This is a highly research area and whilst there is some debate about the reduction in “tooth on tooth impact” when wearing a mouthguard, there is little correlation to that extending to reduced brain movement. This is a common misconception and to date there has not been any conclusive evidence that suggests it is otherwise.
If we consider what causes a concussion it makes it easier to understand. The skull, contains the brain which is surrounded by fluid. This fluid is to cushion the brain from light impact. We receive a concussion when our skull is impacted so forcefully that our brain pushes against the inside of our skull. This collision causes chemical changes in the brain and sometimes stretches and damages our brain cells. When we receive an impact of this magnitude we are hopeful that our mouthguard will protect our teeth from damage and assist in other ways, but a mouthguard will not prevent our brain from hitting the side wall of our skull.