Why Are Schedules Difficult?

Even moderately small leagues can be created in an incredibly large number of ways. Take for example an eight-team league playing a single round-robin (once against each of the other seven teams), playing one night a week at four different times, such as Friday night at 6 PM, 7 PM 8 PM or 9 PM. Once you have created a first draft schedule for this league, how many ways can those games be rearranged in order to achieve the goal of all teams having the same number of 6, 7, 8 and 9 PM games?

There are more than four billion ways! 4,586,471,424 ways to be exact. Optimizing a schedule has been studied by mathematicians for decades, but so far there is no direct mathematical solution (like solving three simultaneous equations with three unknowns). A home PC or webserver computer would take days or weeks to tediously test all four billion possibilities while searching for the optimal schedule.

The only way to optimize a schedule is to create an algorithm that intelligently tests and evaluates only a tiny subset of the total possibilities, rejecting the changes that make the schedule worse (according to a complicated set of criterion) and accepting those changes which improve the schedule. QuickScores.com contains such an intelligent and proprietary algorithm that yields perfect, or nearly perfect, schedules while only testing a few hundred alternatives. The resulting schedule is calculated on the webserver in only a few seconds and is virtually guaranteed to be better than any schedule created by hand.

In the example given above, for each of the 4 billion possible game arrangements, there are more than 268 million ways to arrange the teams in terms of home and away designation. QuickScores.com contains a second proprietary algorithm to optimize the home-away distributions for each team.