Alexander Jablokov lists on his blog “Five reasons writers don’t improve with age”. It’s a depressing thought for an SF writer like him, although he’s one of note, but is it true? Are writers more like lettuce, best when picked fresh off the field, or whiskey, aged for decades in their cellars?
We can have personal opinions about whether the later books from a writer are better than the earlier ones, but there is a more general criterion in the form of book awards. Let’s look at the Hugos for best novel, and see how old the writers were when they won them, and for how long they had been writing at that point:
Authors tend to win after 20 or so years of writing
The youngest winner was Roger Zelazny at age 29 for “This Immortal”, the oldest were Vinge, Clarke, and Asimov at 63, and the average age is 45. The shortest interval from first-published-work to award was again Zelazny at 4 years, while the longest was Asimov at 44 for “Foundation’s Edge”. No surprise there – Zelazny burst on the scene like a nova, and Asimov was a star for generations. The average time from start to award was 17 years. Quite a few people had late starts – having first published in their mid-30s – and still won. I would say that the author who changed the most from his early work to his winning novel was Frederick Pohl, whose 1978 “Gateway”, written when he was 61, is quite different from his famous 50s satires like “The Space Merchants”.
Overall, then, it looks like writers do improve with age, at least up to 20 years or so into their careers. Those careers are pretty long compared to a lot of fields. Joe Haldeman once remarked that when he in college, he thought seriously about going pro in baseball. Instead he went to Vietnam, got blown up, and became a writer. He was in his early 30s when “The Forever War” came out, and was considered a promising young writer. As a baseball player he would have thinking about retirement. 22 years later he won again for “The Forever Peace”, a book quite different in style but playing with the same themes. Imagine being a star baseball player in your 50s!
Now I’m curious about the distribution for other fields like music or drama, but that’ll have to wait for other entries.
A Niche in the Library of Babel 
The conclusion doesn’t really follow from the data though does it?
The chart suggests that awards are distributed fairly evenly across all ages. If you assume that late career recognition is also based on recognising lifetime achievements then the chart shows the opposite of what you suggest – authors write their best stuff while young (on average).
Yes, the awards are fairly even distributed in age, although they start late, with the youngest at 29. Compare that to movies or music, where teenagers win Grammys or Oscars. The years from start to win are also fairly evenly distributed, with similar numbers of writers winning in their first ten years, between 10 and 20 years, between 20 and 30, and after 30 years. It doesn’t look writers peak at 20 years, but they don’t burn out after 5 either. They don’t wilt immediately after being picked!