Dr Tim Paulden (Innovation & Development Manager, ATASS Sports)

Released on 19 July 2018

To view the full article (12 minute read), please click on the “Download Case Study” button.

Summary (2 minute read):

A new data set logging nearly 11,000 World Cup 2018 stickers collected over the last three months has indicated a substantial bias in the sticker frequencies – with “shinies” being systematically rarer than other stickers.

The data set, collated by a group of eleven avid collectors at ATASS Sports, records how many times each of the 682 stickers in the 2018 Panini collection has arisen.

Without exception, all 50 of the special “shiny” stickers were found to have appeared noticeably fewer times than the average – contradicting the conventional wisdom that all stickers in the collection are equally rare. In fact, the typical “shiny” sticker appeared about half as often as one would expect if all stickers had the same rarity.

What’s more, when the data was split up on a team-by-team basis, it was discovered that for almost all teams (27 out of 32), the special “shiny” sticker bearing the team’s logo appeared fewer times than any of the other 19 team stickers. If all stickers in the collection were indeed equally rare, the probability of observing such an anomalous pattern simply by chance would be less than 10 to the power of -30 (or 0.000000000000000000000000000001) – comparable to winning the National Lottery four weeks on the trot.

Although the discovery that shiny stickers are rarer than others would ordinarily be bad news for collectors (and their bank balances), we demonstrate that the savvy collector can adopt a couple of smart measures to reverse this effect – and potentially save hundreds of pounds.

For instance, even when accounting for the shiny sticker bias, we found that a group of ten collectors working together – and taking advantage of Panini’s “buy last 50 stickers” option – would spend an average of just £141 each to finish their collections. This completion cost is five times smaller than the figure of £773 recently quoted in the national media – a powerful demonstration that even in the domain of collecting football stickers, developing a realistic mathematical model can pay big dividends.