"The most important thing is coming out of that place with the win," he says.
But his voice lacks conviction as he speaks those words. Rios is the ultimate fan's fighter and he knows that, in this bout at least, it's not only that he wins but the manner in which he does that it is going to matter most.
This is a 26-year-old who is keenly aware of the expectations surrounding his fight, which will be the opener of an HBO doubleheader on Saturday. Promoters toss around the moniker, "Fight of the Year candidate," lightly, but this is one of those events in which they don't need to do much hyping.
All they need to do to fill the Home Depot Center on Saturday is make certain that boxing fans have seen a Rios or an Alvarado highlight tape.
Promoter Bob Arum calls it "a can't miss fight."
There have only been a handful of fights in the last few years which have been as hotly anticipated among the cognoscenti going in as Rios-Alvarado. They're aggressive, offensively oriented fighters with mean dispositions and killer instincts.
Rios, though, doesn't have that one fight that truly stands out yet. Muhammad Ali had Joe Frazier. Diego Corrales had Jose Luis Castillo. Marvelous Marvin Hagler had Thomas Hearns. And Arturo Gatti had Micky Ward.
No memorable bout graces Rios' resume yet. He hopes that Alvarado becomes the one, though that he knows as much means absorbing a lot of punishment himself in order to get it.
"Even in the amateurs, I had a style where I went for it," Rios said. "I always loved the way Arturo Gatti fought. He wasn't going out there looking to score points. He was going out there to[expletive] you up and beat the [expletive] out of you.
"I go out there that way. But I want to have my Gatti-[Micky] Ward fight, my Corrales-Castillo.
You make your name in those fights. Those are the kinds of fights people never forget."
A Rios-Alvarado fight has the potential to be in that class. Rios is 30-0-1 with 22 knockouts, while Alvarado is 33-0 with 23 knockouts.
More to the point, though, they fight fiercely, courageously and with a chip on their shoulders.
Neither of them has faced an opponent as talented or as tough as they'll face on Saturday.
Rios, who has been heavily criticized in his last two outings for struggling to make the lightweight limit of 135 pounds, sought Alvarado against the advice of his manager, Cameron Dunkin.
Dunkin is one of the more sage men in the game and he knew better than most how difficult a fight with Alvarado would be. He also knew that Alvarado still hadn't made his name among the casual fans and that, as a result, it was a high risk, low reward-type of fight.
Dunkin, though, was unable to convince Rios to go in a different direction.
"This is a fight that Brandon really asked for and it was a fight that I was real hesitant to take, of course," Dunkin said. "I wanted to get him a couple of other fights and I talked to trainer Robert Garcia about that. When it presented itself, Brandon was so excited and I didn't want to disappoint him, so we went to work on this fight and boy, everyone is very excited about it."
Few are more amped than Rios. He's usually a cool customer until the bell rings, but he's so anxious to get it on in this one that he has had to constantly remind himself to relax.
He idolized Julio Cesar Chavez, the sport's ultimate tough guy. Fight after fight, Chavez Sr. would go out and out-will and out-tough his opponents.
Rios has proven so far to have that kind of dedication, but he hasn't had an opponent who could help him put together a fight for the ages.
"I talk to Robert about it all the time, how I want my war," Rios said. "Ever since I came into this sport, I was saying I want to be in a Corrales-Castillo type of fight. I want to experience that. This fight right here, this could be the one, it really could.
"When you talk about all these legendary fights we're talking about, I want someday for the reporters to be asking some other fighters about one of my fights. I want that classic battle so bad, you can't even imagine."