Just got back into playing this in the Brytenwalda mod.
The siege system they have in that one is pretty fun. I just completed a three week siege of Caer Maunguid. They only had food for a week when I started (which was why I thought sieging them was a good idea, heh) so I kept them without food for about two weeks.
I started with 250 men, mostly Bonheddwyr (the tier 2 Briton troops). My ally (I was Marshal, with the faction leader following me around) had 350 men. The enemy city had about 760 men - 460 in the city itself and their faction leader was inside with about 300. So I was outnumbered, 600 to 760. I had my personal engineering skill at 7, so stuff wasn't too hard to build. I started with setting up a circumvallation, then built sanitation. After that was done I just camped out. The first week was mostly uneventful, I lost 20 men to an attack while building the circumvallation but not too bad. Then as soon as they ran out of food they made a desperate sally against me, but I formed my troops into a thick line and managed to wipe them out without too many losses.
After that little fight, I kept waiting day after day. It threw an event at me every day or two, asking to choose things - a few let me pay money to help my men's morale, some were choices that mostly affected honor. After the second week the enemy women, children, and old men abandoned the city and wandered out to the circumvallation begging for food - I paid 400 to get them some food for an honor boost, although it hurt morale (not sure why, my men must be cruel). I had a few more sallies by the defender, but I was still going pretty strong.
The third week they sallied a few more times and hit me pretty hard since now they had more elite troops coming out (early sallies seemed to be mostly lower tier like mine, so it was more evenly matched - these were the heavier infantry and they hurt), leaving with me down to 60 men and my allies down to 200. The enemy side was still showing 500 defenders, so I was getting a bit worried. Then on the 20th day an enemy lord party of 100 came up and got in a battle with my ally, leaving me with a mere 60 men (who were now all tier 3 and 4 from the experience of all the fights). against the 500 defenders in the city. On the dawn of the 21st day they sallied out and attacked again, at which point I figured I was doomed - 60 vs 500? But the enemy only had 40. 500 men in the city, but the starvation had left a mere 40 able to fight.
I charged with my men, and together we wiped them out - including the enemy lord. After that little fight I captured the enemy lord, and was able to take as many prisoners as I could hold (which wasn't many, since my party size had shrunk so much - but I got all the expensive ones).
So that's how I got credit for single handedly capturing 500 men with a party of 60. I must have gained 150 renown from all the victories during the sallies. My faction leader gave me the city too.
The first few caravans to arrive must have made a killing too due to all the price hikes during the siege. Just the tariffs are going to give me 15,000 at the end of the week.