It is The Sound of Music lyric with which we are all familiar. “How do you solve a problem like Maria?” sing the nuns of Nonnberg Abbey.

Yet in the context of professional tennis, it is Maria who has the problem. Maria Sharapova cannot beat Serena Williams. It is a problem that has spanned more than a decade. Sixteen straight competitive meetings. Multiple continents, surfaces, and tournaments.

When these two women – the world’s most recognisable and marketable female athletes and the two most decorated players around – meet across the net, the result is something of a foregone conclusion.

Sharapova has managed to take just one set from Williams in the past seven years.

“I love playing Maria. I think she brings out the best in me,” Serena said. Why wouldn’t she, with a record like that? However, she did add: “I think I bring out the best in her. I thought we had a wonderful final in Australia (this year). It was very entertaining. She played really well.”

Tennis Insights Day 10, Sharapova v Williams

That match was their last meeting, and definitely better than some of the maulings that preceded it. A brutal 6-1, 6-2 drubbing in the 2007 Australian Open final was followed a few months later by a 6-1, 6-1 victory for Williams in Miami. Their London 2012 Olympic gold medal match was one of the most one-sided finals at a significant event in the history of the sport, with the American triumphing 6-0, 6-1 in just 62 minutes.

Unsurprisingly, Sharapova appears to have blocked out much of the history between them since she upset Williams as a 17-year-old in the Wimbledon final of 2004, the first of her five Grand Slam singles titles.

“I mean, look, I haven't played Serena here in 11 years. That would be an incredible moment for me to step out on Centre Court against her again,” Sharapova said after her quarter-final victory over CoCo Vandeweghe.''

It is actually incorrect. In 2010, the pair played out an absorbing fourth-round encounter on Centre Court, one of their better matches. It was a showcase of stunning first-strike tennis and intensity and had the crowd enthralled. Williams prevailed 7-6(9), 6-4.

That match highlighted the key element of the match-up: Sharapova was playing some of her best tennis, yet Williams always seemed to have another gear.

It has been this way for years. It is not like Sharapova lacks weapons; Williams just matches them, and surpasses them. She has the superior serve. She is a better athlete. Her shots have a little extra power and penetration. She has a better B-game. Mentally, too, Serena holds the edge.

They are widely regarded as the two most mentally-tough players in the women’s game, yet it could be said that Serena is in Maria’s head – when they play, Sharapova frequently presses, knowing her shots must be centimetre-perfect against such a quick, powerful foe.

She knows her sometimes-shaky second serve will be treated with contempt, and this puts pressure on her first serve.

Where Sharapova appears anxious in this situation, Williams, conversely, seems to “get up” for matches against her Russian rival. “I think she goes up and wants to play the best tennis against me. That's certainly no secret because she shows that on the court,” Sharapova once observed.

Patrick Mouratoglou, Williams’ coach, believed the reason behind his charge’s dominance over Sharapova was purely technical. “She does not have a mental block against Serena. Serena simply plays tennis much better than she does,” he told the New York Times. “Sharapova is a great champion. She has great qualities. She fights incredibly and has tremendous mental strength. But at some stage, her level of play hits a ceiling.”

That gap in the level of play has been evident this year at Wimbledon. Sharapova has had to grind, showing scratchy play in her fourth-round victory over Zarina Diyas and failing to serve out a straight-sets win over Vandeweghe. She has struggled with double-faults throughout the fortnight. Williams, meanwhile, has improved with each round. She was simply stellar in a magnificent three-set victory over Victoria Azarenka on Tuesday, one of the matches of the tournament.

Azarenka was asked if she had one tip she could give Sharapova for facing Serena in the next round. “If I had one, I would have used it today, trust me,” she said.

Sharapova will arrive at Centre Court for ladies’ semi-final day with the odds stacked against her. She will be attempting to snap that 16-match losing streak and score her first win over Williams since beating the injury-hampered American in the WTA Championships final of 2004.

“(There are) definitely no secrets between each other's games,” she said. “I think it's always a new match. I haven't had great success against her. I would love to change that around. That's how I look at it.”

Williams will do everything in her power to prevent such change. She is gunning for Grand Slam glory, and with a 21st major singles title looming closer – and the chance to inflict another defeat over her most treasured scalp – she won't lack motivation. “For me, I don't feel like I have any pressure going into this match,” she said.

“I don't have anything to prove. I won all the Grand Slams, multiple times. Now I'm here just to enjoy it. I think it's actually making me play better, which is crazy.”