Poke Radar: Better to Run or Ride it Out?

[Dragonstrike]

If you're looking for a specific pokemon and aren't looking for a shiny of whatever you find instead of your target, it's waaaaaayyyy better to just run. You need to start a new chain anyways to find your target, so if you don't want to chain whatever you found instead, don't.

The only real 'drawback' to 'riding it out' is that it can take ages to reach a point where the odds of finding a shiny are decent.

Eevee and Duplicat are the rarest pokemon on Route 13 as well, each with a 5% encounter rate.  It'll probably take awhile to start a chain with them if you aren't incredibly lucky.