mscroggs.co.uk
mscroggs.co.uk

subscribe

Blog

World Cup stickers 2018, pt. 2

 2018-06-16 
This year, like every World Cup year, I've been collecting stickers to fill the official Panini World Cup sticker album. Back in March, I calculated that I should expect it to cost £268.99 to fill this year's album (if I order the last 50 stickers). As of 6pm yesterday, I need 47 stickers to complete the album (and have placed an order on the Panini website for these).

So... How much did it cost?

In total, I have bought 1781 stickers (including the 47 I ordered) at a cost of £275.93. The plot below shows the money spent against the number of stickers stuck in, compared with the what I predicted in March.
To create this plot, I've been keeping track of exactly which stickers were in each pack I bought. Using this data, we can look for a few more things. If you want to play with the data yourself, there's a link at the bottom to download it.

Swaps

The bar chart below shows the number of copies of each sticker I got (excluding the 47 that I ordered). Unsurprisingly, it looks a lot like random noise.
The sticker I got most copies of was sticker 545, showing Panana player Armando Cooper.
Armando Cooper on sticker 545
I got swaps of 513 different stickers, meaning I'm only 169 stickers short of filling a second album.

First pack of all swaps

Everyone who has every done a sticker book will remember the awful feeling you get when you first get a pack of all swaps. For me, the first time this happened was the 50th pack. The plot below shows when the first pack of all swaps occurred in 500,000 simulations.
Looks like I was really quite unlucky to get a pack of all swaps so soon.

Duplicates in a pack

In all the 345 packs that I bought, there wasn't a single pack that contained two copies of the same sticker. In fact, I don't remember ever getting two of the same sticker in a pack. For a while I've been wondering if this is because Panini ensure that packs don't contain duplicates, or if it's simply very unlikely that they do.
If it was down to unlikeliness, the probability of having no duplicates in one pack would be:
\begin{align} \mathbb{P}(\text{no duplicates in a pack}) &= 1 \times\frac{681}{682}\times\frac{680}{682}\times\frac{679}{682}\times\frac{678}{682}\\ &= 0.985 \end{align}
and the probability of none of my 345 containing a duplicate would be:
\begin{align} \mathbb{P}(\text{no duplicates in 345 packs}) &= 0.985^{345}\\ &= 0.00628 \end{align}
This is very very small, so it's safe to conclude that Panini do indeed ensure that packs do not contain duplicates.

The data

If you'd like to have a play with the data yourself, you can download it here. Let me know if you do anything with it...

Similar posts

World Cup stickers 2018, pt. 3
World Cup stickers 2018
World Cup stickers
Euro 2016 stickers

Comments

Comments in green were written by me. Comments in blue were not written by me.
 Add a Comment 


I will only use your email address to reply to your comment (if a reply is needed).

Allowed HTML tags: <br> <a> <small> <b> <i> <s> <sup> <sub> <u> <spoiler> <ul> <ol> <li>
To prove you are not a spam bot, please type "n" then "u" then "m" then "b" then "e" then "r" in the box below (case sensitive):

Archive

Show me a random blog post
 2021 

Jan 2021

Christmas (2020) is over
 2020 
▼ show ▼
 2019 
▼ show ▼
 2018 
▼ show ▼
 2017 
▼ show ▼
 2016 
▼ show ▼
 2015 
▼ show ▼
 2014 
▼ show ▼
 2013 
▼ show ▼
 2012 
▼ show ▼

Tags

exponential growth golden ratio approximation preconditioning dates map projections bodmas captain scarlet triangles talking maths in public probability a gamut of games geogebra geometry error bars royal baby raspberry pi pi sorting speed finite element method london underground programming sound machine learning manchester puzzles royal institution manchester science festival people maths advent calendar gerry anderson pythagoras european cup weather station rhombicuboctahedron world cup frobel pac-man inline code graph theory oeis draughts logic final fantasy christmas card phd tennis electromagnetic field chalkdust magazine asteroids football ucl coins matrix of minors arithmetic folding tube maps tmip trigonometry matrix of cofactors twitter matrices harriss spiral graphs quadrilaterals wave scattering dragon curves sport accuracy golden spiral chess flexagons hats estimation plastic ratio latex propositional calculus sobolev spaces london game show probability statistics python logs game of life weak imposition bempp numerical analysis hannah fry national lottery dataset news binary matrix multiplication fractals go determinants reuleaux polygons menace mathslogicbot polynomials boundary element methods pizza cutting matt parker the aperiodical light radio 4 squares craft php chebyshev interpolation braiding nine men's morris signorini conditions computational complexity pi approximation day mathsjam convergence rugby mathsteroids gaussian elimination palindromes big internet math-off books reddit ternary video games inverse matrices stickers misleading statistics cambridge games folding paper bubble bobble cross stitch curvature realhats wool javascript data visualisation countdown data noughts and crosses platonic solids simultaneous equations christmas martin gardner hexapawn

Archive

Show me a random blog post
▼ show ▼
© Matthew Scroggs 2012–2021