Several studies show that the risks of injury to pedestrians and cyclists are highly non-linear. This means that the more pedestrians or cyclists there are, the lower is the risk faced by each pedestrian or cyclist. On the other hand, the more motor vehicles there are, the higher becomes the risk faced by each pedestrian or cyclist. The relationships found in previous studies suggest that if very large transfers of trips from motor vehicles to walking or cycling take place, the total number of accidents may be reduced. The "safety in numbers" effect for pedestrians and cyclists would then combine favourably with the effect of a lower number of motor vehicles to produce a lower total number of accidents. This paper explores if such an effect is possible, relying on the findings of studies that show the non-linearity of injury risks for pedestrians and cyclists. It is found that for very large transfers of trips from motor vehicles to walking or cycling, a reduction of the total number of accidents is indeed possible. This shows that the high injury rate for pedestrians and cyclists in the current transport system does not necessarily imply that encouraging walking or cycling rather than driving will lead to more accidents.