Last year, I made an expensive running mistake. The darkness and fog promised by my early morning run made me strangely nervous, so I did something I normally don’t – I took my cell phone with me. Just in case, I thought, and stuffed it in the front pocket of my allegedly “waterproof” jacket. I was off in an October-in-Portland morning, so you can probably guess where this is going.
Weatherproof Electronics
Yep. About 3 miles out, I got caught in an absurd downpour. The skies opened and it was like running toward a water cannon. Unable to see the sidewalk before my feet, I soggily forged ahead, figuring I was – again- earning my Portland runner stripes. What I was also doing, unbeknownst to me at the time, was frying the ever-loving circuitry out of my phone.
Save yourself the heartache of lost data and the wallet-ache of replacing it- plastic baggy your electronics – ALWAYS. Even if it looks dry outside. You know better than to buy that, you savvy Oregonian you.

As you suggest here, I keep an empty ziplock bag in my running shell just in case it starts to rain. But ever since I upgraded my smartphone to a Galaxy S5, which is supposed to be waterproof, I’ve felt more secure.
Mind you, not secure enough to test the waterproofing by submerging it in water. More like a backup feature. . . .