When batting, the higher the average is the better. Bowling is an entirely different matter; the best bowlers have the lowest bowling averages. Unsurprisingly, the lower averages for bowlers were obtained in the period when pitches were uncovered, batsmen had less protection and there were no limitations on the number of bouncers bowled per over.
Of bowlers who delivered at least 2000 balls in Test cricket, England's George Lohmann, who played in thge late 19th century, has the lowest career average (10.75). He played 18 matches, scalping 112 wickets and bowled 3.830 balls. His parsimonious economy rate (1.88) and fantastic bowling strike rate (34.1) helped to keep his average low.
Of course, Lohmann's average is not the lowest career average in cricket. Ironically, even Australia opener Michael Slater (1993-2001) has a better career bowling average than Lohmann! Slater averages exactly ten runs for his solitary wicket.
There's a good reason for the number of balls being a qualification: Desmond Haynes played 116 matches for the West Indies and averages 8.00 with the ball. However, he bowled only 18 deliveries and took one wicket.
The lowest ever career Test bowling average is 1.00 - by Barbadian Peter Lashley. Lashley was a part-time bowler who took 1/1 off three overs against England at Leeds in 1966. That was his only spell in Test cricket.
Three bowlers took a wicket without conceding a run. Since a bowling average is runs conceded divided by wickets and 0 is not divisible by any number, they remain average-less. These men are Wilf Barber and Albert Hornby of England and Bruce Murray of New Zealand.
This answer was edited by SpiffyD 217 days ago.
Reason: Edit


