Most chess tournaments of the size of a FIRST regional are paired with what is called a
swiss system. In round 1, the players are seeded (by rating), and split into top and bottom halves. The #1 seed in the top half plays the top seed in the bottom half, the #2 seed plays the second highest seed in the bottom half, and so on and so forth. In subsequent rounds the players are divided into groups by score, seeded inside those groups by rating, and each group is split into top and bottom halves and paired as above. The system's goal is to pair players who are playing well against one another. A variation is the accelerated swiss pairing system.
While the system as used in chess tournaments is not clearly not viable for a FIRST competition, the concept behind it (pair strong players against one another) should be.