On the strength of something
Definition 1 of 2
Pro Tip 1/3Evidence Justification
Used when the reason is considered solid and often tangible, like facts or data. 
The theory was accepted on the strength of scientific proofs.
Pro Tip 2/3Qualification Importance
Emphasizes that specific qualifications are the main reason behind a decision or opinion. 
He became a lecturer on the strength of his PhD.
Pro Tip 3/3Professional Credibility
Indicates that past performance or reputation plays a crucial role in current opportunities. 
The artist had exhibitions on the strength of his reputation.