Which individuals in a network make the most appealing teammates? Which invitations are most likely to be accepted? And which are most likely to be rejected? This study explores the factors that are most likely to explain the selection, acceptance, and rejection of invitations in self-assembling teams. We conducted a field study with 780 participants using an online platform that enables people to form teams. Participants completed an initial survey assessing traits, relationships, and skills. Next, they searched for and invited others to join a team. Recipients could then accept, reject, or ignore invitations. Using Exponential Random Graph Models (ERGMs), we studied how traits and social networks influence teammate choices. Our results demonstrated that (a) agreeable leaders with high psychological collectivism send invitations most frequently, (b) previous collaborators, leaders, competent workers, females, and younger individuals receive the most invitations, and (c) rejections are concentrated in the hands of a few.