Need a little bit of advice here. I'm going to set up two strobes (been using one) to shoot HS basketball. They way the gym is layed out, I can safely mount two strobes behind the team benches on the 2nd level. The 2nd level is not used on that side, so I don't have to worry about curious fingers etc. But, that tends to lead to shadows when shooting. I have places to mount 2 SB800's on the opposite side of the gym (safely out of the way of people) to give a little bit of "fill flash", to eliminate shadows. Will something like this work well, just to the point of eliminating shadows?
Depends on where the camera is relative to the lights. If the strobes are over your shoulder and the SB800s are on the opposite side you'll get flat frontal lighting with backlight from the SB800s. If the lights are on opposite sides and you are under the hoop from the POV of the camera you'll get crossed shadows or in extreme cases heads lit on both sides with dark faces in the middle.
If you want to lighten the shadows from a dominant "key" light the more effective way to do it is to put the fill light over the camera where it is neutral, in the sense of not creating any shadows of its own which are visible to the camera. To visualize this set up your two strobes set at the same power at opposite 45 degree angles to a face. Then keeping one of the lights at 45 degrees to the nose swing the other one around towards the camera in 15 degree increments, keeping the distance constant with a string, until it is directly over the camera. Compare the appearance of the shadows.
Unless you have strong enough lights to light the court evenly (e.g., Speedotron 2400W/S units in each corner) the more effecting way to light what the camera sees is to put a rim light behind the action to create separation, define the shape of the players and create the illusion of 3D depth then use light from over the camera and heads of the players (at a natural downward angle) to get flattering light on the faces and fronts of the uniforms without any harsh distracting shadows.
You could do that by putting an SB800 on a camera flash bracket where it will always be where its needed to supply the frontal lighting, with your studio light up in the stands for the rim light component. You can fire them in sync with TTL control of the foreground by connecting the SB800 to the hotshoe via a TTL cable, with the studio flash triggered via radio from the PC connector. Paramount also makes a modified TTL cord for that mix of lighting:LINK
It all depends on the strobes you are using. The SB800s are pretty good flashes. You could always put them on one half of the court and the strobes on the other half. That way your strobes per side are even. If you direct fire the strobes/flashes, you are going to get shadows in most high school gyms. If you bounce them off the ceiling, you will get shadows, but they will be really diffused, and the SB800s may not give you enough power to bounce them. Last season I used to cheap strobes at one end of the basketball court and 2 Vivitars 285's at the other end and that worked ok. This year I have graduated to 4 AB800's and will be bouncing those off the ceiling in the gym. Of course the ideal location for strobes in a gym are on the ceiling pointed down at the 4 corners of the court. Close to the free throw line halfway between the hoop and the sideline. But since this is not practical for most gyms, if you bounce, pointing the strobes up at the ceiling about in the same location on each side of the hoop and above the free throw line should give you decent results. If you direct fire the strobes, I like pointing the strobes the end of the free throw line on the opposite side of the line from the strobe giving you a cross lighting. I try to point the strobe/flash so the center of the beam is about 5 feet above the free throw line. This usually gives good coverage from baseline to past the three point line.