It won't be anywhere near half the ball of yarn. If you want to do a long-tail cast-on, one good way to guesstimate is to wrap the yarn around both needles (held together) as many times as you'll cast on. If you need ten stitches, wrap the yarn around ten times, then make your slipknot, take the wrapped yarn off the needles, put the slipknot on one needle and cast on. That usually leaves you a bit of a tail, but it's better than under-guessing.
You can also do a knitted cast-on if you like those.