The Surprising Cost Of Filling Your World Cup Sticker Album

19th April 2018

Football fans are not particularly known for their love of mathematics but as we have pointed out before there is a great deal of mathematics in the world of football, and to be a proper fan you need to use your maths skills, even if you don’t even really realise you’re doing it. Just understanding the league tables, and working out how many points each team needs to stay ahead requires quite a bit of mental arithmetic. The World Cup brings this to a fever pitch with pundits and fans having to navigate group selections, penalty points and all sorts of factors to keep track of all the teams progress.

People, young and old from all walks of life follow football (soccer) all around the world and this is always demonstrated most clearly when the World Cup takes place every four years. Football fans from thirty-two countries will be traveling to Moscow this year to watch the action with millions more watching from home.
 

The use of mathematics and probability is - or should be - taken even further when it comes to that other staple of the die-hard international football fan – the World Cup sticker collection.

The Italian company Panini (surprisingly, nothing to do with sandwiches) has been releasing World Cup football collectible stickers since 1970, selling in the UK since 1978 and fans have enjoyed the thrill of trying to collect the full set of stickers ever since.

Although sticker collections are usually aimed at children, when the World Cup collection is released grown men and women become just as obsessed with the ‘Got, Got, Need’ cycle of buying and swapping stickers in order to try and complete the pack. This year there are a whopping 682 stickers to collect featuring the 32 teams, hundreds of players, different stadiums, managers and World Cup legends.

You pay for a starter pack that contains an album and 26 stickers and that costs £2.99 and then it is a game of chance as you buy packs of 5 stickers – but you have no idea which ones you’re buying, it’s all just the luck of the draw. Most people pool their resources with friends and swap their duplicates within a group so they have a better chance of filling their albums.

This year however, people have been unimpressed that Panini have increased the price of a pack of five by 60% since the last World Cup 4 years ago from 50p to 80p.

Adults who were able to successfully complete their albums when they were children are now expressing dismay at the price hike.

This dismay is further compounded when you look at the calculations made by Professor of Mathematics Paul Harper from Cardiff University School Of Mathematics. Professor Harper has been collecting these stickers since he was a child saying "I can still recall the joy of finally completing my first Panini album as a young boy for the 1982 World Cup in Spain.I must have used an awful lot of pocket money to do this, as well as having generous grandparents handing over bundles of packets of stickers, coupled with tense negotiations of swapping duplicates with friends in the school playground. Filling an album has become progressively more expensive over the years since then…”

 

He has now carefully calculated for footie and sticker mad fans just what it will entail to fill a Panini World Cup album and how much it is likely to cost in reality. The results are frankly eye-watering.

The absolute minimum spend is £109.60 – but this can only happen if you buy 137 packs and never encounter a duplicate, which is almost impossible. In reality, Professor Harper explains "The first sticker you buy is absolutely guaranteed not to be a duplicate. The second sticker you get has a 681/682 (99.85%) chance of being a new sticker. The third sticker you get has a 680/682 (99.7%) chance of being a new sticker, and so on." He then added up all of the probabilities to obtain a formula, which he finalised utilising conditional probabilities as they come in packs of five.

The result was that, on average, you would need to buy 4,832 stickers, or 967 packets, to complete the book, costing a staggering £773.60! We don’t think pocket money and donations would quite cover such a massive outlay!

Furthermore he points out that "What is interesting is that to collect just the last 19 stickers for the book, you would still be required to buy 483 packets of stickers, or half the total number of expected packets. Put another way, you are only half way through when you have just 19 stickers left to collect."

Phew, sounds like quite the undertaking to us! Parents online have been expressing their disbelief that their own children are very unlikely to be able to afford to do the same.

Professor Harper says that of course, the cost can be brought down by swapping duplicates with a group of friends, and he has helpfully calculated the difference for us. If you swap with just one friend you can reduce the numbers of packets needed by 30%, and if you swapped with four other friends you could reduce outlay by 57%. If you are part of a group of ten friends all swapping you would still need to cough up, on average, £247 each.

A group of 10 football mad adults could probably swing for that amount, but we’d be surprised if many children could even get close. This is quite sad to be honest, but we think it’s better for everyone to be aware of the odds and potential expenditure.

So, by all means start collecting, but be warned that your chances of completing your album at any sort of reasonable price is unlikely. This is the case with many random collectible buys from stickers to trading cards to mini toys – but perhaps therein lies the challenge which will no doubt respawn the hashtag #GetGetNeed among and kids adults desperate to complete their collection by swapping stickers in real life and online.