In the UK, the averages suggest that you are slightly less likely to be killed cycling two miles to the shops than you are making the same trip on foot, but slightly more likely to be seriously injured.
Over the decade from 2001 to 2010, there were 28 cyclist fatalities per billion kilometres cycled compared to 35 pedestrian fatalities per billion kilometres walked. Including serious injuries, it goes the other way: about 400 people killed or seriously injured per billion kilometres walked against 550 per billion kilometres cycled. (Full Fact summarises Department for Transport "Passenger casualty rates for different modes of travel".)
Other sources give slightly different numbers, and obviously these are all population averages and individual situations vary. Pedestrians include many relatively vulnerable people — children and the less abled and elderly — who are rarely found cycling, at least in the UK, so able adults are safer walking than those figures suggest. On the other hand, somewhere like Oxford is, while better for pedestrians than most UK cities, vastly better for cyclists, so anyone in Oxford is relatively safer cycling.
In any event, the risks involved in walking or cycling this kind of trip are roughly the same. The difference between them is much smaller than the difference between either one and catching the bus (clearly safer) or riding a motorcycle (more dangerous). So why is it that people who wouldn't even contemplate wearing special high-visability clothing or a helmet for a walk to the shops not only do so when cycling the same route, but try to insist on other people doing so too?
(Answer to rhetorical question. This is driven by a media and policy obsession about helmets which is largely a convenient way of blaming the victim, so the first question when an accident involves someone on a bicycle can be "were they wearing a helmet and flashing brightly" and not "was the vehicle driver grossly negligent" or "should someone be prosecuted for putting an 80cm cycle lane right next to 50mph traffic".)
I'm hunting actual figures for medium severity injuries (say all hospital presentations), but it's unclear whether taking those into account will bring the relative cycling/walking relative risk to a level that justifies radically different approaches to personal protective gear (legislative or personal).
However any measure of risk obviously needs to be weighted - all the non-serious and minor injuries put together are probably about the same concern as the fatalities and serious injuries, even if the latter are 100 times less frequent.
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