QWhy is a "Hagoita" battledore ornament displayed on a girl's first New Year?

A“Hanetsuki" traditional battledore and shuttlecock game originated in the Heian period (794-1185). It is said that the tools used for this game evolved into “Hagoita” battledores over time. People believed that hitting feathered seeds of “Mukuroji” soapberry (which can be read as "a child will not be afflicted by disease") with a “Hagoita” is auspicious and to have overlapped with the meaning of warding off bad luck. Later, when a girl was born, “Hagoita” were given as gifts to pray for her good health. From there, it became customary to display “Hagoita” on the First New Year as a prayer for the girl's growth.