The 10%-16% figure comes from examining details of cyclists not wearing helmets.
Erke and Elvik (Norwegian researchers) 2007 stated: "There is evidence of increased accident risk per cycling-km for cyclists wearing a helmet. In Australia and New Zealand, the increase is estimated to be around 14 per cent."
So if helmets did provide 10%-16% protection this would be balanced out by the increased rate of accidents at 14%. As for injuries, head injuries covered by an helmet is about 10% of injuries, 90% other injuries.
1000 cyclists not wearing helmets - 100 accidents say, 10 head, 90 other injuries, total 100.
1000 cyclists all wearing helmeets - 114 accidents say, 11.4 head, 102 other injuries, assume helmets protect 50%, head goes to 5.7, others 102, total 107.7
Comparing head injuries, 5.7 to 10, good for helmets etc, compare total injuries, 100 to 107.7 not so good.
Much of the research promoting helmets focus on the ratio say 5.7 to 10 and they cannot assess the rate of accident involvement, patients arrive and they count head to other injuries and report on that, for helmeted 5.7 to 102 in the made up example provided, 4.75%. For non-wearers, 10 to 90 , 11.1%. Compare the two figures 4.75 to 11.1 and doctors will assume a major benefit.
In general injuries to cyclists are not serious, lowest number of days in hospital compared to other road users. Mills reported that 66% of cyclist's admissions were detained for just one night and most of the casualties with cranium injuries were admitted for overnight observation. http://www.cyclehelmets.org/1182.html
For the 57 cm headform, which fitted more snugly than the 54 cm headform, rotational accelerations from the oblique impact test averaged 13,500 rad/s², a level expected to produce a 35-50% risk of serious AIS3+ brain injury, higher than predicted for a non-helmeted head. Report PPR213 adds: “For rotational accelerations the research shows that concussion, AIS 1-2, can occur at 5,000 rad/s² and fatal injury AIS 5-6 at 10,000 rad/s². This correlates with data from the same research that indicates there is a 35% risk of a brain injury of AIS 3-6 at 10,000 rad/s².”
The conclusion from this info tends towards saying helmets increase injuries and may not provide the head protection expected.