I'm sure this has been covered ad nauseam but after a half hearted search I didn't find the answer to my specific question.

I'd like to get a couple of cycling caps and I'm afraid that wearing them will be an issue with visibility. I have some old ball caps that I currently use as sweat bands and surprisingly, they work pretty well for that but I can't wear them forward because being on a road the bill completely blocks your view of the road so I wear them backwards. How does the small bill on a cycling cap work when you're down in the drop bars? Does it obstruct your view of the road ahead at all or is bill suited for that type of riding?

Curious minds want to know. Well cheap/frugal ones do anyway.