When discussing the history of women’s hats in the United States, the designer and author Steven Stolman was reminded of Stephen Sondheim’s “Company,” in which Joanne wryly asks, “Does anyone still wear a hat?”

Hats come and go in women’s fashion, but there is one place you can always find them. Mr. Stolman is well aware of that. He was in Kentucky to help Britainy Beshear, the first lady of the state, get ready for the 151st running of the Kentucky Derby, which she was attending in a dress he designed and a hat he helped select.

No American sporting event can match the sartorial splendor of the Derby, and Mr. Stolman, who is no stranger to such affairs, having donned a top hat to attend Britain’s Royal Ascot races, had many opinions on what made a good hat (and many more on fascinators and elaborate headdresses being entirely separate things).