How to do up to 20 pullups I do about 9 now
I don't agree that to do 20 pull ups in a proper form (at least your chin above the bar) is so easy, i don't see many that can do it, even on YouTube done in a proper form i can't see many do it above 25.. Besides you have to consider your own weight, if you weight 60kgs or 100kgs we are talking about different universes.. 60kgs 20pull ups is nothing special, if you are 100kgs is probably an elite level.
Regardless, an intresting method that works is this:
present max pull ups/3 , in your case 3. Do as many set of 3 reps as you can with 1minute rest. Done it? how many sets? ok, now 3 times a week do 75% -50%-100% of those sets. for two weeks. the third week in the 100% you try a new record of sets, surely you have improved a lot.
second part: work on doing sets effortlessly. Do three sets of reps for max without grinding reps, do the max it come quickly.. anothe time do a ladder1–2–3–4–3–2–1 with 10″ rest 2 times or 3 times. This is to train to grind reps. Just alternate those two kinds of train for 3 weeks..
At the end you would have a great improvement in 6 weeks