When referring to the department, use the word "Athletics" (with an 's').
The word "athletic" is an adjective used to describe a physical attribute.
The word Roadrunner, when referring to the university mascot, should always be one word and capitalized. The singular usage is correct when describing a particular team. However, the plural usage is correct when describing a group.
Roadrunner baseball NOT - Roadrunners baseball
We are the Roadrunners. NOT - We are the Roadrunner
The same usage holds true for the informal and shortened use of the mascot, 'Runner and 'Runners.)
'Runner hoops NOT - 'Runners hoops
Go 'Runners! NOT - Go 'Runner!
Roadrunner is one word. NOT - RoadRunner or Road runner