What are the factors that make the A.I. sally forth in sieges?

[DevrimJan]

I used to think that besieging the enemy with an army of half the units of the enemy would cause them to sally out. But another time I besieged the enemy with an army with 3/4 the units they had, and they still sallied forth. Another time I besieged the enemy with less then half their units, and they didn't sally forth, so what determines this?

[Ichon]

Usually related to the strength of armies not just the numbers. If you have some strong units you might have less numbers but be 1/3 more powerful, also the generals and other situations matter for example if AI has reinforcements nearby.