This T20 World Cup is the seventh time in the past eight global tournaments that England’s men have reached the semi-finals. There was turbulence en route – not uncommon on the inter-island flights in the Caribbean – but along with the two trophies won, it is a reminder of how far their white-ball cricket has come these past nine years.

Among the constants in this period of uplift has been Adil Rashid, who on Sunday was once again toying with opponents like a street magician. Granted it was the USA trying – and failing – to read Rashid’s sleight of hand. But regardless of the opponent, those four boundary-devoid overs of two for 13 were still a master craftsman at work.

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Things had started rustily for the Yorkshireman, his outings against Scotland and Australia in Barbados pockmarked by too many loose deliveries and perhaps showing why allowing him to play two games in six weeks before leaving the UK was an oversight in England’s planning. For all his recent white-ball specialism, Rashid still needs overs.

Since then, however, he has purred once again to the tune of eight wickets in 18 overs at an economy of just over five, with the lines tighter and his googly very much on point. As a leg-spinner who flights the ball, unlike some of the more modern protagonists who drive it into the pitch, he has been harnessing the drift from the cross-winds too.

Among those in awe is Liam Livingstone, who as a Swiss Army knife spinner – leggie to the right-handers, offie to the lefties – gets to pick Rashid’s brains and similarly those of Moeen Ali. Both are closer to the end than the start – Rashid is 36, Moeen now 37 – and Rob Key, the team director, has already indicated the pair’s knowledge and expertise must be retained in some capacity when the day eventually comes.

South Africa booked their place in the T20 World Cup semi-finals as they edged home by three wickets against West Indies. They had looked in control for much of the rain-affected match in Antigua before late wickets set up a tense finish.

Marco Jansen eventually steered them home with three wickets to spare, sending the co-hosts crashing out of the tournament.

West Indies were dealt two early blows as Shai Hope and Nicolas Pooran fell in the first two overs, but Roston Chase and the recalled opener Kyle Mayers set about repairing the innings. They added 84 for the third wicket before Mayers fell to Tabraiz Shamsi for 35, followed quickly by the captain, Rovman Powell, and Sherfane Rutherford.

Shamsi, who finished with three for 27, added the wicket of Chase for 52 from 42 balls as West Indies slipped to 97 for six – a couple of sixes from Andre Russell lifting them to 135 for eight.

Russell claimed the wickets of Reeza Hendricks and Quentin de Kock in the second over before rain intervened, setting South Africa a reduced target of 123 from 17 overs. After losing Aiden Markram for 18, they looked in control at 77 for three in the eighth over before Alzarri Joseph had Heinrich Klaasen caught behind for 22.

The spin of Roston Chase picked up the key wicket of Tristan Stubbs for 29 as a spell of three for 12 set up a tense finish with five needed from the final over. But Jansen finished it in a hurry, hitting the first ball for six to send unbeaten South African through on top of their Super 8 pool with England joining them in the last four.

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“Rash has been exceptional for 10 years,” Livingstone said, as England waited on events in the second Super Eight group to discover which semi-final they will play (India in Guyana on Thursday). “He is getting better and better. We are incredibly lucky to have someone like him who is ultra consistent, takes wickets and doesn’t go for any runs.

“I have the best of both worlds. I have one of the best off-spinners England’s had and one of the best leg-spinners as well. It’s pretty perfect. Adil is always talking to me, telling me different things to try; what he thinks, and what to do. Moeen is the same. I feel really blessed I’ve got both of them to help make me a better bowler.”

Livingstone’s own campaign has been reflective of a bits and pieces role in the side. He has faced 33 balls but has one massive regret. Having dragged England to 25 needed off the last 18 balls against South Africa by cracking 33 off 17, only to hole out in the clutch moment. “I felt that was my time in the tournament,” he said.

As well as being stationed as a hitter down the order, as opposed to the top four in domestic T20, the 30-year-old also never quite knows if his bowling will be used and, if so, how much and when. He bought the wicket of Rovman Powell in a single over that cost 20 runs against West Indies, then did not turn his arm over in the South Africa game. On Sunday, he was Rashid’s wingman, sending down four overs, one for 24.

Livingstone said: “I don’t feel like I have the most glamorous role in this team to be honest. It’s different from what I’m used to for most of my career. It’s been a mental thing these past few weeks, making sure I’m mentally right on it whenever needed.

“But I feel like I struck the ball pretty well against South Africa and bowled pretty well [against USA]. So I guess they’re the last two performances with bat and ball. Who knows, hopefully I’m not needed in the next two games and we can win a World Cup. Sometimes it is better in tournament cricket to sneak up and nick it at the end.”