Links to

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

A

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.

**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

**Wired.com article**about our project can be found here.**Animations**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.

**Results****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:

- 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.
- At most 3 Canadian teams can be in one division
- A division can span at most two different time zones.

**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.

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 ?

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

ReplyDeleteWe 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.

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

ReplyDelete4 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.

6x3=18

4x4=16

2x24=48

total=82

We did something like that in the paper. See page 16: http://arxiv.org/pdf/1302.4735v1.pdf. 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.

DeleteFor games played with 32 team, we used

6x3=18

4x12=48

1x16=16

total=82

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