Other claims are that President William Howard Taft originated the stretch at a baseball game in 1909 or 1910.
A similar "stretch" has been documented at a Cincinnati Red Stockings' game in 1869, however.
The seventh-inning stretch is a tradition in baseball that takes place between the halves of the seventh inning of any game. Fans generally stand up and stretch out their legs and other muscles and sometimes walk around; it is a popular time to get a late-inning snack as well. The stretch also serves as a short break for the players. If a game goes into a fifth extra inning, a similar "fourteenth-inning stretch" is celebrated. In amateur games scheduled for only seven innings, a "fifth-inning stretch" may be substituted.
There are many apocryphal stories about the origins of the seventh-inning stretch. One popular yarn claims that it began on account of President William Howard Taft. He had been in attendance at a Washington Senators versus Philadelphia Athletics game on April 14, 1910 and had been uncomfortable in his chair; by the middle of the seventh, he could no longer take it, and stood up. The crowd mistook his action, and believed he had decided to leave, and out of respect, stood up as well. However, minutes later, after stretching out his legs, Taft sat back down as did the crowd. This tale is almost definitely false—evidence exists of the practice as early as 1869, when unruly students were called to stand up and stretch to help settle them down. However, the seventh-inning stretch was not a formal practice in professional baseball games until the 1920s.
Another possibility of the origin of the seventh inning stretch is the story of Brother Jasper of Mary, F.S.C., the man credited with bringing baseball to Manhattan College in the late 1800s. Being the Prefect of Discipline as well as the coach of the team, it fell to Brother Jasper to supervise the student fans at every home game. On one particularly hot and muggy day in 1882, during the seventh inning against a semi-pro team called the Metropolitans, the Prefect noticed his charges becoming restless. To break the tension, he called a time-out in the game and instructed everyone in the bleachers to stand up and unwind. It worked so well he began calling for a seventh-inning rest period at every game. The Manhattan College custom spread to the major leagues after the New York Giants were charmed by it at an exhibition game, and the rest is history.
But like many myths, it is difficult to certify any origin. A letter written by Harry Wright of the Cincinnati Red Stockings dated 1869 — 13 years earlier than Brother Jasper's inspired time-out — documented something very similar to a seventh-inning stretch. In the letter, he makes the following observation about the fans' ballpark behavior: "The spectators all arise between halves of the seventh inning, extend their legs and arms and sometimes walk about. In so doing they enjoy the relief afforded by relaxation from a long posture upon hard benches."
17 September 1909, Washington Post, "Taft Sees Giants Win," pg. 1:
In the seventh he (President Taft -- ed.) stood up to stretch with the rest of the Chicago host, but the hunch was of no avail.