Will a filter cause more or less damage when lens is dropped?

I recently dropped my camera bag from around waist level to the ground. The ground is somewhat padded (carpet) and the bag itself has padding (the typical messenger type of bag's padding). The camera was in a facing down position (lens towards the ground). I was shocked to find that after the drop my filter was completely shattered. I don't know how much damage was done to the lens yet as it is in the repair shop now. But just from looking at it the lens is not cracked, but possibly scratches.

So I guess the question is, in a situation like this, will it likely to have more or less damage with the filter? On one hand the filter broke and not the lens, but on the other hand the filter glass might have damaged the lens in itself.

I'm asking specifically to cases such as a drop and big impact damage (lens bumping to a wall etc).