Richard Williams.  Some have accused the man of myth-making, of embellishing what life was like when he accompanied his daughters to the park courts of gang-land Los Angeles, but it is tricky to quibble with Serena’s account in her memoir of “sometimes hearing guns going off from drive-by shootings nearby”. Williams and his then wife Oracene had never swung a racket until the occasion he caught a television commentator remark that a player had earned tens of thousands of dollars in a week: that was the moment which turned him on to the sport. Williams taught himself and then he taught Venus and Serena. Hard to argue against the claims of a man who coached two daughters to the world number one ranking.

Nick Bollettieri. Andre Agassi looked back on his time at Bollettieri’s Florida academy as “The Lord of the Flies, with forehands”. At the age of 80, Bollettieri is still working at his tennis boarding school, rising before dawn to hit the courts. At his age, why bother? Partly, you imagine, it is because his wife, Cindy, is his eighth. But, mostly, it is because he loves it, because he still retains much of what Jim Courier used to call a “paratrooper mentality”. Bollettieri’s numbers (and self-promotion) are legendary – he has had some involvement in the tennis education of 10 players to have held the world number one ranking. They are: Boris Becker, Monica Seles, Courier, Agassi, Martina Hingis, Marcelo Rios, Serena and Venus Williams, Maria Sharapova and Jelena Jankovic. “I hear coaches talking about kinetic change and biomechanics, and all that stuff,” he once said. “To tell you the truth, I don’t know s***. I don’t really know all those expressions, but what I do know is how to relate to people in a manner that fits into who they are. That’s my thing.”

Lennart Bergelin. Strange to think, but Bjorn Borg did not start out as an emotional flat-liner – as an angry teenager, he embraced his inner McEnroe, he raged and spat, he cussed and broke rackets. It was the late Bergelin who transformed Borg from being yet another tennis hot-head, it was Bergelin who gave him the inner calm which brought him 11 grand slam titles. Bergelin, who would take the hotel room next to Borg’s and intercept any groupies who knocked on the player’s door late at night, considered that the most important work he did with Borg was teaching him to control his “passionate spirit” on the court. “We were like father and son,” Borg once said. “Lennart always got me in a good mood and that was a big thing.”

Larisa Preobrazhenskaya. Everyone used to remark on the maternal qualities of the late Preobazhenskaya, who, based at the Spartak Club in Moscow, became known as the mother of Russian tennis. Anna Kournikova called her “my second mother”. Without Preobrazhenskaya, Kournikova would probably never had made the impression she did on the sport, and if Kournikova had never become a Hollywood name of tennis, all the other Russian girls might not have followed (in 2004, there was an all-Spartak Club French Open final, with Anastasia Myskina beating Elena Dementieva). “She was like a second mother to use and that made us feel protected,” Kournikova said. “Playing there at Spartak for nine hours a day, I saw more of her than I saw of my real mother.”

Robert Lansdorp. For years, the story was that Maria Sharapova’s coach was her father, Yuri. Many considered that it was, in fact, Lansdorp. His other clients have included Pete Sampras, Tracy Austin, Lindsay Davenport and Anastasia Myskina. It has been said that his greatest project was Davenport. “He formed the basis of my game,” Davenport once said. “I wouldn’t have achieved what I did without the strokes he gave me.”

Harry Hopman. Anyone who had a teenage John McEnroe addressing them as ‘Mister’ must be doing something right. McEnroe was greatly influenced by the time he spent working with Hopman when the Australian was coaching at the Port Washington Tennis Academy. Hopman’s most impressive achievements came in the Davis Cup, a competition he won 16 times as captain, though he did have some fine players in Frank Sedgman, John Newcombe, Lew Hoad, Ken Rosewall, Rod Laver, Tony Roche and Roy Emerson. While he was at Port Washington, he also worked with Vitas Gerulaitis. Later he opened the Hopman Tennis Academy in Florida, where his pupils included Andrea Jaeger.

Tony Roche. He has worked with four world number ones, in Ivan Lendl, Patrick Rafter, Roger Federer and Lleyton Hewitt. Lendl hired Roche as he believed the Australian would improve his volleys and enable him to win Wimbledon – though Lendl never did go through the draw at the All England Club, he did have success elsewhere with Roche. Roche also worked with Jelena Dokic, a former world number four.

Brad Gilbert. It was the Robin Williams, the actor and comedian, who once described Gilbert as “a tennis sensei”. Gilbert prefers to call himself “a redneck Jew”. The author of ‘Winning Ugly’, which must be the most referenced coaching manual in tennis, Gilbert is best known for the work he did with Andre Agassi. Gilbert was at his most useful in a rain delay during the 1999 French Open final, as Agassi, who had been two sets to love down against Ukraine’s Andrei Medvedev, came back to win the match and win the Musketeers’ Cup for the first time to complete the career grand slam. “Brad taught me how to play tennis – period,” Agassi has said. “He made me understand that you can hit the ball great, but if you don’t play smart you are useless out there. I didn’t utilise my game and Brad taught me how to do that.”

Toni Nadal. Rafael Nadal disclosed in his book, Rafa, that as a boy his uncle Toni had convinced him that he could make it rain. Nadal also used the book to challenge the received wisdom that his uncle Toni “forced me to play left-handed, and that he did this because it would make me harder to play against”. Nadal, otherwise right-handed (he writes with his right hand, and is right-handed when he plays golf, basketball or darts), wrote that being a leftie just came naturally to him. So, some things, Toni cannot be credited for. Yet, without Toni, it is unlikely that Nadal would be the player he is now. Or whether he would even be a tennis player, as he could very easily have been claimed by football. “Toni was tough on me right from the start, tougher than on the other children,” Rafael Nadal wrote in his book. “He demanded a lot of me, pressured me hard. He’d use rough language, shout a lot, he’d frighten me – especially when the other boys didn’t turn up and it was just the two of us. If I saw I’d be alone with him, when I arrived for training, I’d get a sinking feeling in my stomach.”

Bob Brett. The Australian, who has an academy in San Remo in Italy, coached Boris Becker and Goran Ivanisevic, and has also worked with Andrei Medvedev, Mario Ancic and Marin Cilic. He has strong views on what make a great tennis player. “A champion is someone who maximises his potential, not someone who has the world number one ranking,” Brett has said. “A champion has the ability to compete and bring his best performance at the biggest moment, to dig in when things are the most difficult and to beat the odds, whether personal or your game. And lastly, loyalty. Loyalty to yourself, your career, your coach, your family. That is a champion.”