OK, the FTE numbers can still be disputed and there's much more to be settled, but let's face it -- this is interesting stuff to discuss while we're waiting between plays at tonight's first round playoff games.

At any rate, below are my (waaaaaaay too early) projections for the how the region alignments will shake out. The classifications are from Todd's recent post and only reflect football playing schools.

As an important disclaimer, much is still to be decided on the new classifications (did I mention this is waaaaaaay too early?) , not the least of which are the cutoffs for the new Class AAAAAAA and for Class A, from which the other classification numbers will be determined.  Also, it appears, to me at least, there are some unexpected consequences from the out-of-county rule bumping some teams up perhaps too much.  As an example, if the cutoff is indeed 450 for Class A, then Pace Academy, with 451 students and 23.7% from out-of-county automatically goes from Class AA to Class AAA.  Meanwhile, this could potentially put them in the same class as Cedar Grove, who with 1,083 students might be given a chance to go from Class AAAA to Class AAA due to other Class AAA schools being bumped up.

Not sure how, or even if, those issues will be addressed, but Todd's list is good enough to at least get an waaaaaaay too early look.

The projections below were achieved using a process called simulated annealing.  Simulated annealing is commonly used when a combination problem is so large it is impractical to do a exhaustive search of every possibility.  Consider in Class AAAAAAA, the smallest class with 53 teams, there are 1 x 10^42.55 possible combinations.  In Class A, the largest, there are 1 x 10^59.31 possible combinations.  For comparison, consider there are only an estimated 7.5 x 10^18 grains of sand on the entire earth.

In essence, the program starts with a random region alignment and then examines various swaps at random.  If the swap improves the solution then it is accepted, however occasionally the program will make a swap in the opposite direction in an attempt to "jump" to a better solution.  As the program runs, the chances of making a swap in the opposite direction are gradually reduced and the solution "converges" when no further swap can be made in the right direction.

The region alignments take approximately 10,000 swaps before converging.  However, because even that cannot guarantee the optimal solution has been reached, it performs 10,000 restarts from the best previous solution.  This process takes approximately three hours for each classification and while simulated annealing does not guarantee the optimal solution, it provides one that can’t be significantly improved upon with additional effort.

Although we'll never know for certain if we've found the optimal solution, we can judge the solution found by how often we realize that same answer out of the 10,000 restarts.  Class AA realized the same results 5,744 times, meaning that 57.4% of the time the solution is the same, giving us a great degree of confidence that it is the best we can do.  On the opposite end, Class AAAA only realized the same solution 3 times out of 10,000 restarts, indicating the optimal solution is more difficult to find.  But here again, the one we have can't be significantly improved upon with additional effort.

The program attempts to minimize the Great Circle Distance ("as the crow flies" distance) between schools.  Schools in the same district are counted as the square root of the distance to encourage their placement in the same region.  The program also seeks to keep regions a similar size.

Below the teams are organized by "Groups", going from the east to the west according to the average longitude of the teams in the group.  This "Group" is not intended to be the region designator.

Region projections (waaaaaaay too early . . .)

AAAAAAA

AAAAAA

AAAAA

AAAA

AAA

AA