Concussion claims worry the insurance industry, and that means higher premiums, policy exclusions, and coverage disputes for sports leagues high and low, lawyers tell Bloomberg BNA.

The concerns are fueled by abundant concussion litigation, new medical research, and hints of an emerging toxic tort theory modeled after that used in asbestos litigation.

The NFL reached a $1 billion concussion settlement with retired players last year, but it was followed by a wave of litigation by insurers. They question their obligation...