Helmets do not reduce accident numbers; they potentially reduce the injuries caused by accidents. We know that cyclists are safer when there are more of them around (drivers are more aware of them). Helmet laws reduce the number of cyclists on the roads, making cyclists more likely to be in an accident.

This doesn't even touch on other benefits (e.g. reduced heart disease, greater Vitamin D, less traffic) of more cyclists on the road.

The only effect in reducing the number of accidents that helmet laws make is in reducing the total number of cyclists that are on the roads; the proportion of cyclists in accidents doesn't go down with helmet laws.

Helmets good; helmet laws bad.