Generally you get more for the % of your troops that you lose in battle, that part is important because if you can follow your vassal with his 4k stack into battle you usually end up getting 5 tradition as well.
From the screenshot it looks like France followed Armagnac into battle and lost so Armagnac lost most their forcelimits (or whatever the measure is?) in men and therefore get a nice +5 trad.
You get +1 per successful siege so you'll be fine after you win the HYW

I think your vassals contribute to that as well although I'm not 100% sure. It used to work before 1.8 that you could let an ally siege up to whatever you want to risk, say 21% and breached walls, then move your 2k on and they'll move off giving you the siege and army trad (unless it was their claim/core) but that doesn't work reliably anymore
