A box's average is not what a box usually returns
The expected value of a randomised purchase, from the box and pack calculator.
- Read as
- An expected value close to the price means the purchase is roughly break-even, so most purchases come back worth about what they cost.
- Actually
- The average is carried by the rarest outcomes. A box whose average sits near its price can still return a fraction of that price on nine purchases in ten, because one outcome in a hundred holds most of the mean.
Take a $100 box: a 1% chance of an item worth $2,000, a 9% chance of one worth $150, and a 90% chance of one worth $40. The average is 0.01 × 2,000 + 0.09 × 150 + 0.90 × 40 = $69.50, which sounds like a purchase that returns about two thirds of its price.
What actually happens nine times in ten is a $40 item. The median purchase returns 40% of its price, and the chance of coming back with less than $100 of value is 90%. Both figures are computed from the same odds table that produced the $69.50.
The single outcome at 1% contributes $20 of the $69.50 average — nearly a third of it. Remove it and the average falls to $49.50. That is what it means for a mean to be carried by its tail, and it is the normal shape of a product sold on a headline prize.
This is why the median, the chance of a losing draw, and the average size of that loss are published beside the expected value rather than beneath it. The average answers 'what does this return over very many purchases'. The other three answer 'what happens when I buy one', which is the question almost everyone is actually asking.
The method behind this figure
Randomised purchase economics — box-economics v1.0.0. Its formula, assumptions and limitations are published in full on the methodology page.
Related: Mystery box and pack EV calculator, Recorded boxes and packs, Glossary, Reading the numbers