Analysis of the Strength Factor on Thrashing and the addition of a "Rate Cap"

Yesterday I introduced the "Strength Factor" to force teams to visit the other divsion and cut down on late season "thrashing" in the milage. Lots of interesting details came out of that and more than likely many more are still hidden. A mysterious "M" graph of the League Total Milage forms as the Strength Factor is increased from 0 through the Demand/2 to the Demand.

Taken from Sheet 3

Today I ran some more tests on the thrashing, results can be seen in this excel file but it may be tough to interpret.

I have also included one of the final important peices of the program that has been missing. This is a "cap" in the milage a team must travel. until now, teams could be required to travel 1000 miles in 1 night and as much as 2000 miles in 2 nights (thrashing). It has taken a lot of work and through on how to remedy this, but by tracking how many "days off" a team has, and then multiplying it by an arbitrary "cap" we can find the allowed "range" for a team to travel between games. Currently I have the "Cap" set at 900 miles per day. I have seen this miles in an actual schedule before, so I feel comfortable with this. Since the maximum travel distance between two cities in the league is currently less than 1400 miles, a team can travel anywhere with 2 days off. This capping currently simply rejects a game request that requires excessive travel. This has cause several more games to be kicked out of the file and in rare cases there have not been enough "prostpective home dates" to complete a full schedule. I am currently working with 330 home dates (33 per team) to schedule 290 games (87% of the dates are used). As I noted earlier, the 2001-2002 Memphis schedule implies a much lower percentage (35 used out of 47 available, or 74%). With more available dates, my algorithm would choose better match ups and reduce the milage even further. I could also safely lower the "Cap" and generate less hurried travel.

Currently the "Strength Factor" is still causing some "thrashing" no matter where it is located in the season, since all teams use the same number. I am exploring makig the strength factor different among teams. Perhaps one division gets 1 strength factor that is different from the other divsion. This is similar to the CHL 96-97 season where all Eastern division teams played their Western division road games in the first half of the season (SF < Demand/2) and all of the western division opponents played their eastern division road games in the second half of the season (SF > Demand/2).

I may also explore having the home date selection program choose when a team should go west base on when that team's longest streak without home dates happens. Perhaps even using a constantly changing factor tied directly to the time until the next home date. This would allow for multiple shorter inter-divisional trips if neeed.

the last major problem to address are "unbalanced" schedules. the reason my work has centered on the 96-97 season is because it is perfectly balanced. Balance is rare, and in fact the CHL has not had balanced scheduling since the 96-97 season. Almost no other sports leagues I know of have balanced scheduling, so this is an important issue.

My current thoughts on the unbalancing is to continue to use the demand matrix, but allow higher values that will approximate the "maximum" number of match ups. This should force through the minimum meetings easily and approach the maximum as other demands become less important. There may be a requirement for a "Maximum" matrix to force a team to quit visiting an opponent once it has hit the maximum number of times. This will hopefully be explored tomorow.

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