In 1975, Davis travelled to Australia to compete in the World Championship, where he played Dennis Taylor, but lost by a single frame, 15–14. The 1975 Watney Open in Leeds provided some consolation, and Davis beat Patsy Fagan 13–9 and John Spencer 13–12 before losing 17–11 in the final to Alex Higgins. Davis stated that a win over Spencer convinced him that he could still compete at the highest level of tournament play. World rankings were introduced in 1976. Despite Davis's abilities peaking long before this, but he was still ranked number 4 that season. In 1977 Davis was ranked number 9, rising to 6 during both the 1978 and 1979 seasons; he maintained his form as the tour expanded, still being ranked inside the top 16 players in 1982, aged 67, and only falling outside the top 64 in 1988, aged 74. Although Davis lost 15–13 to Eddie Charlton in the quarter-finals of the 1976 World Championship, having beaten Werbeniuk 15–12 in round one, he came close to winning his first professional title for twenty years at the 1976 Pontins Professional. With victories over Willie Thorne, 7–4 in the quarter-finals, and Graham Miles, 7–2 in the semi-finals, he faced Reardon in the final. Davis missed a crucial in the , having made a break of 107 during the match, and Reardon won 10–9.