In Nottinghamshire from at least the 1950's until at least the 1990's, when I heard my own children playing versions of the same game, "Tig" was referred to as "Dobby". There were diferent versions such as "Dobby off ground", where the person who was "on" couldn't "dob" you if your feet were off the ground. "Dobby Little-Man" meant you were protected if you crouched down before being "dobbed" etc. Various "Dips" were indeed used to decide who was "on". "Dip, dip, dip,
          my blue ship,
          sails on the water,
          like a cup and saucer,
          O - U - T spells out!"
Some "Dips" required a number being picked by the first child to be identified e.g.
   "Mrs. Ink fell down the sink,
    how many miles did she fall? (the child now identified choses a number, such as "five". The child "Dipping" now continues counting around the circle)
    "One, two, three, four, five and O-U-T spells out!"