# Nike MAG Shoes: A Postive Expectation Raffle

Although it has become a very popular hobby, I do not consider myself a “sneakerhead” (I prefer Allen Edmonds). But a recent ESPN article on the Nike MAG shoes caught my attention because there’s some probability and statistics there. With a limited production run of 86 pairs of shoes, Nike decided to have a global raffle where you could buy a $10 ticket for a chance to win; the majority of the proceeds went to a charity associated with Michael J. Fox. In this article, we can see how it’s possible that this was a raffle with a positive monetary expectation, otherwise known as positive expected value or positive EV.

Here’s some basic parameters presented in an article by ESPN on the raffle:

- 86 pairs were raffled off
- Each ticket to the raffle was $10
- A total of 675,000 raffle tickets were sold

As for the resale value of the shoes, ESPN adds a bit of validated speculation.

It’s not known how much the lucky winners will be able to sell the shoes for on the open market, should they choose to do so, but Nike has auctioned off three pairs at events which might help set the market. One pair in Hong Kong sold for $105,000, and another one in London sold for $56,800.

### Nike MAG Shoes: The Probabilities

Let’s assume that we buy 1 ticket into the raffle. We can apply some math to figure out our chances of winning with some probabilities as shown below.

This first pass gives us a probability of 0.00014815% of winning a pair of the Nike MAG shoes. Not exactly high odds!

But there is a potential silver lining – they are auctioning off 86 pairs of shoes, not just one. Surely that must increase our odds, right? We can rely on the geometric distribution to find an answer. In essence, if you have X probability of something and you’re going to have Y chances at it, the geometric distribution tells us our overall probability of winning. When you use Wolfram Alpha to plug in these numbers, we get a resulting table like the following.

Pairs of Shoes (x) | Probability |
---|---|

x < 86 | 0.0001272 |

x = 86 | 0.00000148 |

x > 86 | 0.999871 |

So from this table, we can see that if we take all 86 pairs of shoes as a total raffle, then our probability of winning at least one pair actually increases to 0.0129%. We have now improved our odds, but still a long shot to win.

### Nike MAG Shoes: The Expected Value

The next part of our equation is to think about how much we can sell the shoes for. Let’s assume that you have no interest in keeping the shoes and want to auction them off. Let’s also assume that you can sell them to a rich sneakerhead that can pay $100,000 USD for the shoes. We now have all the items we need for our Expected Value (EV) calculation.

As you can see from the above, due to the high potential resale value of the shoes, we actually have a *positive* expected value of $2.91 for each raffle ticket we purchase. Said another way, Nike was selling you a product (a raffle ticket) worth $12.91 for only $10. To be clear, it is extremely difficult for you to realize this value into hard dollars, but the statistical value is undeniably there.

Make no mistake about it, positive EV situations like this are rare, especially when they are available on a broad basis. While we are making some assumptions along the way, this situation is mostly created by the high potential resale value of shoes. Without that part of the equation, the positive EV quickly fades away.