I have read that attackers should outnumber defenders, 20 to 1 or better 50-100 to 1 in sieges in a book about conquest of İstanbul, though I can not find its reference right now. I remember that this book claims that no attacker has even won a battle with lesser numbers without help (treachery) from inside in middle ages and before.
Is there any references about these numbers, or similar numbers about sieges' opposing forces ratio. It is understandable that attackers should outnumber defenders, but how much?
I would like to learn average Average Attacker to Defender Ratio in Middle Ages for sieges with references to journal articles or books.
EDIT: Actually, any reference to respected historian is enough for me. Comments give reference of Sun Tzu but I would like to get number for Middle Ages European if it is possible. But if it does not exists, it seems I would have to accept Sun Tzu Art of War.