There’s a very subtle difference. On the sports ground implies you’re referring to the actual pitch, field, track, court etc. At the sports ground refers more generally to the area or place where the sport is played. The whole sports ground or stadium or arena. Where are you right now? Oh I’m at the sports ground. What are you doing right now? I’m playing tennis on the spurts ground. But personally I think it’s fine you use either of them in the example you gave