Don't sports photographers know how to pan and catch the pak of action anymore?
In the early 40's while in high school I photographed high school basketball games with Indoor Kodachrome (Weston speed 12) and flash bulbs with a Kodak 35. The maximum shutter speed was 1/200, lens f 3.5.
Of course, the little #5 flashbulbs put out immense amounts of light but panning was certainly necessary as was catching the action at its peak.
A little practice at panning and learning to catch action at its peak will go a long way in eliminating the blurring.