You'll win, you've got good odds. It might not work the first time, but try enough and you'll win, that's the awesome part of being outnumbered.
You've got good units as well: I'm not that familiar with shogun, but it's better to have melee against archers anytime. Their arrows WILL run out, and they WILL have to charge if they want to succeed, if they don't, the battleclock runs out and you've won automatically.
Just defend with the melee, stay away from the wall and be sure to corner every unit climbing up. Don't try to get the general, only if he comes to you and you can take him.
I've once had 6 militia units in napoleon total war, faced against 2000 men full of line infantry and cavalry. I couldn't afford to lose. i've lost that battle about 10 times, but the 11th I was able to get everyone running and had 16 men left myself (men, not units
). I'm stil proud of that to date.
1600 against 2000, while they're mostly archers + you're defending. Dude actually, if you lose that, you're not worth it
jk, it'll go smoothly from the first time. You shouldn't be surprised if you actually keep 1100 men from that battle.
all this depending on difficulty ofcourse