A children’s game: = hat ball n.
1909 Ft. Wayne Weekly Sentinel (IN) 4 Aug /2 (newspaperarchive.com), Baby in the hat is another old time game still very popular in the city streets. 1913 Washington Post (DC) 15 June /1 (newspaperarchive.com), After dinner the afternoon was spent in playing baseball, baby in the hat, and quoits, the party returning to Washington about sundown. 1917 Boy Scouts Amer. Official Hdbk. 399, Hat Ball, Baby in the Hat, or Roley Poley. . . A soft ball and a supply of marbles, pebbles, or small sticks are provided. These latter are called “babies.” One scout is chosen “it”; the others line up each behind his own hat. “It” throws the ball at the hats. Each time he throws and misses, a “baby” is placed in his hat. When the ball lands in a hat, the owner of the hat takes the ball, while all the other scouts run away. As quickly as possible he throws the ball at one of them. If it hits the scout, a “baby” is placed in that scout’s hat and he becomes “it” for the next game. If he misses, a “baby” is placed in his own hat and he becomes “it” for the next game. . . Where hats are not available, small holes are dug in the ground and the ball is rolled into them. The game then continues as above. This version is called Roley Poley. 1957 Sat. Eve. Post Letters cnNY (as of c1900), You do not mention one of the best [games] i.e. “Baby in the Hat”! This was played with a tennis ball. We stood in line, excepting the kid that was “It,” with our hats (usually caps) on the ground in front of us. “It” then took the ball and dropped it in someone[’s] hat, who in turn tried to hit any one of all. The one hit then was “It.” 1967 DARE (Qu. EE33) Inf DC2, Baby-in-the-hat. Everybody put cap down on ground in a row. “It” standing by now with ball—walk up and down and tease—then drops it in one hat. Owner would grab ball—all [players now] run—and try to hit any player. If he missed he remained “it”; if he hit [a] player, that one became “it”; PA28, Baby-in-the-cap.