The 6D AWB can sometimes be a bit off, especially in that weird auditorium light.
1/160, f/4, ISO 6400, 70-200 f/4L USM
A quick dropper fix.
For Judo, the 6D would probably be fine, but for football/basketball, etc. not so much. I think the 5d3 or 7D and a nice prime/2.8 zoom would suit you nicely.