I looked at 325 psychology study replication results today, and the best simple rule I found for telling if a study would replicate is this:
When the original study's p-value was at most 0.01, about 72% of the papers replicated.
Whereas when p>0.01, only 48% replicated.
Others have found similar results.
For instance, @uebernerd has suggested p=0.005 as a cutoff: