Originally published on Camstew’s View on Baseball.

For a variety of different reasons, hardcore baseball fans have a certain affinity for their team’s AAA-affiliate. Prospect-hounds love to watch top prospects progress through the minor league system and AAA is often the last test before they are promoted to the major league team. When players get injured, they will play rehab games with the minor league teams, which gives us another reason to be aware of exactly where the affiliate is.

But one thing that isn’t necessarily thought about much, except on rare occasions, is the distance between the big league team and the AAA affiliate. Your starter has a freak injury in the morning, and you need an emergency call-up to start the game? It’s a lot easier to get a pitcher up from AAA if you’re Seattle, whose AAA affiliate is just a short drive down I-5 to Tacoma. This is not quite the case for the New York Mets, who are over 2000 miles away from their highest minor league affiliate in Las Vegas.

So what I wanted to do is to look at this in an analytical way, and try to find the optimal affiliate for each team. First, I’ll share the results, and then down below I’ll show my methodology for those who are interested.

As you can see, there are 12 teams that get to keep their current affiliate, and 18 teams that would change affiliates under this method. Of the 18 teams that would change their affiliate, only 5 teams would have an increased travel distance, while the other 13 teams would decrease the travel distance. Only the Rangers would have a huge increase, moving from Round Rock to El Paso which is about a 417 mile increase. The Dodgers, Mets, A’s, and Astros all get massive travel savings, especially the Mets who would no longer send their AAA players to Las Vegas, but rather to Syracuse.

The White Sox, Astros, Marlins, Pirates, Padres, and Rockies all get reunited with former AAA affiliates. The Sky Sox and Rockies split ways only 2 years ago, after a 22-year player development relationship, but are probably the most obvious MLB-AAA geographic pairing that doesn’t currently exist.

Also, with these new optimized MLB-AAA pairings, total travel distance between all 30 teams and their affiliates has been reduce by over 55%. Obviously travel distance isn’t the most important factor that teams consider when negotiating new Player Development Contracts, but I imagine it would certainly be one of the considerations.

Methodology

My first challenge was to collect the data, which I did by using a simple online calculator for straight-line distances between cities. I didn’t differentiate the Los Angeles, Chicago, New York, and Bay Area teams from one another, just to make the data collection a little quicker. The distances were put into a 30-by-30 matrix (Matrix #1), 900 MLB-to-AAA distances in total.

I then created two more matrices next to the original one, which would help me enter the problem into the Excel optimization add-in, OpenSolver. Matrix #2 was left blank by myself, but would be changed to either a 1 or 0 by OpenSolver. Matrix #3 simply multiplied the distance from Matrix #1 with the corresponding binary value from Matrix #2. I also created a column to sum each row in Matrix #2, a row to sum each column for Matrix #2, and a column to sum each row in Matrix #3. Finally, the summed column on Matrix #3 was itself summed together, which is the Target Cell to be minimized.

The OpenSolver optimization problem was set up as follows. The Target Cell (total distance of the selected 30 MLB-AAA pairings) is set to be minimized, with the following constraints:

1. All 900 cells in Matrix #2 must be binary (1 or 0)
2. The sum of every row (AAA team) in Matrix #2 must be exactly 1
3. The sum of every column (MLB team) in Matrix #2 must be exactly 1

These constraints make sure that every AAA team and every MLB team has one and only one “1” input into the corresponding row/column. A “1” in Matrix #2 indicates that the MLB-AAA pairing has been selected, which then allows Matrix #3 to pull in the distance from Matrix #1 for only the cells with a “1” in Matrix #2.

Another variation of this analysis would be to add another constraint, requiring every selection to be less than 600 miles in distance, as to make sure no team gets unnecessarily screwed on travel just to benefit the league on the whole. Adding this into the problem changes the results, but only slightly. Atlanta and Miami would swap affiliates, since Gwinnett is the only AAA team within 600 miles of Miami, and Charlotte is the second-best option for Atlanta, making a perfect fit for a 1-for-1 swap. The overall total mileage is only increased by 131 miles, or 2%.

And there are many other ways in which the problem could be adjusted to satisfy certain conditions, but these are certainly the most relevant.