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Kohli, who had struck a fine 136 in the day-night Kolkata Test against Bangladesh last week to reach 928 points, is now five points clear after Smith’s knock of 36 in the Adelaide Test against Pakistan saw him slip to 923 points from 931 before the match.
Cheteshwar Pujara has held on to his fourth spot, while Ajinkya Rahane has come down a spot to sixth in the latest update.
Among the bowlers, Jasprit Bumrah is the highest-placed Indian at the fifth position. Senior off-spinner R Ashwin was also static at ninth in the rankings.
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Australian fast bowler Mitchell Starc is another Australia player to gain in the latest rankings, which also takes into account performances in the drawn New Zealand-England Test in Hamilton and the one in Lucknow that saw the West Indies defeat Afghanistan by nine wickets.
Starc has moved up four places to 14th after grabbing seven wickets in the Adelaide Test.
Pakistan middle-order batsman Babar Azam has moved up two places to 13th, thanks to his fighting knock of 97 in the first innings, while left-handed opener Shan Masood has gained 10 places to reach a career-best 47th position after striking 68 in the second innings.
England captain Joe Root is back in the top 10 after spending a week outside it, his innings of 226 pulling him up to seventh from 11th. Rory Burns’s second Test century has pushed him into the top 40 for the first time.
For New Zealand, Ross Taylor has gained two places to reach 16th among batsmen and Tim Southee has moved up one place to 13th among bowlers.
West Indies captain Jason Holder’s five wickets have helped him move up one slot to third place with a career-best 830 rating points and he has also consolidated his position at the top of the all-rounders’ list.
Off-spinner Rahkeem Cornwall has broken into the top 50 with a 10-wicket haul while centurion Shamarh Brooks has risen 68 places to 62nd.