"What are the odds?" Getting Swept After Sweeping in the NHL Playoffs

A sweep in the NHL playoffs isn't extremely rare, but what is rare is a team sweeping 4-0 in one round and then getting swept 0-4 in the next round. And it happened twice last year, in back-to-back-to-back series:

• New York Islanders swept Pittsburgh Penguins 4-0 in round 1
• Carolina Hurricanes swept New York Islanders 4-0 in round 2
• Boston Bruins swept Carolina Hurricanes 4-0 in round 3

Going back to the 2009-10 NHL playoffs, these are actually the ONLY two instances in which this has happened (back-to-back sweeps). Over the 71 playoff series in the 2nd round or later, this amounts to 2.82% of the time.

Over all 150 series though, there have been 18 sweeps, or 12%. 12% * 12% is a 1.44% probability, if you assume that each series is independent - which isn't a fair assumption at all, so there must be a better way to estimate it.

Don Luszczyszyn recently reran his playoff probabilities back to 2010 at the series level, which means I can estimate the game-by-game probabilities to calculate the chances of a sweep in each series. On average, the home team has had a 12.1% chance of sweeping, and the away team 5.9% - giving 12.1% * 12.1% = 1.47% (almost identical to above) at the high end, 5.9% * 5.9% = 0.35% at the low end, or 12.1% * 5.9% = 0.72% in between. Of these, somewhere between the middle to high estimate seems the most plausible, since NHL's weird playoff seeding could result in a mismatch in one home/away pairing and then a different mismatch in the next series.

As for the actual results that happened last year (listed above): NYI had a 0.4% chance of sweeping Pittsburgh, times an 8.3% chance of Carolina sweeping NYI = 0.03%, or 1 in 3,176. And then that 8.3% sweep * 15.8% chance of Boston sweeping Carolina = 1.31%, or 1 in 76 (this represents the alternating mismatch scenario described above).

However, the two sets of results happening back-to-back-to-back? 0.005%, or 1 in 20,123.