How many players have taken a wicket with their first ball in Tests as Shamar Joseph did?

Shamar Joseph's first two Test wickets were Steve Smith and Marnus Labuschagne, who both average over 50. How rare is this sort of start? asked Brian Williams from Australia
The exciting young West Indian Shamar Joseph turns out to be the 11th bowler whose first two Test wickets were a batter with an average of 50 or above (given a qualification of at least 4000 runs at the time). His victims in Adelaide last week were Steve Smith, who ended the match averaging 57.80, and Marnus Labuschagne (52.03). The last bowler to achieve this was another West Indian, Shermon Lewis, against India in Rajkot in 2018-19. He dismissed Cheteshwar Pujara and Virat Kohli - but India still ran up 649, and Lewis won only one more cap.

Pride of place has to go to the old England captain Norman Yardley, whose first two Test wickets were both none other than Don Bradman, who was averaging over 100 at the time. This was during the second and third matches of the 1946-47 Ashes series in Australia, which were Yardley's fourth and fifth Tests (he didn't take a wicket in the first three). Again, it didn't lead to much joy: Bradman had made 234 and 79, and Australia went on to win the series 3-0.

Three others dismissed a high-averaging opponent twice to start their careers. Neil Johnson began by removing Sachin Tendulkar in both innings as Zimbabwe pulled off a surprise win over India in Harare in 1998-99. Sri Lanka's Angelo Mathews dismissed Younis Khan twice in Galle in 2009 . And Moeen Ali marked his debut for England, against Sri Lanka at Lord's in 2014, by having Kumar Sangakkara caught behind, and got him again in the next Test at Headingley.

Three men started their Test bowling careers by dismissing the prolific Indians Virender Sehwag and Rahul Dravid: the Sri Lankan pair of Dhammika Prasad (in Colombo in 2008, when his third wicket was Tendulkar) and Suraj Randiv (also in Colombo, but in 2010), and Australia's Jason Krejza during his debut 8 for 215 in Nagpur in 2008-09.

Jonathan Agnew, now a distinguished broadcaster, made a fine start to what was a brief Test career by dismissing the West Indians Gordon Greenidge and Viv Richards at The Oval in 1984. And in India's series in Australia in 2003-04, Irfan Pathan started with the wickets of Matthew Hayden in Adelaide and Steve Waugh in Sydney.

Shamar Joseph took a wicket with his first ball in Tests. How many people have done this, and has anyone started with a batter with better numbers than Steve Smith? asked Joey Dimattina from Australia
Following a breezy 36 from No. 11 in his maiden innings in Adelaide last week, the new West Indian find Shamar Joseph then became the 23rd bowler to take a wicket with his first ball in a Test match.

His first victim was Steve Smith, who had scored 9526 runs at an average of 58.08 at the time. That's the highest average of any of the victims - Kumar Sangakkara had 8438 runs at 56.25 when he fell to Nathan Lyon's first ball in Test cricket, in Galle in 2011. But one man had more runs than Smith: Alastair Cook had amassed 9840 (at an average of 46.85) when he fell to Hardus Viljoen's opening delivery in his only Test for South Africa, in Johannesburg in 2015-16.

I noticed that Mayank Agarwal has scored four Test centuries, all of them in India. Is there anyone whose career included more hundreds, all of them at home? asked V Mohan from India
India's Mayank Agarwal is one of five men who have scored four Test centuries, all of them coming in home games: the others are Joe Hardstaff junior (England), Guy Whittall (Zimbabwe), and the Sri Lankans Roshan Mahanama and Arjuna Ranatunga. Agarwal's haul includes two double-centuries; Hardstaff, Mahanama and Whittall all made one.

But there are two men who made five Test hundreds, all of them on home soil. The first was the old England player Stanley Jackson. His five included two in the 1905 Ashes series, in which he captained England, won all five tosses, was the leading scorer on either side, and also took 13 wickets. All of Jackson's 20 Tests came in England, as his Wisden obituary noted: "Unfortunately he could not go on any tour to Australia owing to business reasons, and the presence of Lord Hawke in command of Yorkshire until 1910 prevented him from ever being the county captain, though he was occasionally in charge of the side."

The second batter with five Test centuries all on home soil is Chandu Borde, whose five all came in India between 1958-59 and 1966-67. He did play several Tests abroad, and reached 93 against West Indies in Kingston in 1961-62.

Neil Harvey is the oldest living Australian Test player. Is he still the youngest Australian to score a Test hundred? asked Ian Hugo from France
You're correct that Neil Harvey is the second-oldest surviving Test player as I write - he turned 95 last October. He's currently one of 21 Test players who are still alive in their nineties. The only one older than Harvey is the South African Ron Draper, who turned 97 just before Christmas: he played two Tests - against an Australian side including Harvey - in 1949-50.

And Harvey is still the youngest Australian to score a Test century - he was 19 years 122 days old when he made 153 against India in Melbourne in 1947-48. That broke the previous national record by a month: Archie Jackson was aged 19 years 152 days when he made 164 on debut against England in Adelaide in 1928-29. The only other teenager to score a Test century for Australia is Doug Walters, who was aged 19 years 357 days when he hit 155 against England in Brisbane in 1965-66.

Who has scored the most runs without ever making a fifty in Test matches and one-day internationals? asked Sean Fanning from Australia
The leader on the Test list at the moment is Australia's Nathan Lyon, who has scored 1427 runs in 126 Tests so far with a highest of 47, against South Africa in Cape Town in 2017-18. In second place is another current player, the West Indian Kemar Roach, with 1165 runs and a highest of 41.

It's not impossible that both Lyon and Roach might yet post a half-century, in which case the record would revert to Pakistan's Waqar Younis (1010 runs, highest score 45), the only other man into four figures in Tests without a fifty.

The record in ODIs is held by India's Harbhajan Singh, whose 1237 runs included a highest score of 49. Zimbabwe's Paul Strang made 1090 runs in ODIs with a highest of 47. And Waqar Younis is lurking in third place on this list too, with 969 runs and a highest of just 37.

Just to complete the set, the the T20I record is currently held by the New Zealander Jimmy Neesham, whose 900 runs include a highest of 48 not out.