© 2013 Michael Parkatti SNS0317-Orr2

Optimizing the NHL Divisional Alignment, Part II

A couple of days ago I wrote a post in which I used discrete mathematical programming to optimize the NHL’s divisional realignment with respect to minimizing travel distances between each team in each division.  I didn’t impose any constraints to my model beyond allotting either 7 or 8 teams to each of the 4 divisions — it was essentially an academic exercise to figure out how you could arrange the teams in the most efficient way without any consideration to real world demands.  If you want background into my methodology, I urge you to read the post above for a full description.

There were two ways that I wanted to improve my model.

  1. Allowing for league expansion: You’ll notice 30 teams do not divide evenly into 4 divisions — you’re left with two divisions having 8 teams and two divisions having 7 teams.  This creates inherent imbalances in terms of scheduling and odds of making the playoffs.  I think it’s pretty obvious that the NHL has chosen such a structure to provide reason to expand the NHL to 32 teams (“hey, we *had* to do it!”).  In my analysis below, I’m assuming that the two new franchises will be located in Quebec City and Markham, Ontario, just outside of Toronto.  These two cities have long been rumoured to be interested in having franchises, and are both in the process of building NHL-calibre arenas.  There is also a good shot that Phoenix may be relocated in the short term — but I’ve assumed that if they do, it will move to a Western location such as Seattle to keep it within the same division.
  2. Adding constraints for key rivalries: A few people pointed out that the NHL doesn’t operate in a detached world where the only thing that matters is cold efficiency.  Rivalries matter, because rivalries drive revenues.  Most rivalries are driven purely by geographical proximity — I can almost guarantee that I don’t need to add a constraint to say that Calgary and Edmonton should always be in the same division, because it would be mathematically inefficient to separate them.  However, there are natural rivalries that do need some hand holding.  I’ve given the model the following constraints to to ensure these teams are located in the same division: a) Philadelphia and Pittsburgh, b) Toronto, Ottawa, and Montreal, c) Vancouver, Calgary, Edmonton, and d) NY Rangers, NY Islanders, and New Jersey.  These are the key rivalries that seem to be sacrosanct, so ensuring they remain intact makes sense.

Suggested Current Alignment

nhl-map (1)3



The map and table above encompass my suggested divisional alignment that the NHL should pursue in the present reallocation process.  I’ve located teams in such a way to minimize the sum of distances between each team and every other team in its division.

Right away, you’ll notice that the 8 team divisions are now in the west — Colorado has been added to the Pacific division, while Tampa Bay and Florida are added to the Central division (yes, I can assure you that this is the optimal arrangement).  Why is that?  Well, if you’re going to be expanding the NHL in the already concentrated Northeastern portion of North America, it stands to reason that you should leave an empty slot open in the two Eastern divisions to accommodate them.  Why start playing with 7 team western conferences when you’ll just have to uproot multiple franchises and place them in different ones when expansion occurs?  This way, the Western divisions will stay fixed beginning immediately into the foreseeable future.  Stability is a key element in harvesting rivalries — isn’t it a bit odd to add Colorado to the central division, only to boot them over to the Pacific division when things get crowded?  It seems arbitrary and lacks foresight.

One major constraint that I added to this model was that the two future Eastern teams needed to be accommodated into two different divisions.  This way, we can have two divisions of 7 in the present-time as opposed to having one division of 8 teams and another of 6 teams.  This leaves a rather clunky-looking addition of the Nordiques to the neatly-clustered Atlantic division.  What if we relax this constraint, and imagine what the optimal alignment would look like in the future NHL?

Proposed Long-Term Alignment

nhl-map (1)5


Here is what my proposed long-term alignment of the NHL looks like to minimize travel divisional distances while still respecting rivalries.  Essentially, Carolina switches to the Atlantic while Quebec joins the Northeast division.

Doesn’t this just feel more balanced and make more sense than the ‘crescent moon’ arrangement of the current proposed alignment?

Again, to view my methodology, please look at the previous post in this series.  Adding these 2 extra teams and the constraints in this analysis basically jammed up my computer for the better part of a weekend.  I was only able to solve them because I downloaded the trial version of Frontline’s Premium Solver Platform.  It’s like what you get in Excel, just way, way, better.  I swear, using that Solver upgrade allowed me to solve these incredibly complex problems within minutes.  Using the native version of Solver would have taken me many days (weeks?).


  1. Gaelan
    Posted March 4, 2013 at 10:45 am | #

    What is missing from this analysis is that travel isn’t the prime consideration of realignment. Realignment driven by TV/time zone issues. The NHL doesn’t really care about travel costs or time. They care about time zone differences. It would be interesting to see the same analysis to minimize time zone shifts for TV.

    • Michael Parkatti
      Posted March 4, 2013 at 10:54 am | #

      Uhh, yes I agree. Did you look at the divisional alignments?? Please tell me how this could be improved by time zones? There are only two eastern time zone teams in the central. The entire two eastern divisions are eastern timezone. The entire pacific division includes the only teams in the pacific and mountain time zones.

      In any case, the NHL does care about travel costs — to think they don’t is completely off base. Do you want to pay dozens of times a year to charter a flight to a location farther than you needed to fly?

  2. Gaelan
    Posted March 4, 2013 at 11:19 am | #

    I wasn’t making a criticism. Merely pointing out that the driving force behind realignment is TV and the concern over starting/ending times in different time zones.

    I don’t have a better solution in mind, I was curious if you had run a similar analysis trying to optimize timezones. Looking at the map, this scenario appears to recreate the Detroit/Columbus problem for Tampa/Florida.

    Without evidence to the contrary I think the NHL has already come up the most optimal configuration considering their priorities. I also think the concern over the unfairness is overblown. It comes out to missing the playoffs once every fifteen years or so.

    Realignment is the one area that the NHL has done everything right.

  3. Knighttown
    Posted March 4, 2013 at 4:02 pm | #

    How big a deal would it be to the total miles to grab Winnipeg into #4 and put the Avs in #3. Basically run the script again but lock in Cal, Edm, Van and Win like you’ve done with Que, Mon, Ott and Tor

  4. Harlie
    Posted March 8, 2013 at 9:02 am | #

    Any thoughts on Salt Lake City getting a team? I’ve driven through SLC a few times and its a big city and they have a nice barn in place left over from the Olympics. They also have a bit of a history of hockey as well. Booze sales would be abysmal but location wise they make good fit short and long term for Western teams.

  5. Colin
    Posted March 13, 2013 at 10:07 am | #

    First thing: you’re trying to keep rivals together, but Montreal are separated from Boston! And from the hypothetical resurrected Nordiques. Granted, those teams are likely to sell out their barns regardless of who’s playing in them, but this seems a curious oversight.

    And that brings me to a related point of why the NHL’s going for the odd crescent-moon division. It’s basically financial aid for the Florida teams to ensure they play against Canadian opponents a lot, because those games apparently make a big difference in the number of tickets they sell, to travelling Canadian hockey fans as well as snowbird expats.

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