What's the biggest difference between a batter's highest and next highest scores?

I noticed that the South African batsman David Callaghan's highest score in ODIs was 169, while his next highest was only 45. Is this difference of 124 a record? How about Tests and T20 internationals?? asked Elamaran Perumal from the United States
That undefeated 169 by Dave Callaghan came for South Africa against New Zealand in the Mandela Trophy in Centurion in 1994-95; his next highest score was indeed 45 (also not out), against India in Port Elizabeth in 1992-93. There's just one man with a bigger difference between his biggest and next highest scores in ODIs: the West Indian opener John Campbell hit 179 against Ireland in Dublin in May 2019, and 30 against England a few months earlier in Bridgetown, a difference of 149. The Ireland match was, oddly perhaps, the last of Campbell's six ODIs to date - and any future involvement might depend on him overturning a recent ban for a doping violation.

The Test record is held by India's Karun Nair, with an eye-popping difference of 277 between his highest two scores - 303 not out against England in Chennai in December 2016, and 26 against Australia in Bengaluru a few months later. Nair took the mark from Reginald "Tip" Foster of England, who scored 287 on his Test debut against Australia in Sydney in 1903-04, and 51 against South Africa at The Oval in 1907, a difference of 236.

The current leader in T20Is is Afghanistan's Hazratullah Zazai, with 162 not out against Ireland in Dehradun in February 2019, and 82 against them in Bready six months earlier, a difference of 80. Next comes Australia's Damien Martyn, with 96 against South Africa in Brisbane in January 2006, and 17 against them in Johannesburg the following month, a difference of 79. He played only two other matches.

With the next tournament about to start, who are the leading run-scorers and wicket-takers in the history of the T20 World Cup? asked Thom Jackson from Australia
The first T20 World Cup (then called the World Twenty20) took place in South Africa in 2007; the upcoming tournament will be the eighth. The leading run-scorer to date - and the only man with more than 1000 runs overall - is Sri Lanka's Mahela Jayawardene, with 1016. Chris Gayle is currently second with 965, and Tillakaratne Dilshan third on 897. Then come a trio of current players who are set to play in the 2022 edition in Australia: Rohit Sharma with 847 runs, Virat Kohli 845, and David Warner 762.

Leading the overall wicket-takers in T20 World Cups, with 41, is Shakib Al Hasan, two ahead of Shahid Afridi and three clear of Lasith Malinga. Shakib is likely to extend his lead at the top in 2022: leading the way for the other current players are R Ashwin with 26, Mitchell Starc 24, and Tim Southee 22. Watch out for Afghanistan's Rashid Khan, who has so far taken 19 wickets in just 12 T20 World Cup matches since his debut in 2016.

Rohit and Shakib should become the first men to play in all eight T20 World Cup tournaments. Gayle, his fellow West Indian Dwayne Bravo, and the Bangladesh pair of Mahmudullah and Mushfiqur Rahim also appeared in the first seven.

What unique distinction in Tests is shared by Alf Valentine and Sammy Guillen? asked Jerome Robinson from Barbados
I think the answer to this one hinges on the fact that the Trinidad wicketkeeper Sammy Guillen played Tests for both West Indies and New Zealand. In Auckland in 1951-52, Guillen stumped John Reid off the bowling of West Indies' slow left-armer Alf Valentine.

Guillen then decided to settle in New Zealand and, when West Indies toured again in 1955-56, he played in three of the Tests against them. Back in Auckland, New Zealand completed their first Test victory after 26 years of trying when Guillen stumped Valentine, off medium-pacer Harry Cave. Valentine had frustrated the home bowlers for a while but, said Guillen, "a stumping was on the cards, as he was at least a foot outside the crease when he played forward".

In New Zealand's second innings, Guillen had made 41 before being stumped himself - off Valentine. So in his Test career he took a stumping off Valentine, was stumped off Valentine's bowling, and also stumped him.

India scored 258 for 0 in 50 overs in a women's ODI against Ireland in 1999. What are the highest wicketless totals in ODIs? asked Mit Chowdhury from India
That match in Milton Keynes in June 1999 is easily the record total in a women's one-day international without losing a wicket. The partnership featured centuries by wicketkeeper Reshma Gandhi and 16-year-old Mithali Raj, both of whom were making their ODI debuts.

The next highest total in a women's ODI without losing a wicket was also made by India, earlier this year. In Pallekele in July, openers Shafali Verma and Smriti Mandhana made 174 for 0 in just 25.4 overs, to overhaul's Sri Lanka's total of 173. There have been 14 more totals of over 100 without loss in women's ODIs, all of them in the second innings of the match; none involved the full 50 overs.

The men's record is South Africa's 282 for 0 to overhaul Bangladesh's 278 for 7 (in Kimberley in 2017-18. Quinton de Kock made 168 not out, and Hashim Amla an undefeated 110. The highest in the first innings of a match without loss is a modest 37 for 0, by England in a rain-affected match against South Africa in Cardiff in 2012. Pakistan did make 399 for 1 batting first - after an opening stand of 304 between Imam-ul-Haq and Fakhar Zaman - against Zimbabwe in Bulawayo in July 2018.

After reading the question about high totals without a double-century in last week's column, I was wondering what the highest was without an individual hundred? asked Ben Fanders from England
This record was broken during the just finished English season: playing against Kent in Beckenham in May 2022, Surrey made 671 for 9 declared, with the highest individual contribution being 96, from Ollie Pope. Ben Foakes and Jamie Overton also made it into the nineties without reaching three figures; in all there were seven half-centuries (plus a 44), and the only man not to reach 20 was Hashim Amla, who was out for 12. In doing so, Surrey broke their own record for the County Championship: in Bristol in 2005, the highest contribution to their total of 603 against Gloucestershire was Azhar Mahmood's 89.

The overall first-class record was previously held by Namibia. In an Intercontinental Shield match against Uganda in Windhoek in September 2010, their total of 609 included six half-centuries (and a 48), but the highest was Ewald Steenkamp's 87; Gerrie Snyman made 86. The highest in a Test is India's 524 for 9 declared against New Zealand in Kanpur in 1976-77, when the highest score was just 70, by Mohinder Amarnath.