They don't even allow themselves to think as they did in '06, when Brette always told Matz, "If this horse can't win the Kentucky Derby, I'm never going to saddle another horse."
"Every time I led him over, I never ever thought for one minute that he would get beat," Brette said. "I would have been heartbroken if he had gotten second. It's really strange and silly to think about now."
Here they are again at Churchill, site of their greatest triumph, Barbaro's 61/2-length romp, the largest winning Derby margin in six decades. Barbaro's ashes are buried outside the front gate, by the Barbaro memorial. But this isn't a week to stay in the past. Union Rags is easily the best horse they have had since Barbaro. Winning a second Kentucky Derby? It would be an amazing accomplishment.
"I wouldn't say I had slim years, but I don't get the horses every year that I'm going to have a horse that runs in the Derby," Matz said. "Mostly I get fillies that are horses that are homebred, that are nice fillies. I don't get that many colts.
"The odds of me having another horse that's as good as Barbaro - whether he's as good, or whether he's better, we don't know yet - but he's pretty darn nice and he looks like he's pretty special. Some people never get one in their lifetime. Now I might have a second. That's pretty special. You just never know how it works."
Brette believes Union Rags has power that can't always be measured with a stopwatch.
"It's a feeling - for me, it's never about the time," Brette said. "The time is secondary to the feeling that he gives you, the power, the balance, everything that comes along with it. It was the same with Barbaro."
Matz, a three-time Olympian equestrian who lives on a farm outside Coatesville, a silver medalist at the 1996 Atlanta Olympics who carried the U.S. flag in the closing ceremonies, has shown grace under pressure in all sorts of circumstances. One reason he was selected by his fellow Olympians to carry the flag was his role in helping some children to safety in 1989 after United Flight 232 crashed in an Iowa cornfield, killing 111 people.
Brette, who grew up in Stockton-on-Tees, in the northeast of England, also was on horses as a teenager. He became a jockey in Dubai, a champion jockey, then private trainer for the late Sheikh Maktoum bin Rashid Al Maktoum, the ruler of Dubai. Eight years ago, Brette came to the United States and he soon signed on with Matz, working out of the Fair Hill Training Center in Elkton, Md.
Now, Brette and Matz have the kind of horse that creates big dreams.
"It's obviously a big responsibility," Matz said of training horses of this caliber. "You want to make sure everything goes right."
Brette, the exercise rider for both Barbaro and Union Rags, spoke of the differences between the two physically imposing horses.
"If I was going three-eighths [of a mile] with Barbaro, I'd go 12, 24, 36," Brette said, explaining that every furlong would be 12 seconds. He meant every furlong, he said, until he worked to pull Barbaro up. "I'd gallop out in 48, gallop out [another furlong] in a minute, gallop out [another furlong] in 1:12. Every time."
"This horse, I can go 12, 24, 36, then he'd gallop out in 52 [seconds], then [another furlong in] 1:04, quite happily," Brette said.
"He's very easy to come back to you. When you finish your work, he's very easy to come back. He's very nice, very kind. Whereas Barbaro, you'd put him on the rail and physically I'd have to pull him off.
"This horse is much kinder [as it regards responsiveness and control]."
If that sounds like damning Union Rags with feint praise, Brette didn't mean it like that. Having a horse that is less headstrong has its advantages, he said.
"Barbaro was always on the pace, always - just off the pace," Brette said. "This horse is very amenable. If it's a real fast pace, he can sit a little farther back. If it's not, he can be a little forward."
Another difference, and this was obviously to Barbaro's advantage: "Barbaro just did everything instantaneous. Whereas this horse, I think he needs to go through the gears to get to his top speed."
Brette said Union Rags, owned by Phyllis Wyeth of Chadds Ford, to be ridden in the Derby by Julien Leparoux, has that top gear. He's shown it multiple times, most recently when he blew away the field by four lengths in February's Fountain of Youth Stakes at Gulfstream Park in Florida.
"He just needs a little more time to get there," said Brette, who, like Matz, considers a third-place finish in the Florida Derby on March 31 to be a throwaway because the horse got boxed in most of the way.
Matz and Brette don't express concern about Union Rags getting the 11/4-mile distance required of the Kentucky Derby, or about the 20-horse field.
"I think the Derby will suit him," Brette said. "They go so quick. He's a big boy. If he gets roughed up, it's not going to be the end of the world. If they go fast enough, as [jockey] Calvin Borel's shown, you can win from anywhere in the Kentucky Derby. All you need is the clean trip. That's what we'll hope for."
They can still see that final Kentucky Derby burst of Barbaro, "seeing him coming down the stretch, knowing that whatever we did to get him there was the right thing," Matz said.
"When you lose a horse like that, as good as he was, and we'll never know how good he was going to be," Matz added, "it certainly . . ."
The trainer paused for several seconds, then added one more word ". . . hurts."
"It's a fine line, a sharp edge between absolutely brilliant elation and devastation," Brette said. "I guess that's why people keep coming back."
Contact Mike Jensen at 215-854-4489 or firstname.lastname@example.org or @Jensenoffcampus on Twitter.