7 of 9 added a citation for this being a legitimate question in the wild.

Does wearing a bicycle helmet make the cyclist safer?

Does wearing a helmet while bicycling make an individual cyclist safer?

That is, in the case of an accident, is one safer wearing an helmet? If yes, are the odds of an accident lower, higher or identical if one is wearing a helmet? If the odds of an accident are higher when wearing an helmet, does the added safety of an helmet in the case of an accident makes the practice worthwhile?

To substantiate this claim being in the wild, Mikael Colville-Andersen in a TEDxCopenhagen talk says they make things worse:

"To my surprise, it didn't take me very long to figure out that the bicycle helmet doesn't have a very impressive track safety record, scientifically. The scientific community has been completely split for years on the subject 50/50 down the middle. If you look at this way, if the bicycle helmet was a vaccine or a medicine there is no way it would be anywhere near getting approved by a ministry of health. There is simply not enough proof. [...] There are actually scientific studies that show your risk of brain injury is higher when you wear a helmet. You have a 14% greater chance of getting into an accident with a helmet on."