straight forward and I want to say you are talking about using weapon kits to reduce RNG, but I still want clarification. I don’t see how better odds increases RNG.

Same thing with not being able to keep good loadouts in the trade up process; it increases RNG.
If a players goal is a Silver SM41 Nader, they can go directly for a Silver SM41 Nader. If a players goal is a Cobalt SM41 Nader, then they have no use for a Silver SM41 Nader. I can COMPLETELY understand your point on this one. You don’t randomly get the card you want during the process, but at a lower rarity. HOWEVER, if your goal is for a SHINY version of a card(and not just the loadout itself), then you do not want a lower rarity. Overall RNG has decreased based on this new system. Think about it. You want a Cobalt KE43 Proxy or something like that. You performed all of the Lead->Iron->Bronze->Silver->Gold tradeups. MAYBE you get 1-2 copies of KE43 Proxy in that mix. You still have DOZENS UPON DOZENS of FAILURES. The RNG is actually worse then just going for the cobalt directly. You are purposely excluding the dozens of other trade-ups you need to do to MAYBE get that loadout you actually want in cobalt at a lower rarity. That is not decreased RNG, that is simply low odds of a specific event happening one of out of nine times.

You do, let’s say 30 trade ups on the way to Cobalt Proxy. You get 2 KE43s and the rest are trade up fodder. You don’t care about the bronze KE43, because you managed to get a Silver KE43, so that is trade up fodder as well. Your rationale is that because you got the loadout you wanted it is a ‘success’ and ‘less RNG’ even though you didn’t get the card you actually wanted in Cobalt AND you had a huge pile of failures/fodder. During this entire process you may spend less credits then the new system, but your failure rate, without weapon crates, is relatively the same.

Sure, this is partially mitigated by the cheaper trade ins, but trade ins are still pretty bad value-wise, and crafting a low rarity card becomes a huge loss if you want to recycle it later for crafting a higher rarity loadout. I think there’s still room for improvement there.

The only reason to craft a lower rarity is if you don’t care about shiny. I traded in 3 useless cobalts and made a decent pile of gold loadouts out of it. I like the gold loadouts better then cobalt myself, so I had no problem doing that. It really comes down to preference and resources in the end.

The new system does have better RNG for getting the card you want at the tier you want. The problem, as stated in the OP, is that there is no ‘checkpoint’ like getting the loadout you want at a lower tier. It is all or nothing. Less RNG, but a failure is an abysmal failure.

But please, don’t call more attempts(and thus more success) as less RNG overall. It is the same RNG when not using weapon crates, you just try fewer times overall.


(ArsonistCow) #20

Higher chances of high rarity loadouts from equipment cases. Increasing the chance for rarer items to drop while keeping average costs similar will increase the cost-disparity between the tiers (that’s why all loadouts fell in trade up value).

If for example they made Equipment cases drop 100% Lead cards while keeping costs relatively similar we’d have a system completely devoid of RNG. I hope you understand what I mean.

Pretty much.
I’d just like to highlight the sheer number of attempts you get along the way:
96 Bronze, 24 Silver, 6 Gold and 1 Cobalt. So you have 127 tries at getting the loadout you want. That’s a really big deal.

Even if you want a specific skin you could be looking at more attempts with the old system if you optimized your route. For example: if you like Bronze Stoker, Silver Bushwhacker, Gold Sawbonez and Cobalt Skyhammer you could simply trade up in that order to get a significantly better chance of obtaining the loadout you want in the rarity you want. And this is more than just an off-hand example, I actually did this very thing myself. I love the look of Silver Urban Bushwhacker (with the objective-yellow hat-strap), so traded up to Silver Bushwhacker like 30+ times (never got that Urban C41 tho ;( ) and then traded up the failed ones for a Gold Sawbonez, because I think the Gold Crown look goes really nicely with his glasses (I did get Crown SM72 tho, after like 20 tries).
And each time I failed I didn’t feel completely screwed over, because I knew that I had more mileage to gain out of the failed trade up without significant reduction in efficiency.

First off, aren’t you kind of contradicting yourself here? This statement holds true for your other statement as well:

RNG per try hasn’t been decreased, you just get more tries at that Cobalt.

And secondly: more success per resources is what I’d class as less RNG. So yeah, I’d agree that RNG has been decreased for Cobalts. But it has also been increased for Bronze, Silver and Gold, resulting in an overall increase in RNG if you care about more rarities than just Cobalt.