Psychology is the study of the human mind. If we were simply robots, coaches wouldn't have to have any knowledge of psychology. However understanding human behavior and things like motivation, anxiety, concentration, and interaction. I will say this however to make a strong point. Studying psychology will not make you the best coach, any more than studying psychology makes you a great clinical psychologist, or studying human anatomy makes you a great doctor.
Great coaches understand the role of the mind and how the game of basketball is played.
Most coaches have had some psychology classes but rely more on human experience to teach them how to motivate and deal with the mind of their players. Teams are brought together by having clearly defined goals and player and staff roles that are totally accepted and executed to the best of everyone's ability. Championship teams will attest that they each do their part to the best of their ability to contribute to the team's overall success. When individuals and their goals and desires become more important than the team's you will never achieve the success a team is capable of achieving. The coach brings a team together by constantly communicating roles, and the team needs versus the individuals.