At close on the Oct 10, 2019, which was the first day of the second India-SA Test at Pune, South Africa was yet to bat.
So Senuran Muthusamy temporarily holds the record of the most runs in a Test career without ever being dismissed:
He is now ahead of the long-standing record of Afaq Hussain who made 66 (HS 35*) in 4 unbeaten innings in 2 Tests in 1961-64.
http://www.espncricinfo.com/pakistan/content/player/38975.html
Azhar Mahmood scored 128* and 50* on debut and thus scored 178 without being dismissed. He added another 19 in his third innings before he was dismissed for the first time.
JA Rudolph scored 222* on debut, and 71 in his next innings in his second Test.
The above table shows those with short careers who finished with no dismissal. SG Law scored 54* in his only innings, while his fellow debutant Ricky Ponting (96) went on to better things.
There are a few there who played in 3 Tests. However, the real achievement was that of Aijaz Cheema:
http://www.espncricinfo.com/pakistan/content/player/39821.html
In 7 Tests in 2011-12, he batted in 5 unbeaten innings for a total of 1 run.
We now move on to the related topic of the highest batting averages. Most statistics sources such as Cricinfo give this with a cutoff of 20 innings, as in this:
http://stats.espncricinfo.com/ci/content/records/282910.html
Which is headed by Bradman (99.94). followed by SPD Smith (64.56) and AC Voges (61.87). The only others with averages over 60 are Graeme Pollock, George Headley and Herbert Sutcliffe.
But what if we do not have a minimum number of innings? After Muthusamy and his unbeaten friends, we get:
(On Oct 10, 2019):
Highest batting averages (with no minimum number of innings):
This is headed by current players KR Patterson and PP Shaw who are expected to play Tests in the future. Next is AG Ganteaume with his average permanently stuck at 112.00. Only then we have Bradman’s 99.94, followed by a couple of 1-Test players in the 90s. Further down we have SPD Smith (64.56) and AC Voges (61.87).
Soon we can expect Ganteaume to be back on top. And RE Redmond who is stuck on 81.50, followed by other 1-Test players such as JK Moss (60.00) and JA Morkel (58.00).
abn397 