February 19, 2013
Greater Than Plus Minus
NHL Realignment, Part 1

by Brian Macdonald

Along with friend and colleague Bill Pulleyblank, I recently finished a project titled Realignment in the NHL, MLB, the NFL, and the NBA. The main goal was to develop a way to choose the conferences and divisions that would minimize travel for each league. A large portion was focused on realignment in the NHL, a topic that should be of interest to readers of Hockey Prospectus.

Part 1 of this series of articles on realignment will describe the first step of the project: estimating how much individual teams, and the league as a whole, would need to travel in a proposed realignment plan. In order to compare potential realignment plans, we need to be able to estimate travel without knowing the schedule ahead of time. Fortunately, it turns out that we can do a pretty good job of this.

A quick preview of what will come in Part 2: we'll talk about how to generate thousands of possible realignment plans, we'll sort them by league travel distance, and we'll give the best 100 results. Specifying extra conditions like "Philadelphia and Pittsburgh have to be in the same division", we'll give the top solutions that satisfy these extra conditions.

We'll also examine the four-conference realignment proposal that the NHL made about a year ago. We estimate that this four-conference solution with the more balanced schedule would require the league to travel about 100,000 more miles than our best six-division solution.

We'll then consider new realignments in the event that there are franchise moves (e.g. Phoenix to Quebec) or in case an expansion to 32 teams occurs within the next few years.

But first, let's talk about some background information and what motivated the project.

Background and motivation

Atlanta moved to Winnipeg before the 2011-12 season:

(Original image was taken here)

Since Winnipeg stayed in the Southeast Division, some sort of major or minor realignment plan was needed: Winnipeg might be in the southeastern part of its own province, but is nowhere near the southeastern part of the United States. Here we show the divisions before (dotted purple) and after (solid purple) the move:

Since the move, the NHL, the media, and fans have discussed different proposals for what should be done about realignment. For example, the NHL proposed a new four-conference structure, which had TB and FLA with teams in the current Northeast Division.

This proposal is what motivated this project. From the viewpoint of trying to minimize distance traveled by the league, it was definitely not optimal. Of course, the NHL had other reasons for choosing that proposal, and were not focused solely on travel distance. But we became interested in answering the question "how can we choose a realignment that minimizes the total distance that the league would have to travel during a season?"

Estimating team travel without knowing the schedule

One major hurdle to answering this question is this: we will not know the exact team and league travel requirements until a realignment plan is accepted and a schedule is made. So in order to compare different plans for realignment, we must develop a way of estimating league travel without knowing the league schedule ahead of time. It must be based only on the league's structure.

This might seem impossible at first, but here is a fairly simple method that works very well. We compute a "weighted distance" for all teams in the league. As an example, let's consider Toronto in the league's current configuration. TOR is about 300 miles from MON by air, and TOR plays three away games at MON every year, so we say that this is a weighted distance of 300*3 = 900 miles. TOR is 350 miles from NYR, and TOR plays two away games at NYR each year, giving a weighted distance of 350*2=700. TOR is about 2000 miles from VAN, and they play at VAN a little more than once every two years, giving a weighted distance of 2000*0.6=1200. We compute this weighted distance for every team in the league, and add up all the weighted distances.

Minimizing this weighted distance would tend to put teams that are far apart, like TOR and VAN, in different divisions and conferences. If VAN were put in TOR's division, TOR would play more games against VAN, and TOR's weighted distance from VAN would increase to 2000*3=6000. Therefore, a realignment involving TOR and VAN in the same division would not be one that minimizes weighted distance.

While minimizing this weighted distance would do a good job of giving good solutions, what is not clear is whether this weighted distance is any good at estimating actual travel miles—either travel by individual teams, or travel by the whole league. Fortunately, Dirk Hoag posts his Super Schedule every year and calculates the miles each team will have to travelin that year's schedule. We can compare his data for actual travel miles from 2008-09 through 2011-12 with our weighted distance to see how well our weighted distance correlates with actual travel.

Surprisingly, weighted distance correlates very well. A plot of the actual travel vs. estimated travel is given below for the three seasons before ATL moved to WPG (2008-09 thru 2010-11), and one season after (2011-12).

We also tested this method for MLB, the NFL, and the NBA and got good results for those leagues as well. A picture for the MLB is in Section 2 of our paper.

Since we have gained confidence that our weighted distance gives us a good estimate of the league's travel without using information about the schedule, we'll use this to rank potential solutions. In our next article, we'll generate a lot of solutions, rank them based on weighted distance, give our top 100, and discuss considerations other than distance.

Brian Macdonald is an author of Hockey Prospectus. You can contact Brian by clicking here or click here to see Brian's other articles.