# Ceramic Opening Analysis

bantel_cat
Posts:

**969**✭✭✭✭✭So the Monster Mash 10 x Ceramic (1A, 1B) took me over 200 recorded Ceramics.

Time for some analysis given its a reasonable sample size, well not for S or A pulls but here goes anyway.

If you get to the bottom of this post you are likely as sad as me. If I ever meet you I'll buy you a pint for your perseverance :-)

Introducing Paulie's Spreadsheet of Joy/Woe*

* Delete as applicable (mainly woe for me)

EDIT: Spreadsheet available in post below.

EDIT: Spreadsheet available in post below.

Assumptions:

Pack openings are discrete events with a yes/no outcome so follow a Binomial distribution, at larger sample sizes could use a Normal distribution too.

Have combined Card 4/5 odds into one overall, reasonable for larger sample.

All Premiums have the same odds (seem to remember this isn't true for some manufacturers)

Once rarity has been decided you are equally likely to get any car in that tier - confirmed by Hutch.

Odds (%):

Ceramic

S - 0.75

A - 2.75

B - 14.5

Premium

S - 0.5

A - 2.1

B - 11.325

So for my 205 packs...

Expected Values (118 Ceramic, 87 Premiums ):

S - 118 x 0.0075 + 87 x 0.005 = 1.3

A - 118 x 0.0275 + 87 x 0.021 = 5.1

B - 118 x 0.145 + 87 x 0.11325 = 27.0

What did I actually get?

S - 0

A - 3

B - 26

So almost spot on for the Bs and somewhat unlucky with S/A but nothing really unusual.

Using a Binomial Calculator you can assess your 'luckiness'

Chance of getting B or better for me here is 16.27% or 33.4 cars expected.

I got 29.

Binomial Distribution says that the chance of getting more than 29 is 76%

So I am in the lowest quartile, pretty unlucky but there you go.

Where I was even more unlucky was with the 'quality'.

All 3 Epics were RQ23. Chances of that happening are roughly 2%

Now, this is where it gets really boring... still here?

Continuing on the quality theme, obviously you want to pull upper tier cars especially S/A/B (not 3 x RQ23!)

So what is the average RQ you can expect per Rarity drop? Yep I actually got the total cars of all RQ levels to calculate the average even factoring in those high RQ Epic Audis... so sad

S - 28.2

A - 24.7

B - 20.5

C - 16.4

D - 12.4

E - 8.5

F - 4.6

So what does my quality look like?

S - In my dreams

A - 23 (arrgghh!)

B - 20.6 (hurrah, I win!...just)

C - 16.4 (spot on)

D - 12.4 (spot on)

E - 8.4 (just under)

If anyone is interested in the spreadsheet let me know.

All you should need to do is put your pack pulls into the relevant worksheets like this:

Everything else should auto-calculate.

Everything else should auto-calculate.

Post edited by bantel_cat on November 2018

## Comments

1,767✭✭✭✭✭Did you factor in the lower odds given by premium cermaics ?(sounds counter intuitive)

969✭✭✭✭✭320✭✭✭106✭✭✭950✭✭✭✭✭502✭✭✭✭969✭✭✭✭✭1,908✭✭✭✭✭721✭✭✭✭✭648✭✭✭✭470 Ceramic packs (no Premiums!):

(upper row is what I got, lower row is what chances suggest)

50 Carbon Fiber packs:

Seems like, I am just at the average. While I was above average at the beginning of September (5 Legends and 9 Epics in about 2 months), my luck turned away in the more recent time (nothing above B since end of September).

969✭✭✭✭✭https://drive.google.com/open?id=1qGOsLiT4ELbhP1cE6p_uYiqt0y28fEUK

The link above is for the blank spreadsheet which should be ready to paste (or enter) your data into.

If there are any issues and you want to see how it should work, or you just want to look at my data, the populated sheet is here:

https://drive.google.com/open?id=15ZO4m1b2aFWwA0Sz5GTOUh6I9YXJn_CW

Some pointers on using it...

You enter data into the 'Ceramic' and 'CF' Worksheets.

The 'Summary' and 'Calcs' worksheets should auto-populate when there is data.

The one thing you will need to do is a drag down autofill of Columns I to M to match the number of rows of data you have entered, this will drive the 'Other Stats'

Data is entered in columns A to G. Make sure you put the cards in ascending order like they appear in TD, i.e lowest RQ value in column A up to highest RQ value in column E.

Column F is where you put whether it was a Premium or not (or Manufacturer for CF). If you enter any text in column F the calculations will assume it is a Premium pack. If it is left blank for that row the calculations will infer that it is a standard pack. For the CF worksheet it doesn't affect the calculation but it does affect the count on the Summary sheet.

Column G is where I record any A or S Cars I get, it doesn't get used anywhere, its just a record.

Don't enter anything in any of the other columns, aside from the fill down of I to M.

Quick Walkthrough...

Will start like this:

Enter or copy data in.

If you copy data in, make sure to do a 'Paste Values', this will preserve the formatting.

Here I have pasted in some data:

Sometimes the cell formatting (i.e the colour) doesn't appear right away. You may need to go to another worksheet and come back again.

Now if we look at the Summary worksheet:

We see we are starting to get some data but the 'Other Stats' are wrong.

So back in the Ceramic worksheet we do a drag fill down of columns I to M.

Do this by highlighting I2 to M2 and dragging the bottom right corner down:

Giving:

This should mean the stats are now correct:

Now do the same with the CF worksheet and you should be good to go.

I have also included a 'Farming' worksheet where I have recently started recording daily totals.

It is pretty self-explanatory.

If you don't have a lot of data the Binomial 'Luckiness' figures won't really mean too much but as your sample size grows it becomes more statistically accurate.

Hope you find it useful and if you have any questions, just let me know.

If you have any suggestions, other possible stats to calculate etc I'd love to hear from you.

i.e could add the date each pack was opened to start doing graphs, trend analysis etc

Cheers,

Paul

1,882✭✭✭✭✭1,908✭✭✭✭✭46✭✭✭I'm too lazy to do all this stuff but it's nice to see others actually making sure hutches drop rates are correct.

2,742✭✭✭✭✭969✭✭✭✭✭You have highlighted the first error in the spreadsheet, have corrected.

It was calculating the Expected C incorrectly.

You can either download again or change B22 in the Calcs worksheet to be:

=(B15*F15)+(B16*F16)

1,365✭✭✭✭✭Three 7RQ

Two 8RQ

Three 9RQ

Three 10RQ

Two 13RQ

One 14RQ

One 16RQ

One 17RQ

One 18RQ

and these:

969✭✭✭✭✭Not only did you pull 2 x B and 1 x A, but the A you pulled is awesome and not the usual RQ23 **** that I get

721✭✭✭✭✭969✭✭✭✭✭Spreadsheet will incorrectly assume it is is an S based on its RQ.

I'll have to figure out a way to handle this, easiest way probably will be to add a column 'Epic Audi > 26RQ' to act as a flag though you could theoretically get two in one pack. I'll have a think

1,365✭✭✭✭✭That’s five Ceramics in two days, pulling four Super Rare, two RQ21 Ultras, an RQ22 Ultra, and an RQ29 Epic. Watch me now have terrible luck for the next six months.

969✭✭✭✭✭The RQ29/30 Epic Audis are a headache.

Normally you can use the RQ level to also determine the Rarity, except for these 7 cars.

So you need two bits of information on them to be able to gather statistics accurately.

But this needs to be simple, the whole point of the spreadsheet is to analyse your pulls.

We don't want to be entering in all sorts of info for cars when we will sell/fuse 95% of them.

So the approach I took is if you get an Epic Audi of RQ29 or RQ30, just enter 29A or 30A into the spreadsheet

Stats before my imaginary mega lucky Ceramic..

Entering the lovely RQ29 and RQ30 Audi I got in a Ceramic...

Note that there are some more columns on the right to fill down.

This gives...

It has correctly counted them under Epics and increased the Epic average 'quality'

There is probably a more elegant way of doing it but this seems to work.

I've also added an Aluminium worksheet but not done anything with it yet.

Does anyone want Steel and Plastic?

Changelog:

04/11/18 - 1.0 - Original release

06/11/18 - 1.1 - Correct Super Rare Count

09/11/18 - 1.2 - Correctly handle Epic Audis, add Alu placeholder worksheet

721✭✭✭✭✭969✭✭✭✭✭Shame I didn't start recording Aluminiums earlier, the 4 packs prior to recording gave me 3 x C and 1 x B, incredible luck, why oh why cant that translate into Ceramic or CF.

Have created a new Spreadsheet here:

https://drive.google.com/open?id=1BjojeMUAzsCX-60g1mvvOjCrnywpQvq-

If you are not interested in Aluminium then continue using the other.

821✭✭✭✭✭2✭969✭✭✭✭✭969✭✭✭✭✭However, I have gone 28 Ceramics with no B or better and others have gone longer. Things will (sort of) even out in the end

721✭✭✭✭✭1,767✭✭✭✭✭