Installing long 20ft metal poles in concrete around a football pitch
The primary stress in this case will be wind. Typically you'd embed a pole at a ratio of 1:4. In your case, if the poles are 20' above ground, you'd want to be 4-5 feet down. If your poles are 20' in length (16-17' above ground), 3-4' may be adequate. 

I'd probably use form tubes (or cleanly-dug holes) of a 10 or 12" nominal diameter (at least 3 time the pole diameter). You wouldn't want less than 3-4" of concrete outside the pipe to prevent breakout.