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This is one of those statistics where the method of recording greatly impacts the variance in data provided. Compulsory helmet use in sports cycling often results in a flimsy helmet becoming a damaged helmet during a crash and then being recorded as a head injury where no head injury was sustained as a possible impact is derived from the helmets condition, where in other sports no helmet is worn to act as an indicator and so the threshold for registering head injury is much higher. It's like if you walked around in a tissue paper suit and then went into hospital showing the tissue paper suit was ripped, any smart medical person would record "possible x" anywhere the suit was ripped even if just to cover themselves, exactly the same with helmets.
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For what you say about these statistics to be true, i.e that many of the recorded incidents involved no injury, it would make this statement above the stats a lie:
"the number of sports related head injuries seen in hospital emergency rooms:" Ambulance staff rarely take un-injured people to ER.
I think a bigger problem with the stats is they are not recorded against time spent engaged in the sport, or against number of individuals involved in the sport, without which they mean little.
I've fallen off my bike twice this week on the ice and I have a sore wrist and shoulder.
This site has put together data from the US for sports, not percentagised though, but you could work that out if you could be bothered
For 'football' obvs read 'American football'
http://www.brainandspinalcord.org/brain-injury-statistics/
Cycling: 64,993
Football: 36,412
Baseball and Softball: 25,079
Basketball: 24,701
Powered Recreational Vehicles (ATVs, Dune Buggies, Go-Carts, Mini bikes, Off-road): 24,090
Skateboards/Scooters (Powered): 18,542
Soccer: 17,108
Skateboards/Scooters: 16,477
Winter Sports (Skiing, Sledding, Snowboarding, Snowmobiling): 16,120
Water Sports (Diving, Scuba Diving, Surfing, Swimming, Water Polo, Water Skiing): 12,096
Horseback Riding: 11,759
Health Club (Exercise, Weightlifting): 11,550
Golf: 8,417
Trampolines: 7,075
Hockey: 5,483
Gymnastics/Dance/Cheerleading: 5,459
Ice Skating: 3,703
Fishing: 3,560
Rugby/Lacrosse: 3,281
Wrestling: 2,640
The top 10 head injury categories among children ages 14 and younger:
Cycling: 32,899
Football: 17,441
Baseball and Softball: 13,508
Skateboards/Scooters (Powered): 11,848
Basketball: 10,844
Skateboards/Scooters: 10,256
Winter Sports: 7,546
Powered Recreational Vehicles: 7,460
Water Sports: 6,498
Trampolines: 6,360