Not that experienced with it but I believe it is an umbrella holder. It is probably larger due to the normal size of umbrella posts. Get a wooden dowel close to the inside diameter of the umbrella holder and drill a hole in the dowel the size of the sportsbrella shaft (considering you can find a dowel close to the diameter needed). Or some shaft collars could be used (McMaster-Carr, can normally be found at your local hardware store). Down and dirt way would be to wrap electrical tape around the sportsbrella shaft (just have to do two locations, at bottom of shaft and up from that however tall the umbrella holder is).
Other folks that have experienced your problem may have better thoughts though.