The way I was trained, it's not like you'll have fewer thoughts - because the nature of mind is to think, it's more like, your mental balance will shift from thoughts to "nothing" that "does not change" as thoughts come and go. So instead of taking the thoughts too seriously and getting carried far away, as your practice develops you should be letting go of them a lot more easily, until they are just like children with their toys. The children can get excited or upset and crying over their toys, but you're like: "whatever, in a minute they will forget about it, not a big deal".
What's more important is not thoughts (although over time they will change too, but that's just a side-effect) - it is integration in the space beneath the thoughts. It's the feeling of no inner conflict, no fighting with oneself, not blaming - that's what should improve over time.
IMO, paying attention to breath and especially on the diaphragm/abdomen area helps see that "space beneath the thoughts" - which is where trouble is most of the time. Coming back from a movie played by the thought is important because what you're working on is that space, not the thoughts. And then at some point things should get peaceful enough that you don't need to worry about that space either. Thoughts come and go, the emotional foundation has some signless syrup slowly boiling, and everything is just the way it should.
Remember, what you are after is not any particular state, but rather, the whatever-happens-is-fine attitude of peace and integration, so having no thoughts is not the point, the point is having no worries - including worries about worries.
Of course, it's not like on your way to this attitude of all-acceptance you don't work at all. There is a lot of hard work in paying attention, letting go, and integrating - but it is a type of "hard" opposite to what we call "hard" when we torture ourselves. It's like slowly letting oneself fall into a bottomless abyss, which involves constant fight with one's fear and the instinctual grabbing on stuff, and that's where all struggle is.
And then as you go through this, if you're paying any attention, you will inevitably start learning about "the way things work" - and then things like Four Noble Truths etc. suddenly start making total sense, referring directly to your first-hand experience.
That's my experience anyway, your mileage may varyTM.