Soon after winning a Professional Snooker Association of Canada's Invitation Event, in which he defeated Paul Thornley in the final in May 1970, Davis suffered the first of two heart attacks, and did not participate in the 1970 World Championship, which was held in Australia and won by John Spencer. He lost 31–21 to Spencer in his first match in the 1972 championship, but defeated David Greaves 16–1 in the second round of the 1973 championship before losing to Alex Higgins, the defending champion, 16–14 in the quarter-finals, a match most notable for a leak in the roof which forced rain to stop play while a cover was found and the position of each ball marked.