What is the probability that the NHL’s scheduling gamble for starting the second round of the 2020 playoffs would work out as perfectly as it did? If you follow hockey, feel free to skip the setup and scroll down to the last section.
What Could Go Wrong?
Yesterday Hockey Twitter was abuzz with the news that the NHL had scheduled the opening game of Round 2 of the Stanley Cup Playoffs before waiting to see if the remaining Round 1 series would require the maximum seven games:
At the time of the decision to schedule the series opener between the Colorado Avalanche and the Dallas Stars, those two teams were the only Round 2 matchup set in stone. Two series, one in each conference, were still going and would be decided either that night or two days later on Sunday, a day after the start of the Colorado-Dallas series. Traditionally, an NHL playoff team plays games every other day with additional off days built into the schedule to accommodate travel. Because teams are isolated into bubble cities by conference for the 2020 iteration of the playoffs, the NHL doesn’t have to worry about travel days and can get a bit more creative with their schedule. Moving up Avs v Stars to Saturday gives the NHL a televised game for a prime weekend spot that they otherwise wouldn’t have. The downside of that decision is potentially having to resolve future scheduling issues. Here’s a timeline of the worst-case scenario resulting from starting the Colorado-Dallas series on Saturday:
| DATE | ROUND | GAME |
|---|---|---|
| 8/20/20 | 1 | Dallas v Calgary, Game 6 |
| 8/21/20 | 1 | St Louis v Vancouver, Game 6 |
| 8/22/20 | 2 | Colorado v Dallas, Game 1 |
| 8/23/20 | 1 | St Louis v Vancouver, Game 7 |
| 8/24/20 | 2 | Colorado v Dallas, Game 2 |
| 8/25/20 | 2 | Vegas v St Louis or Vancouver, Game 1 |
What Actually Went Wrong?
Nothing! Last night both the Vancouver Canucks and the Philadelphia Flyers closed out their series, thus completing all Round 1 games. Had either or both teams lost it would have pushed closing game(s) to Sunday and thrown the Eastern Conference series, the Vegas v St Louis/Vancouver series, or both off the pace of the Colorado v Dallas series. But none of that happened, so the NHL should have an easy time coming up with a sensible Round 2 schedule.
How Likely Was That Outcome?
I kept my analysis pretty simple because this is a really low stakes “problem” and I just wanted to get a sense of how likely it was for everything to have worked out the way it did. I went to Hockey Reference to consult their handy tables of historical playoff results and used that data to construct this table of possible outcomes for a team leading three games to two in a series:
| RESULT | TIMES IT HAPPENED |
|---|---|
| Leading team wins in 6 games | 228 |
| Leading team wins in 7 games | 91 |
| Trailing team wins in 7 games | 87 |
On seeing those raw counts my first thought was if you have a 3-2 series lead, pull out all the stops trying to win Game 6 because Game 7s are a crapshoot. Good work, Flyers and Canucks! Next I just calculated the percentage of 3-2 series that ended in six games using this formula:
Leading team wins in 6 / (Leading team wins in 6 + Leading team wins in 7 + Trailing team wins in 7)
That works out to a 3-2 series ending in six games roughly 56% of the time. If we’re only examining the Western Conference playoff schedule, then the NHL picked the slightly more likely outcome in scheduling Avs v Stars on Saturday and hoping Vancouver would take care of business on Friday. If we want to consider that decision in the context of the entire playoff schedule, then we just need to calculate the combined probability of those two independent events like so:
Probability Philadelphia wins in 6 * Probability Vancouver wins in 6
In my simple analysis based solely on past outcomes, both of those probabilities are the same, making their combined probability the square of the probability of a 3-2 series ending in six games. That works out to a little under 32%, meaning at least one of the remaining Round 1 series going to seventh game was the likeliest outcome by a decent margin. So maybe the NHL got a bit lucky but everything worked out for them and now I get to watch the Avs take on the Stars on TV tonight!