The answer is: persuasive influence.
Persuasion is the act of stimulating needs and making someone do or believe something through reasoning or argument. Influence, on the other hand, is the capacity to have an effect on somebody's behavior or character.
In the paragraph, the author wishes to encourage young people to take part in competitive sports, and provides sensible reasons to prove why they are beneficial. For example, he or she mentions team work and self-confidence.