Forgot the actual screenshot.
I'm missing something about the actual war making or it is actually extremely dumb in this game, starting to become extremely frustrating.
Actually makes me want to play Victoria II again, instead, which, imo, is a far superior game in this genre.
War in EU3 is decided by a few factors, once you break it down it becomes easy.
Terrain. (Never fight in mountains if you can, or across rivers)
Supply Limit. (Never fight in deserts with big stacks of troops if you can.)
Generals. (Always have one, they transfer instantly between armies.)
Discipline(How much damage your troops do. The difference between 90% and 120% is doing 1-10 damage per tick, and 1000-2000 per tick.
Morale(How long your troops stay in battle. Essential early game, not as much late game.)
Technology. (You aren't Shaka Zulu, African spearman die HORRIBLY when fighting muskets.)
Past actual combat, your goals are...
Increase enemy war exhaustion. (The fastest way is having their giant army in a low supply limit province.)
Take over their land for more war exhaustion.
Kill their armies.
In that order...
So to win a war, use the above mechanics against your enemy as much as you can. Fight in your mountains or hills, do your best to have comparable tech, don't skimp on discipline. Take Military Drill early on if you can, amazing first tech. Do whatever it takes to get the enemy war exhaustion up before they do it to you. Lure them into desert provinces if you have and scorch the land. Let them stay and starve, then strike. Even on the offensive, the AI will attack you. So always play defense. Don't feel bad about scorching land, you won't ever make the long term if your short term gets annexed.
(My above Transcaucasia game started as Georgia. The only reason I survived was scorching EVERY SINGLE PROVINCE I owned in order to starve out the neighboring hordes.)