If someone threw pebbles towards me, the chance of one hitting my helmeted head would be proportional to the cross-sectional area visible to them. If I fall off my bike, the chances of my helmeted head hitting the ground is different. It depends on whether I manage to stop my head in time, perhaps by letting another bit of me absorb the impact. Making my head bigger will make this more difficult, and this will vary with the additional radius that the helmet gives to my head, though probably not in a simple ratio.
Think about a long pendulum swinging in a small room. The swings can be of varying amplitude. You can also increase the size of the bob. Whether it hits a wall will depend on the size of the swing and the radius of the bob.
A head on a springy neck attached to a falling body behaves rather like a pendulum. Land on your back, shoulder or outstretched arms and immediately after contact with the ground, your head will continue moving towards it. If the fall is gentle and you are fully conscious, you will probably be able to keep your head from hitting the ground hard. If your fall is faster, your head may have too much momentum for your neck muscles to be able to stop it before it hits the Tarmac. In that case, how hard it hits the Tarmac depends on how soon it hits the Tarmac, in other words, on how thick your helmet is.