Luck Index: The missed run-out that could have saved South Africa's day

South Africa needed to beat New Zealand to retain realistic chances of reaching the final four in this World Cup. New Zealand had already knocked them out of the World Cup on two previous occasions, having defeated them in the quarter-finals of the 2011 World Cup and in the semi-finals in 2015, and had not lost a World Cup fixture against them in 20 years. The last time South Africa emerged victorious against this opposition in the World Cup was at the same venue in 1999.

There was history to be redressed, and to do so, South Africa needed to grab all the chances that came their way. Two of them came in the final over bowled by Imran Tahir. Colin Grandhomme offered a tough chance to David Miller at short midwicket; Kane Williamson edged Tahir to Quinton de Kock, who didn't fail to pouch it. But he did fail to review the umpire's not-out decision.

But those lapses paled compared to the mess that Miller made of a chance to run the New Zealand captain out in the 41st over. Here's how ESPNcricinfo's ball-by-ball commentary called the action -

"Rabada to Williamson, 1 leg bye, Oh my, a comedy of errors at Edgbaston. Awful mix-up between the wickets. Miller fluffs a run-out chance and reprieves Williamson. This was another well-directed short ball at the body, comes off pretty slow off the surface. Williamson is early into the pull and wears it on his body. De Grandhomme wants a single, Williamson doesn't. Rabada, the bowler himself, swoops down on the ball. The throw is to Miller at the non-striker's end. He is in a rush. He is under pressure. He dislodges the bails without collecting the ball. What a big miss for SA. Is that the game?"

According to ESPNcricinfo's Luck Index, that that was almost certainly the game. Had Williamson been run out on that ball, it is calculated that New Zealand would have still needed 14 runs to win from the final three balls of the game, which of course went unbowled after the non-dismissed Williamson nudged the winning boundary through third man.

That figure is reached by simulating the New Zealand innings, assuming that Williamson had been dismissed in that moment. Luck Index estimates that, given de Grandhomme was to lose his wicket with 15 required off 11 balls (which would have been a different and tougher situation had Williamson got out), and Mitchell Santner was the only recognised batsmen left, the remaining New Zealand batsmen would have managed to score 14 runs fewer off the 23 deliveries that Williamson faced after he was reprieved.

Luck Index is a part of Superstats, a new set of metrics by ESPNcricinfo to tell more enriching and insightful numbers-based stories. To know more about Superstats, click here.