Notoriety seems to be short-lived here, too, to judge by the appearance of Matt Lauer, the former NBC co-anchor, at the Hampton Classic on Wednesday morning, a day of near Biblical rain. Despite having been, as Mr. Robbins said, “socially exorcised” from the Hamptons after his dismissal from NBC in 2017 amid allegations of sexual misconduct, there was Mr. Lauer grinning broadly beneath a Yankees cap as his ex-wife, Annette Roque, took photos of their 15-year-old daughter, Romy, in the show ring.

Contradictions, after all, are as essential an element of the Hamptons as sweet corn and farm stand tomatoes at $6 a pound. And the tales still told of talented but impecunious riders scrapping their way to the Classic on the back of some gifted nag discovered in a barnyard seem more than ever like myth.

“Everything about it is costly,” Kevin Babington, a leading rider said Thursday morning.

After schooling his award-winning Irish chestnut gelding, Mr. Babington dismounted in a tent set aside for top riders and handed him off to a groom. Son of the owners of a small department store in County Tipperary, Ireland, Mr. Babington expressed the same amazement a neophyte to the horse world might feel that one of humankind’s oldest pursuits has evolved into one of its costliest.

Bodily risks aside, Mr. Babington added, the sport is clearly not for the faint of heart. Consider, he said, the $4,000 monthly fees charged by some barns for boarding; the $1,500 Der Dau boots favored by many riders; an imposing list of tack-room essentials (bridles, saddles, martingales, girths, blankets, coolers, fly nets, galloping boots, spurs and crops for a start); the $300 fees required to enter certain show classes; the $100 it costs to braid a show horse’s mane and tail; and the fact that many horses require new shoeing almost as often as Sarah Jessica Parker.

There is, too, the steep price tag on the animals themselves. In the barn Mr. Babington shared this week with fellow professional riders there was more than one horse whose value exceeded $5 million.