There is a great deal of information that comes only from the minimap, more than you are implying. Improving is not as nebulous as you think.
A few things, that go a long way.
Obviously you cannot win every game of SC or Dota, and in both games you can lose when you play well. A single mistake can throw away large leads and swing the outcome of either game. Yes you may not be directly responsible for your teammate making a bonehead mistake, but you can be aware of what kind of bonehead thing is about to happen to him. Sometimes you have to back up the stupid in dota, because the consequence of not backing up the stupid is outright losing. Think of it like a SC2 battle that you really can't retreat from after a certain point. You're looking for as favorable a trade as you can squeak out and you're planning and plotting how you're going to handle this period of disadvantage into the best plan that might still win the game.
So quick and dirty on vision. The most important part of the dota minimap is what it tells you but does not show you directly and really the theory behind where to ward or how to ward go hand in hand. If you understand how to ward the map - you will understand how to draw strong solid conclusions about what's happening in the fog. You will know that you are really beginning to grasp the concept behind where to place wards, and subsequently from the ward placement you dictate the pace of your play from that point forward. So this is my attempt at explaining the following in 3 pictures, So I'll just add these to the post then comment on them.
So these would be game starting defensive wards for the Radiant. The blue lines represent all possible paths into the jungle, between the middle tower, and the two wards it is impossible to enter the jungle without being see unless you are invisible, or smoked. If the lane is at the bottom tower, given the early warning the safe lane farmer should be able to hide behind the tower or TP out - one should never die to heroes that must show up in lane by walking there.
This is a scenario where radiant takes down middle and bottom tower - the new ward placements give even more information than before but provide all the same protection, You can now see someone entering the ancient camps from at least the T2 direction. and you can infer their map position based on their role (can they farm ancients) and where they didn't appear (if they don't end up being spotted by the river ward then they are standing around up there or went to the mid t2)
This scenario has the radiant lose its T1's and it attempts to show that proper ward placement that is flexible can remove more possible avenues into the radiant jungle than just placing them where you always have.
So the conclusion that you should make from these pictures is that I'm terrible at paint, but more important this analysis of how to ward and where to ward gives you a much stronger sense of map positioning, when its safe to farm in their safelane past the river, when its safe to farm past the river in your own safe lane. When its time to ward offensively in the jungle and if you do ward offensively, your team needs to commit to owning the territory that those wards show vision of. Its knowing when defensive wards are required to keep your team in the game or when offensive wards are needed to choke the enemy out of the game. And those pictures only involve one thing - protecting the radiant jungle.