Mine That Bird, with jockey Calvin Borel, came from the back of the field to win the 2009 Kentucky Derby by nearly seven lengths as a 50-1 long shot. (Jamie Squire/Getty Images)

He dwells at the end of a pretty but unpretentious driveway lined at its outset with stouthearted yuccas. He takes visitors with or without appointments in a paddock that’s easy whinnying distance from two modest one-story houses. He resides on the high plains, outside a city of about 48,000 where tourists might drop by after seeing the International UFO Museum.

Ten Kentucky Derbies ago, Mine That Bird was his own sort of UFO — unidentified at the top of the stretch even by a great race-caller, flying from hopeless yonder to a 6¾ -length blowout, an object of mass bewilderment. At 50-1 odds he forged an upset that tied him with Giacomo in 2005 for second biggest in race history, behind only Donerail at 91-1 in 1913. Mine That Bird’s narrative continues to giggle at the supposed nonfiction of it.

Everyone knows about living Derby winners. They inhabit lush, verdant, Kentuckian farms with names such as Ashford Stud, WinStar, Darley’s Jonabell, Taylor Made, Claiborne, Calumet. Some venture abroad. In a quirk nowadays, two live in Oregon. In a bigger quirk, one lives here, not far down the Texas-bound road past the sign indicating that Tatum lies 71 miles ahead, Lovington 93.

How many Derby winners live behind a fence with a sign reading, “PLEASE DON’T CHASE BIRDS”?

Further, the smallish bay gelding lives here for one hell of a reason: He’s beloved. “He has that connection with me and [co-owner] Mark [Allen] that we’re not going to let him go to any home or any farm,” said co-owner Leonard Blach, 84, retired lately after 58 years of veterinary practice. “And not that there’s anything wrong with that. It’s just that he’s one of the family.”

Mine The Bird, in retirement earlier this month at the Double Eagle Ranch outside Roswell, N.M. (Chuck Culpepper/The Washington Post)

To visit Mine That Bird, go through downtown Roswell with its statues of extraterrestrials, including a gigantic one at Dunkin Donuts, in honor of a visit the area might have received from non-earthlings in 1947. Turn left just before the UFO museum and the alien store. Follow the unprepossessing boulevard east 3½ miles past the silo, the Cowboy Cafe, the house with an alien out front and a dinosaur in the garden, the stand selling honey, pollen and beeswax. Turn right at the billboard advertising Allen’s Double Eagle Ranch.

Drive the driveway, hear the screeching birds and gasp, if you will, 1,200 miles from Louisville, at what comes next: a replica of the twin spires at Churchill Downs. Blach designed it. A local tinsmith made it. Mine That Bird lives below it, in a good, clean, functional, unostentatious shed with four stalls. Blach lives directly across from it, across Route 254 at his Buena Suerte Ranch with its Buena Suerte Equine Clinic.

“I drive in there probably, I’d say, almost once a day, usually in the morning,” Blach said, “because I get up early and have breakfast with buddies in town. I come home just to check on him, and in the summertime we leave him out. A little Shetland’s in there with him, and that keeps him quiet. The training center over there behind . . . the horses would gallop, he could see them, and he’d just pace that fence.”

So Blach got Winston, the Shetland, and while the two horses aren’t all that gaga about one another, they make do. “They don’t really get along,” Blach said, “but they don’t fight or anything.”

The vet figures Mine That Bird has a long, happy, New Mexico life ahead, maybe even to age 30 or so, with bags of peppermints still arriving from human admirers afar and burial slated for just below those spires.

For this Derby weekend, Mine That Bird will make an appearance at Sunland Park close to El Paso. The horse finished fourth at the facility’s biggest race, the Sunland Derby, in March 2009 before finishing 1-2-3 in the 2009 Triple Crown series. He would not win another race in nine starts between the Derby and retirement.

It all remains merrily ludicrous, 10 years after the post-Derby quotation of trainer Chip Woolley, which went, “To be honest, I didn’t have any real feeling that I could win the Derby.”

The two minutes of life in which they did left Blach’s office permanently renovated. Photos of May 2, 2009, crowd the walls of the house across the street from the residence of the horse who caused such shock. A stirring one just to Blach’s left as he sits at his desk focuses upon Mine That Bird as he enters the first turn, trailing his 18 rivals with a palpable absence of hope.

Ten years on, it’s still jarring to hear Blach say casually: “And I never thought we could win the race. I only hoped and prayed after he started that he’d run up in the pack someplace — fifth, sixth, 10th — and just sort of get lost in there, so we’d run in the Kentucky Derby and we didn’t run last.”

And then: “And then what a downer that was, watching him do that thing [of getting bumped out of the gate and then trailing]. ‘Oh, Lord, just don’t let him run last.’ Then here he comes, you know, picking his way through that crowd and onto the rail with Calvin [Borel, the jockey], win by six and three-quarters, and it’s a high then.”

And: “I just can’t, even today, put into words how exciting that was.”

Each anecdote Blach revisits seems to pile on allure, one decade on.

There’s the one about the Churchill Downs racing secretary calling Allen about a month before the race to suggest the owners try the Derby because their horse had earned enough money as a 2-year-old in Canada and Allen thinking the call was a prank and the racing secretary calling again the next day. There’s the one about the Derby connections party on Derby eve, when a hostess saw the cowboy hats in the Mine That Bird group and admonished, “This is a private party,” before correcting the error and sending them to their allotted Table 23 in a distant corner.

There’s the one about Allen and Blach not realizing they lacked a Kentucky racing license until the Thursday before the race and trying to alert someone in an office that evening by throwing twigs and whatnot up at the windows. There’s the last-place finish in the Breeders’ Cup Juvenile at Santa Anita in fall 2008, after which trainer Richard Mandella both advised Allen and Blach to take their horse home and encouraged them about his quality.

There’s the very idea their spring plans included not the Derby but ventures to southwestern tracks such as Lone Star Park in Texas and that the TV cameras kept going right past them in the run-up to the Derby in Louisville and that they felt relieved about that and that after they won the Derby, certain relatives of Blach didn’t even realize he had entered the race until seeing him on TV winning it.

There’s the eternal detail of the 1,200-mile road trip Woolley took from Roswell to Louisville, hauling Mine That Bird’s spiffy van.

“A miraculous miracle,” Blach called it, which didn’t ring as overstatement.

On a late morning during Derby week 10 years on, he drove across Route 254 as he always does, got through the driveway and past the houses and stopped his truck next to the paddock fence. He got out and called for Mine That Bird, who was all the way across the space alongside the Shetland. At first Mine That Bird either didn’t hear or pretended not to, whereupon Blach said, “Don’t be so lazy,” and, “Get over here,” and then, “He knows.”

In the high plains of eastern New Mexico with the horizon that looks halfway to forever, one of the world’s most beautiful UFOs lumbered across, maybe even playacting his trudge for effect, until he reached the humans and the peppermints. As he and Blach cavorted like old chums, horse and human, so far in every way from Kentucky, it still seemed implausible that 10 years ago they epitomized that, at its best, sport remains a mystery.