According to this post over at Blue's News, Blizzard is actively working on reducing Overwatch draws. Hit the link for the complete rundown.
Responding to a post on the Overwatch Forums, Blizzard's Jeff Kaplan agrees with the sentiment of the post complaining about draws in Overwatch. He says testing of changes meant to reduce their frequency will begin soon in the multiplayer shooter: "We have changes coming to the PTR very soon. These changes will greatly diminish the number of draws. More details inc. extremely soon."