Q: What is the highest score by a number-eleven on debut?

A :The highest score by a number-eleven on debut in a Test match is 46* by Warwick Armstrong for Australia against England at The MCG in 1901/02. This score was made in Australia's second-innings, and contributed to a tenth-wicket stand of 120 with Reggie Duff. Armstrong had made 4* in the first-innings, but had gone in at number-nine.

The highest score in a number-eleven's first ever Test innings was 40 from only 46 balls by Chamila Gamage Lakshitha (who enjoys the fantastic initials of MKGCP Lakshitha) for Sri Lanka against Bangladesh at SSC, Colombo in 2002.
Q: Have the eight to eleven batsman's averages significantly changed over the past few decades?

A: The combined average from the 1930s onward for eight:
1930s: 20.12
1940s: 20.99
1950s: 20.25
1960s: 19.74
1970s: 19.97
1980s: 21.58
1990s: 20.80
2000s: 22.81

The combined average for overall (eight-eleven):
1930s: 14.22
1940s: 15.57
1950s: 14.05
1960s: 15.78
1970s: 14.79
1980s: 16.05
1990s: 14.34
2000s: 15.26

So the answer is no. While the raw averages have improved very slightly for eight, it's merely kept up with the increase in scoring across the board, and even then, the increase is very small, and possibly statistically insignificant. There is no real increase in terms of the overall lower order (eight-eleven). The idea of the modern lower-order doing more than in previous decades is exaggerated. The strike-rates of the lower-order has also increased correspondingly, so it's not like the lower-order of today is better at "hanging around".
Q: How many players currently playing international cricket were born outside of the country they are playing for?

A: If we exclude non-regular teams (Canada, Bermuda, etc.) who are mostly made-up of players who were not born within their boundaries, and define "current" as having played more than 2 Tests or ODIs in the last year and not announced their retirements, there are:
Tim Ambrose (England) - born New South Wales, Australia
Grant Elliott (New Zealand) - born Gauteng, South Africa
Jehan Mubarak (Sri Lanka) - born Washington DC, USA
Kevin Pietersen (England) - born Natal, South Africa
Matthew Prior (England) - born Gauteng, South Africa
Aaron Redmond (New Zealand) - born Western Australia, Australia
Luke Ronchi (Australia) - born Manawatu, New Zealand
Owais Shah (England) - born Sind, Pakistan
Mathew Sinclair (New Zealand) - born Australia
Andrew Strauss (England) - born Gauteng, South Africa
Scott Styris (New Zealand) - born Queensland, Australia
Andrew Symonds (Australia) - born Warwickshire, UK
Q: What is the slowest Test century of all-time?

A: Unfortunately, strike-rates and balls received were not always calculated, so it is impossible to say for certain. Furthermore, it is possible that a player accelerated after making his century, thereby ending on a higher strike rate compared to his first hundred runs - number of deliveries for a century has not always been recorded either.

However, it is estimated that Jackie McGlew of South Africa took 480 balls for his century (he made 105 off 499 balls in total) at Kingsmead, Durban against Australia in 1957/58, which equates to a strike-rate of about 20 for his century and 21 for his total score. This is lower than anything definitively recorded.

Another way to look at it (for innings where we do not have accurate data) is runs-per-minute. The slowest innings by that measurement would be Sunil Gavaskar's 172 against England at Chinaswamy Stadium, Bangalore in 1981/82, which took an amazing 708 minutes. The longest innings of all-time belongs to Hanif Mohammad, at 970 minutes, but he scored 337 runs during that time. With that said, even though Gavaskar's innings lasted 708 minutes, he only faced 472 balls during that time, giving him a comparatively brisk strike rate of 36.44.

Finally, if we limit the criteria to only completed innings and only matches that we have good data for, then the slowest century belongs to Sanjay Manjrekar of India, who scored 104 against Zimbabwe at Harare Sports Club in 1992/93 at a strike rate of 24.64.
Q: Which Test country currently has the weakest nine-ten-eleven batting average wise and which country has the strongest?

A: If we define current as the time since the last break in the Test schedule, which was September 2007 and the ICC World Twenty20, Australia come out on top, their nine to elevens combined averaging 17.21. Pakistan are bottom, theirs managing a really fairly pitiful 6.17. Even Bangladesh, with 8.88, have done better than this.
Q: What is the lowest individual and team score that has never been gotten?

A: In Test terms (it's obviously not possible to look definitively in First-Class ones), it is 229 (for individuals) and 18 (for teams). If you wanted to look a bit higher, 56 has also never been made. And next it's 525.
Paul Harris was born in the then-Rhodesia in 1978.

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