Life is truly strange -- back in (much) younger days, I helped shoot some of the games at the college my brother was attending. We hand-built a couple giant softbox-like contraptions specifically to eliminate lighting like this.
Lighting like this is easy: a reasonably power strobe pointing straight down, mounted on the ceiling, about halfway between the basket and the free throw line. Normally you want it on a radio slave, so it only goes off when the "right" people shoot.
The "softbox" in question was only vaguely like a normal one, but still worked reasonably well. Basically, the strobe was still mounted on the ceiling pointed straight down, but something like 3 or 4 feet below that, we suspended about a 3x3 foot piece of plywood covered on the top with somewhat crinkled aluminium foil to reflect the light back upward. On the ceiling around the strobe was a considerably larger square of crinkled aluminium foil (probably 8x8 feet, or so, if memory serves). Then, probably seven feet down from the ceiling was a frame built out of PVC pipe (probably something like 12x12 feet), with white cloth stretched across it on the bottom. Canvas on the sides with still more crinkled aluminium foil kept all the light going where we wanted it.
With these, we got pretty even lighting almost where most of the action took place, at least in basketball. It wasn't quite so good for volleyball, where the action is mostly at mid-court, but even for that it wasn't too bad (a lot better than its predecessor, anyway). FWIW, I believe they stayed there in regular use until a new gym was built something like 15 years later.
