# Using algorithms for better realignment in the NHL?

The NHL recently announced realignment plans. However, a group of West Point mathematicians developed an algorithm they argue provides a better realignment:

Well, a team of mathematicians at West Point set out to find an algorithm that could solve some of these problems. In their article posted on the arXiv titled Realignment in the NHL, MLB, the NFL, and the NBA, they explore how to easily construct different team divisions. For example, with the relatively recent move of Atlanta’s hockey team to Winnipeg, the current team alignment is pretty weird (below left), and the NHL has proposed a new 4-division configuration (below right):

Here’s how it works. First, they use a rough approximation for distance traveled by each team (which is correlated with actual travel distances), and then examine all the different ways to divide the cities in a league into geographic halves. You then can subdivide those portions until you get the division sizes you want. However, only certain types of divisions will work, such as not wanting to make teams travel too laterally, due to time zone differences…

Anyway, using this method, here are two ways of dividing the NHL into six different divisions that are found to be optimal:

My first thought when looking at the algorithm realignment plans is that it is based less on time zones and more on regions like the Southwest, Northwest, Central, Southeast, North, and Northeast.

But here is where I think the demands of the NHL don’t quite line up with the goals of the algorithm to minimize travel. The grouping of sports teams is often dependent on historic patterns, rivalries, and when teams entered the league. For example, the NHL realignment plans generated a lot of discussion in Chicago because it meant that the long rivalry between the Chicago Blackhawks and the Detroit Red Wings would end. In other words, there is cultural baggage to realignment that can’t only be solved with statistics. Data loses out to narratives.

Another way an algorithm could redraw the boundaries: spread out the winning teams across the league. What teams are really good tends to be cyclical but occasionally leagues end up with multiple good teams in a single division or an imbalance of power between conferences. Why not spread out teams by records which then gives teams a better chance to meet in the finals or other teams in those stacked divisions or conferences a chance to make the playoffs?b