THE World Cup is still two weeks away, but for children worldwide (plus disturbing numbers of adults), the race to complete the Panini Brazil 2014 sticker book started long ago. Panini, an Italian firm, has produced sticker albums for World Cups since the tournament in Mexico in 1970; this year’s version has 640 stickers to collect (Brazilians are being forced to find nine sponsor cards, too). The market for the stickers is not just for kids, however; it is also for micro-economists. Getting every slot filled delivers an early lesson in probability; the value of statistical tests; the laws of supply and demand; and the importance of liquidity.
When you start an album, your first sticker (they come in packs of five) has a 640/640 probability of being needed. As the spaces get filled, the odds of opening a pack and finding a sticker you want lengthen. According to Sylvain Sardy and Yvan Velenik, two mathematicians at the University of Geneva, the number of sticker packs that you would have to buy on average to fill the album by mechanically buying pack after pack would be 899. That assumes there is no supply shock to the market (the theft of 300,000 stickers in Brazil in April left many collectors fearful that Panini would run short of cards).
It also assumes that the market is not being rigged. Panini says that each sticker is printed in the same volume and randomly distributed, although every collector will be haunted by a single recurrent card. In a 2010 paper Messrs Sardy and Velenik played the role of “regulator” by checking the distribution of stickers for a 660-sticker album sold in Switzerland for that year’s World Cup. Out of their sample of 6,000 stickers, they expected to see each sticker 9.09 times on average (6000/660). They tested to see whether the actual fluctuations around this number were consistent with the expected distribution of stickers, and found that it was. Such