NHL Draft Favors the Oilers?

I don't follow the NHL, but a lot of my friends do.  At dinner on Friday, one of my friends was telling me how unbelievable it is that the Edmonton Oilers won the first pick in the NHL draft for the third straight year.  I thought I would investigate how (un)likely it is that they would win the first pick for three straight years.

Here's how the NHL draft works.  The teams are ordered by their regular season and post season record.  The team with the worst record is listed first, and the team that wins the Stanley Cup is last (30th).  The teams are weighted based on their position (more on this in a second), then one team is chosen.  The team selected moves up the list 4 positions, and all other teams remain in the same order.  This is the draft order.  So the team with the worst record will win the first pick as long as none of the other top 5 teams on the list (i.e., worst 5 records) are selected.  If a team lower than 5th is picked, then it will move up, but not enough to take the overall number 1 pick.

Let's look at the weight of the top 5 teams in the lottery.  That is, the probability that each team will be selected and move up to the top of the draft list:

1. 25%
2. 18.8%
3. 14.2%
4. 10.7%
5. 8.1%

This adds up to 76.8%, with the remaining 23.2% going to teams that cannot move up to the top draft position.  (See here for the full breakdown.) So the team with the worst record will take the top pick if they win the lottery (25%) or a team outside of the top 5 wins (23.2%).  Adding these probabilities up, the team with the worst record will win the top pick 48.2% of the time.

In 2010 and 2011, the Oilers had the worst record and had the top overall pick.  This year (2012), the Oilers had the second worst record, but won the lottery (with 18.8% chance) to move up to the top pick.  Given that the Oilers finished 30th, 30th and 29th, and that the lottery results from year to year are independent, we can calculate the probability that the Oilers win 3 first picks in a row as:

0.482 * 0.482 * 0.188 = 0.0437

So we would only expect a team with the same record as Edmonton to win the first pick in three straight years less than 5% of the time.  While this is small, it is still not that unlikely.