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There’s an internet cycling claim, attributed to Mayer Hillman, that not riding a bike (at all) is ten times more dangerous than riding a bike, because it is so unhealthy to be unfit. I haven’t been able to find the statistics that back up this claim, even when I bought the book from which it allegedly came Cycling: Towards Health and Safety. The closest it comes is the statistic that in a group of commuting cyclists, roadway crashes (of all kinds) accounted for only 1.4% of deaths (whereas heart attacks in this group killed 33%, and the known reduction in heart attack risk with exercise suggests a substantial net reduction in mortality).

However, happily, I just found this:

Even after adjustment for other risk factors, including leisure time physical activity, those who did not cycle to work experienced a 39% higher mortality rate than those who did.

Unless you think a 39% boost in your risk of death is “safe”, a little old unarmored bicycle, no belts, no airbags, no roll cage, is safer than a car, at least for the first 50-100 miles of travel each week.

And there’s more (via UtilityCycling.org):
Conclusions: On average, the estimated health benefits of cycling were substantially larger than the risks relative to car driving for individuals shifting their mode of transport.