The Yankees finished 79–75 in 1959, in third place, their worst record since 1925, as the White Sox, managed by Lopez, won the pennant. There was considerable criticism of Stengel, who was viewed as too old and out of touch with the players.
After the 1959 season, Weiss made a trade with Kansas City to bring Roger Maris to the Yankees. Stengel was delighted with the acquisition and batted Maris third in the lineup, just in front of Mantle, and the new Yankee responded with an MVP season in 1960. Stengel had health issues during the season, spending ten days in the hospital in late May and early June, with the illness variously reported as a bladder infection, a virus or influenza. The Yankees were challenged by the Baltimore Orioles for most of the year but won the pennant by eight games, Stengel's tenth as manager, tying the major league record held by McGraw. The Yankees played the Pittsburgh Pirates, again a team Stengel had played for, in the 1960 World Series, and Stengel picked Art Ditmar, who had won the most games, 15, for the Yankees, rather than the established star, Whitey Ford. The Pirates knocked Ditmar out of the box in the first inning, and won Game 1. Ditmar was also knocked out of Game 5; Ford won Games 3 and 6 of the seven-game series with shutouts, but could not pitch Game 7, as he might have if Stengel had used him in Games 1 and 5. The Pirates defeated the Yankees in Game 7, 10–9, on a ninth-inning Bill Mazeroski home run.
This strategic selection also applied to the pitchers, as Stengel leveraged his staff, starting his best pitchers against the best opponents. Although Stengel is best known for doing this with the Yankees, he also did it in his days managing Brooklyn and Boston, and to a very limited extent with the Mets. Rather than have a regular pitching rotation to maximize the number of starts a pitcher will have, Stengel often rested pitchers longer to take advantage of situational advantages which he perceived. For example, Stengel started Eddie Lopat against Cleveland whenever possible, because he regularly beat them. Stengel's 1954 Yankees had the highest sabermetrics measurement of Leverage Points Average of any 20th century baseball team. Leveraging became unpopular after choices of starting pitchers based on it backfired on Lopez in the 1959 World Series and on Stengel in the following year's—he waited until Game 3 to start Whitey Ford because he felt Ford would be more effective at Yankee Stadium rather than at the small Forbes Field. Ford pitched two shutouts, including Game 6 at Forbes Field, but could not pitch in the Yankees' Game 7 loss. Stengel's philosophy took another blow in 1961 when Houk used Ford in a regular rotation and the pitcher went 25–4 and won the Cy Young Award—he had never won 20 games under Stengel. Today, teams prefer, for the most part, a regular rotation.