There are some things in sport that can be assessed from the outside and there are others that only those who have been through the same thing before can really understand. As Andy Murray prepares to lead Great Britain’s Davis Cup quest against the United States in Glasgow this weekend, the former world No1 Andre Agassi believes the Scot is at the same stage in his career as Agassi was after he won his third grand slam title, at the Australian Open in 1995.

Though Murray followed his US Open triumph in 2012 by winning Wimbledon the following summer, his tally still stands at two. After a 2014 in which he took time to recover full confidence after back surgery the previous September, Murray looked back to his best in Melbourne this January, all the way until the latter stages of the final, where he was outplayed by Novak Djokovic, his sixth grand slam final defeat. Agassi understood.

“It appears to me that what he’s gone through is not much different from what I went through,” Agassi said. “Which is: he was let on to this dirty little secret; that winning a slam doesn’t change anything. If anything, it makes you realise that this better be about something else. You have to figure out a way to engage with the game differently. You have to figure out a way to make yourself better, despite being the best. There are a lot of working components. And it doesn’t help to have Djokovic on the other side of the net.”

In an era when the world No1 Djokovic is fast approaching double figures and when Rafael Nadal is just three short of Roger Federer’s grand slam record of 17, it’s easy to see how difficult winning a slam is for anyone else, let alone Murray, who turns 28 in May. Happily, Agassi feels his best days are ahead of him.

“I think it’s likely [he will win more] because he’s one of two or three people that should win,” Agassi said. “It’s likely he is going to win again despite himself. I leave a lot of room for his best years still to be ahead of him. It may not be as many years as he could have had, but I think we will see his best still.”

When Agassi says “despite himself” he knows what he’s talking about. Together with all the highs, there were also plenty of lows. Anyone who watched him at Wimbledon in 1996 against Doug Flach, an American ranked 281, will remember him spraying the ball everywhere, with little care for the result.

In 1997, he skipped the French Open and Wimbledon as he sunk into what he later described, in his autobiography Open, as depression. But having almost fallen off the edge of the tennis world, with his ranking down at 141, he dragged himself back, heeding the advice of his coach, Brad Gilbert, to go easier on himself and his “second career” brought him five more grand slam titles and the No1 ranking.

“Andy holds himself to a far higher standard than anybody else, I assure you,” Agassi said. “You can see it when something isn’t good enough for him, even though things are going pretty well. He just believes that he can do it better. Even if he does do it better, it doesn’t scratch an itch for him. There’s no arrival. Until he starts really embracing his strengths and his weakness … when he learns to understand himself in context, I think he’ll learn not to be as hard on himself. Because he will know how he’s going to feel that way and that’s it’s OK to feel that way. Just get back to work.”

Along with eight grand slams and an Olympic singles gold medal, Agassi also won the Davis Cup three times. The second of those, in 1992, came with a team consisting of Agassi, Pete Sampras, John McEnroe and Jim Courier, who will captain the USA this weekend. On paper, it was a dream team but Agassi draws a distinction.

“We played and we really weren’t a team,” he said. “We were just pretty good individuals who realised they needed each other. We went out to do a job. I just don’t know if we didn’t believe we could win, if we would [have felt] that sense of camaraderie to try to win together. It’s not who we were, it was the environment we were in: we were all trying to beat each other, to be the best.”

This USA team – John Isner, Donald Young and the world No1 doubles team of Bob and Mike Bryan – are not in the same league as that 1992 vintage but they will fight hard under Courier, especially having been beaten on home soil by Britain last year. Agassi said it will be a 50-50 match.

“I’m from Vegas so I like dealing with odds,” he said. “[You’d think] 2-0 Andy, 2-1 Bryan Brothers and then hold your breath. I think everything is decided there. Isner is going to have to step up. He’s going to have to get at least one win. It’s 50-50. You guys have payback coming.”

Andre Agassi is launching his BILT by Agassi & Reyes fitness range, which is available at selected David Lloyd Leisure clubs