Bandanas are the scarf of the poor world - with its countless designs and many ways to tie it, you can always find an inexpensive way to show your style, it keeps the hair in place and can quickly bring some cooling wet with water.
With a headband or sweat band, you quickly get control of the beads of sweat on your forehead when you go to it with the training both outside and inside.
A visor screen or sun screen can be the difference between a hit or a miss when playing with the sun in your eyes and you don't want to ruin your hairstyle with a hat - or are nervous that the wind will play along.