There are many symbols and signs used during basketball matches by both players and referees. The linguistic analysis of such symbols and signs is tenable with proper theoretical guidance.
This is similar to multimodal analysis. There are several variants. You can take a multimodality based on Lakoff or multisemiotics based on Kress & Van Leeuwen
It is a bit older now, but the work of Jabari Mahiri might give you some ideas. He did his fieldwork on youth and schooling by coaching a basketball league.
Mahiri, Jabari. Shooting for excellence: African American and youth culture in new century schools. National Council of Teachers of English, 1111 W. Kenyon Road, Urbana, IL 61801-1096 (Stock No. 44632-3050: $19.95 members, $26.95 nonmembers)., 1998.