LogFAQs > #901279581

Progression is random yes, although each character has pre-determined max potential stats. If they get way ahead of their average progression, that stat becomes less likely to get a boost. Similarly, if they get way behind that stat becomes more likely to get a boost.

On your first playthrough you only get partway through the total progression so there's plenty of room for randomness in which characters end up with top stats. The randomness in Serge's STR progression is actually a significant concern in speedruns of Chrono Cross.