World-number-one male tennis-player rankings

World-number-one male tennis-player rankings is a year-by-year listing of both the male tennis player who, at the end of a full year of play, has generally been considered to be the best overall player for the entire year, and of the runner-up for that year.

Before the open era of tennis arrived in 1968, rankings for amateur players were generally compiled only for a full year of play. Professional players were ranked by journalists, promoters, and players' associations usually at the end of the year. Even for amateurs, however, there was no single official overall ranking that encompassed the entire world. Instead, nation rankings were done by the national tennis association of each country, and world rankings were the preserve of tennis journalists. It was only with the introduction of computerized rankings in the open era that rankings were issued more frequently than once yearly. Even the end-of-year amateur rankings issued by official organizations such as the United States Lawn Tennis Association were based on judgments made by men and women and not on mathematical formulas assigning points for wins or losses.

In 1938, for instance, when Don Budge won the amateur Grand Slam, it was easy to conclude that Budge was not only the U.S. No. 1 but also the world No. 1 amateur player. It was far more difficult, however, to decide who was the best overall player, amateur or professional, for that year because both Ellsworth Vines and Fred Perry, now professionals, were still at the top of their form. Two different sources, however, carefully studied the performances of the players for that year and both concluded that Budge was the best overall player, with Vines a close second. For the previous year, 1937, one of these same sources concluded that all three players, Perry, Vines, and Budge, deserved to be called the co-world No. 1 players.

In 1946 Bobby Riggs, a professional, had clearly established himself as the best player in the world. In 1947, he was still the best professional player but Jack Kramer had a sensational amateur year. Kramer, having turned professional in November after the Pacific Coast amateur Champs, met Riggs three times in late December on fast indoor courts and Riggs won twice. But at the end of their long series of matches in May 1948, Kramer had led Riggs decisively in head-to-head meetings. It is feasible to argue, therefore, that Riggs and Kramer were possibly the co-world No. 1 players for 1947.

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