People generally continue growing in their mental abilities until they reach the peak and then start going down. Age of the peak varies greatly. Many achieve at 20, but others are growing into their 90s.
So, for a politician any age past 50 may be a time of decline and by 80, they are a danger to the world, while a talmid chacham is still on the way to the peak and may refuse a position (yet). Just has this in the end of Ketubot – a Tanna refusing to become Rosh Yeshiva in favor of an (even) older colleague and taking it after the death of the older one.