What makes a “good” schedule?

The measure of a schedule's quality has many different, sometimes conflicting, aspects. QuickScores takes all of the following issues into account when creating a schedule.

• In a round-robin league, each team plays every other team the same number of times. In a fractional round-robin league, such as eight teams playing a ten-game season, a team may play some opponents more often than other opponents, but there will never be more than one game difference.
• All teams are distributed equally across the available game days, venues and times. No team has a disproportionate number of early games or late games, nor weekend games versus weekday games.
• The schedule has complete flexibility in terms of when and where a league plays, meaning a league can play on multiple days, fields and times, and no day-field-time selection affects any other day-field-time selection. All teams have the same number of home and away games.
• If a team plays multiple times in a week and the league plays on multiple days, that team's games should be distributed across the days to minimize the chance of a double-header on a particular day. If a team must play two games on the same day, those games should be on consecutive time-slots and on the same field.
• In leagues with odd numbers of teams, optionally replace the byes in early weeks by moving up games from late weeks. This not only minimizes the number of byes (every team wants to play every week), it shortens the season as much as possible and leaves the maximum number of bye games at the end of the season for rain-outs.
• The schedule must be able to block out specific days, such as national holidays, and still have an optimal distribution on the remaining days that are played.
• Flexibility in terms of games per week, such as teams playing one game per week for part of the season and two games per week for the rest of the season. This includes varying the number of games per week in order to stretch the season out to a particular desired end-date.

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 would take days or weeks to tediously test all four billion possibilities while searching for the optimal schedule.

The only practical way to optimize a schedule is to have 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 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 contains a second proprietary algorithm to optimize the home-away distributions for each team.