Add a dot or similar metric to race against on a route you have run previously yourself or a friend.

[anchskier]

The Strava Live Segments feature pretty much does this (not a map, but shows the time ahead or behind as you go through a segment) already.  You would have to make the "route" into a "segment", but it can be done.  

[Jane]

Hello!

Thanks for your post.  I would encourage you to check out our live segments feature.  That feature allows you to race against your own PR or a friend's PR.  Find out more about Live segments

Also, check out this blog post where some Strava employees describe how they use the feature to compete with themselves and others.