Summary
Those who run the Hogsmeade School District (namely, McGonagall) are sick and tired of the students' lack of ability to behave. So, she comes up with a plan to unite them by placing them into groups and making them compete for points. It just so happens that by chance, fate, divine intervention, or the schemes of an old widow, James, Sirius, Peter, Remus, and Lily are in a group.