The great England batsman was born at 10 Wellington Terrace, South Shields. His father, a wine merchant, left Shields for London in 1877 and young Stoddart's reputation was made in London club cricket. By 1885, Stoddart was playing for Middlesex. The following year, playing for his club side Hampstead, he scored 485, at the time a record.
For the next ten years, Stoddart was in the front rank of England amateurs, playing for England in all three 1893 tests. He was named as Wisden's Player of the Year in 1893. In 1894, he captained a representative England side in Australia and played a great part in winning the ashes. A second tour in 1897, however, was a disaster and Stoddart virtually retired in 1898, though he made his highest score of 221 for Middlesex against Somerset at Lord's in June 1900. Stoddart was a forcing bat, a fine fieldsman and a useful change bowler. He was also a rugby three-quarter, and played for England in 1886 and 1893.
Stoddart committed suicide in London in 1915. A street in South Shields is named after him.