Richmond and Washington play Water Baseball

I note that the Richmond Braves are not the AAA affiliate of the Washington Nationals, and my assignment of major league teams to AAA minor league teams in my previous post did not pair the Richmond team with the Washington Nationals, either. That's too bad. I think the Hungarian algorithm did not pair them because it saw a better virtue in avoiding the long distance between the Baltimore Orioles and the Durham Bulls. Instead, Richmond wound up with Baltimore. I think it's too bad, because the Richmond Breeze (can't call them Braves any more) and the Washington Nationals would be a perfect match for each other.

Last year, the Richmond Braves ballpark flooded during storms because of poor drainage, and several home games had to be played as road games. They fixed up the park, but there are some people in Richmond who want the Braves in Shockoe Bottom. A serious problem with this is that it could flood. Shockoe Bottom experienced a major flood last year when Tropical Storm Gaston hit. Seems the Braves will be flooded out no matter what happens. But this makes them a perfect match for the Washington Nationals, as a recent game (2005 April 30) there was so badly affected by huge puddles at RFK stadium that both teams protested the game.

Yes, the Richmond and Washington teams would make a perfect match. But then they should be renamed the Washington Ark and the Richmond Noahs.

Minimizing distances between major league and AAA baseball teams

On 2002 August 20, I posted a blog about how I did a study that found a pairing of major league teams to their AAA minor league affiliates that minimized the total distance traveled. I found, among other things, a three-way swap among the Baltimore Orioles, Atlanta Braves, and Pittsburgh Pirates that cut down the total driving times between these clubs and their AAA affiliates. I sent letters to the Atlanta, Richmond and Rochester newspapers about the proposal but did not get any response. Later, a three-way trade did occur, among Baltimore, Minnesota, and Montreal (now the Washington Nationals) that actually increased the travel time.

There have been a lot of changes since then. The Albuquerque Dukes left town, and then came back as the Albuquerque Isotopes. The Canadian teams were hard hit. Once there were two major league teams and four AAA ones in Canada; now there is only one major league team and one AAA minor team. With all those changes, what would happen if I tried it again?

I used the Hungarian method, as I used before. I will describe the details elsewhere, but in this method, a table of distances is derived. I used a trigonometric formula together with the latitudes and longitudes of all the baseball teams to create the table of air, or "as the crow flies" distances. This should be a good approximation of the actual distances traveled. I then subtracted the minimum distance from each row, and the minimum distance from each column, to create a zero in each row and column. I then tried to assign as many zeroes as possible, with no two such assigned zeroes being in the same row and column. Then I tried to increase this by taking a major league team without an AAA affiliate. I found the minor league teams that have a zero for this major league team. If one of these did not have a AAA affiliate, I assigned it to the major league team and increased the number of teams with affiliates. Otherwise, I found the major league parents of these teams and searched for alternative AAA teams. I kept doing this over and over again until I either found a minor league team that is not assigned (in which case I did a bunch of swapping to increase the number of major league teams with affiliates) or I found that all major league teams that I am trying to find alternatives for did not have any. In the latter case, a failure, I changed all the distances by a formula designed to preserve the solution and increase the number of zeroes. I kept doing this whole thing over and over again until all teams were paired.

This turned into a real struggle at the end, with iteration after iteration failing, until a huge swap affecting just about every team occurred at the end, starting with the Pittsburgh Pirates and ending with the Tacoma Rainiers. This is the resulting arrangement, with changes in bold:

Arizona Diamondbacks - Tucson Sidewinders
Atlanta Braves - Nashville Sounds
Baltimore Orioles - Richmond Breeze
Boston Red Sox - Pawtucket Red Sox
Chicago Cubs - Iowa Cubs
Chicago White Sox - Omaha White Sox
Cincinnati Reds - Louisville Bats
Cleveland Indians - Indianapolis Indians
Colorado Rockies - Colorado Springs Sky Sox
Detroit Tigers - Toledo Mud Hens
Houston Astros - Round Rock Express
Kansas City Royals - Oklahoma City Redhawks
Los Angeles Angels - Salt Lake City Stingers
Los Angeles Dodgers - Fresno Grizzlies
Florida Marlins - Charlotte Knights
Milwaukee Brewers - Columbus Clippers
Minnesota Twins - Norfolk Tides
New York Mets - Ottawa Lynx
New York Yankees - Syracuse Sky Chiefs
Oakland Athletics - Portland Beavers
Philadelphia Phillies - Scranton WilkesBarre Red Barons
Pittsburgh Pirates - Buffalo Bisons
St. Louis Cardinals - Memphis Redbirds
San Diego Padres - Las Vegas 51s
San Francisco Giants - Sacramento River Cats
Seattle Mariners - Tacoma Rainiers
Tampa Bay Devil Rays - New Orleans Zephyrs
Texas Rangers - Albuquerque Isotopes
Toronto Blue Jays - Rochester Red Wings
Washington Nationals - Durham Bulls

Many close pairs, such as Detroit-Toledo and Boston-Pawtucket, got assigned with each other, and this is indeed their actual arrangement. There are some differences. In two cases, I had to change the name of an AAA team because it would become inappropriate - Omaha Royals to Omaha White Sox, and Richmond Braves to Richmond Breeze, as in Sweet Virginia Breeze. The Minnesota Twins got paired with the Norfolk Tides (they are right now paired to the Rochester Red Wings). This is one of those odd relationships that are forced. If one attempted to get something closer for Minnesota, such as Iowa, other swaps would be forced, and the total distance of the result would be greater. An interesting pairing was the two Indian teams, Cleveland and Indianapolis. So this arrangement would clear up that ambiguity, although Native Americans might want the names of both changed.

I am not sure how much adopting this arrangement would save in travel costs for major league baseball, but I expect that in the future that efficient arrangements like this may be necessary because of the impending running out of cheap oil.