The state doesn't pay that huge deficit. The school does. Apparently they find considerable value in doing so. Perhaps they realize that excellence in sports has elevated UConn toward excellence in education. Perhaps they recognize that the state has chosen to invest in the university, at least in part because of the goodwill generated by its outstanding athletic teams. Perhaps they, correctly, realize that having competitive athletic teams is attractive to students, who are the university's lifeblood. Perhaps they understand that having successful athletic teams create a brand for the university and name awareness in students, and their parents.
In the end all of those things contribute to being able to pay for the college of arts and sciences, and many other schools as well, because if they didn't realize it, why would the university be doing so? Let me state this again, the state of Connecticut does not directly pay the athletic department, the University does. It probably does so for good business reasons.