A process for sorting students into diverse teams

I have recently agreed to teach a class during the Fall 2014 semester, so I am listening more closely than ever to conversations related to forming students into teams as I anticipate teaching in one of the active learning classrooms.  Don't get me wrong, I've used group work in classes many times before, but there is something about the active learning room being focused on students working in groups that has me thinking more carefully about group formation.  What is the best way to organize students into teams?  In the past, I've tried a variety of approaches, including organizing students by major/program and gender (with the hopes of a somewhat even distribution), allowing students to choose their own, and enlisting our course management system to randomly assign students to groups.  Other instructors on campus have students join teams based on availability for meetings, skills/strengths that align with group roles, grades in prerequisite courses - the list goes on and on.  As with most other things, the best option for organizing students into teams seems to largely depend on the objective.  

Given that there are options aplenty, one group formation approach at a time will be highlighted here in order to allow room for some discussion of the when and why aspects.  Today's focus is on the approach recommended by the Team-Based Learning Collaborative, which aims to provide all teams with equal chances at success.  The general advice from the Collaborative (see response to forming teams FAQ here) points to three recommendations:

1. distribute assets and liabilities ("background factors that are likely to make a difference in students' performance in this class") as evenly as possible across groups, 
2. be sure that teams do not include pre-existing subgroups that may hinder the team's ability to work together as a whole (e.g., three roommates paired with two other students who do not know each other), and 
3. teams are formed using a process that is transparent to the students.

Luckily, the Collaborative's website also offers Michael Sweet's example of how to quickly form student teams according to these guidelines (see "Forming Fair Groups Quickly" halfway down the page).  In this example, the formation of the teams actually takes place in the classroom; however, the instructor has a couple of key decisions to make ahead of time.  The "sorting criteria" - that is, the characteristics that should be evenly distributed across the student teams - must be determined and prioritized in advance.  What strengths ("assets") should be distributed across teams?  What challenges ("liabilities") are best to spread out?  If students who have completed an advanced statistics course, for example, are likely to be at an advantage in the course, then identifying this as a sorting criterion and ensuring those students are evenly dispersed is important.  Likewise, if students without experience collecting data are going to be at somewhat of a disadvantage, then that experience/lack of experience should be evenly distributed as well.  Once these criteria have been identified and prioritized, then the sorting of the students and counting off into teams can commence.  This approach is likely to work best for instructors that are interested in forming (strategically) diverse teams that have an element of randomness to them so that each team has a pretty even chance at succeeding on the project or in the course.