One thing I noticed early in my RAGNAR training was that I was getting some severe headaches after my runs, as well as some irritation around my eyes. We found out that the irritation was due to really high salt levels in my sweat. It turns out that it didn't matter that I was hydrating well and replacing electrolytes after my run. I was running on a "dry engine" and to some extent overheating my body.
So I started having a glass or two of water before I went out on my runs. I was concerned at first about this since it was an early morning run (soon after waking) and that too much fluid in my stomach would give me stomach cramps during my run. I've had that problem before and I think it is worse than the problem I was facing.
It turns out the average body can handle a glass or two of fluid shortly before a run with no problems. I found that my "overheating" issue went away immediately, and I haven't had any headaches since!
So take it from me, hydrate before you run!