Links to Hockey Prospectus articles:
Part 1 - Estimating Team Travel without knowing the schedule
Part 2 - Generating solutions, and the best 6-division solutions.
Part 3 - Best 4-conference solutions, franchise moves, and expansion
Part 4 - Analysis of the NHL realignment plan that was made official on 3/14/2013.

The full paper can be found here.
A article about our project can be found here.


Here are some animations related to this project.  More detailed explanations can be found in Part 2 of the Hockey Prospectus series. 

First we find the lines between every pair of cities in the league: 

Then we check if the lines split the league into equal halves.  If a line does not split the league in half (for example, the line between LA and VAN does not), we remove it from consideration:

Finally, for conferences, we remove lines that are too horizontal.  Using horizontal cuts would result in conferences that span all four time zones and poor travel requirements. We will not remove horizontal lines when we do divisions.

For each of these remaining lines, we form two conferences:

Note that some lines give two possible ways to divide the league in half.  Also, in some cases, two different lines can yield the way to divide the league. 

For each conference of 15 teams that we found above, we repeat a similar process and find all ways to divide the conference into two groups, one 5-team group and one 10-team group.  The only difference in this process is that we do not remove the horizontal lines.

With each 10-team group, we repeat the process one final time and find all ways to split each 10-team group into two 5-team groups.


NHL realignment -  Here are the top 100 configurations for the NHL, with no constraints added.

Here's a slideshow, in case you want to scroll thru more slowly.

Notice that TB and FLA are not in the same division for some of those solutions.  Below we give the top 100 configurations with the following constraints:
  1. The following teams must be in the same division: Tampa Bay and Florida; Philadelphia and Pittsburgh; NY Rangers, NY Islanders, and NJ Devils; Calgary and Edmonton; Anaheim and Los Angeles. 
  2. At most 3 Canadian teams can be in one division
  3. A division can span at most two different time zones.
Here's a slideshow, in case you want to scroll thru more slowly.

MLB Realignment - Here are the top 100 configurations for MLB:
Here's a slideshow, in case you want to scroll thru more slowly.  Here are the top 10 if we don't allow teams to switch from the AL to the NL, and vice versa.
Here's a slideshow, in case you want to scroll thru more slowly.

NFL Realignment - Here are the top 100 configurations for the NFL:
Here's a slideshow, in case you want to scroll thru more slowly.

NBA Realignment - Here are the top 100 solutions for the NBA:
Here's a slideshow, in case you want to scroll thru more slowly.


  1. With the new system of the NHL, two conference of the 2 divisions, one with 16 teams and the other with 14 team. What is the best configuration without constraint and whit constraints ?

  2. Alexandre, I believe your question is answered in Part 4 (see link at top of this page). See the paragraph before the 4th figure.

    We look at the "best" solution, according to distance, subject to a couple of constraints:
    -14 teams in the West and 16 in the East,
    -CBJ and DET are the two teams that move East
    -the NY teams have to stay together,
    -PHI and PIT have to stay together, but that PHI and PIT do not have to be with the NY teams.

  3. What if Quebec City and Las Vegas get a team and you use my calendar system?

    4 conferences of 8 teams divided each divided in 2 divisions of 4 teams. Each teams play 6 times versus its division, 4 times versus its conference and 2 times versus others conferences.


    1. We did something like that in the paper. See page 16: The solution isn't bad, but in some places it's kind of silly, like FL teams being in the west, which is sort of ridiculous. If we were to do it again, we'd probably force them east.

      For games played with 32 team, we used

      So the results would be a little different for the games played you listed.

  4. Can we have an update with all the NFL moves and the NHL expansion?

  5. keep up the good work. this is an Ossam post. This is to helpful, i have read here all post. i am impressed. thank you. this is our site please visit to know more information
    data science training in Hyderabad

  6. Thanks for the information about Blogspot very informative for everyone
    data science malaysia

  7. Very awesome!!! When I searched for this I found this website at the top of all blogs in search engines.

    Best Institute for Data Science in Hyderabad

  8. Always so interesting to visit your site.What a great info, thank you for sharing. this will help me so much in my learning
    artificial intelligence course

  9. Such a very useful information!Thanks for sharing this useful information with us. Really great effort.
    data scientist courses aurangabad

  10. Great & nice article with a lot of information to read...great people keep posting and keep updating people..thank you If you want to get a Tourist visa to Turkey, you can fill out the Turkey eVisa application form in minutes, & then You must give permission to enter Turkey legally.

  11. This is really an inspiring and helpful article. I am fully satisfied with your effort .There is no need to meet Kenya embassy specially for to get a valid Kenya e visa .The Government of Kenya grants the online Kenya e-visa provide.

  12. This is really an inspiring and helpful article. I am fully satisfied with your effort .There is no need to meet any embassy, especially to <a href=">apply for Indian visa from Australia</a>. You can easily apply online and easily get your evisa on your email id.

  13. Informative blog and knowledgeable content. Thanks for sharing this awesome blog with us. If you want to learn data science then follow the below link.
    Best Courses for Data Science in Hyderabad

  14. Wonderful . I am surprised after reading your articles . And I will try to discover more articles like this . Do you want to know more about the Azerbaijan evisa ? read on this web site you will definitely find what you want .

  15. Hello guys, Many people ask, how to apply for an e visa online. You can apply for a visa online. And you can get a visa after a successful application depends on the country you have applied for. While in some cases, you can get a visa in as little as 30 minutes time, others may require a few days. In some countries, we also offer a fast-track visa option if you need it urgently. You can read more information about visas through our Visacent website.

  16. This comment has been removed by the author.

  17. I'm perpetually captivated by your blog! The way you seamlessly blend profound insights with eloquent storytelling, guiding readers on a well-planned journey through the universe of knowledge, is truly exceptional. Your knack for simplifying intricate ideas is genuinely commendable. Furthermore, I'd like to provide valuable insights on scheduling a US visa appointment in Saudi Arabia. Scheduling a US visa appointment in Saudi Arabia is a pivotal step for individuals aspiring to visit the United States. This process involves careful coordination through the official channels, ensuring a smooth and organized commencement of the visa application journey.

  18. Do you thought about rearranging the pages on your website? I think your writing is excellent, and I agree with all you say. Maybe you could add a few more items, though, to enhance people's ability to interact with it. You have an amazing quantity of text and one or two photos. Could you perhaps divide it out more evenly?
    Hence, a person must fill out the application, upload the necessary files, pay, Indian visa fees for Australian citizens and wait for approval in order to receive an electronic visa for India from Australia

  19. I'm excited about the opportunity to showcase snippets from your articles on my blog. You'll be duly credited, with proper source acknowledgment. Given our shared interests, I believe your content will enhance my audience's engagement. Your collaboration would be greatly appreciated. Thank you. How long does it take to get Azerbaijan evisa, The processing time for an Azerbaijan eVisa typically ranges from 1 to 3 business days. However, it's advisable to apply at least a week before your intended travel date to account for any unforeseen delays in the processing.

  20. Your poignant examination of the subject matter strikes a chord with me. Your insights reveal layers often unnoticed, prompting contemplation long after the initial read. Allow me to share a great information for US citizens. "Do American citizens need e visa for Bahrain?" Yes, American citizens require an e-visa for entry into Bahrain. The e-visa system facilitates the application process, allowing travelers to apply online before their trip. This electronic visa simplifies the process and expedites entry into the country.