I grease the groove quite a bit. The number of times and amount each time always vary and decided as I'm doing them. I've even hung a bar in the bathroom door before so every time I had to piss while drinking I knocked a few out. I also start every workout session with pull ups in my warm ups. About 2-3 sets of 5-10. At my peak I could knock out about 40 deadhangs. Though lately I'm around low 20's. I also feel weighted pull ups are key to reaching higher numbers. Rosie had a good point lean out and your are not pulling up as much weight. Last summer I did a 100 day pull up challenge that was tremendous for me reaching higher numbers, BUT there was a snafu. At day 73 I just couldn't do any more and had injured my left shoulder. In retrospect and the next time I do it coming up I'm going to do two 50 days totaling 100. I'll lay the idea out below...
Day 1 you do 1 pull ups
Day 2 you do 2 pull ups
And so on till 100 pull ups on day 100
(Next time at day 51 I will start back at 1 and go up to 50 pull ups again to total 100 days. This should allow better recovery, prevent overuse injuries and CNS burnout)
You can do them all at once, sets of 5, 1 every 10 minutes, what ever as long as you get the number done that day
You can do strict dead hangs, kipping, butterfly, jumping pull ups, band assist, have a buddy push you, over hand, under hand, false grip, whatever, as long as you get your chin above the bar
If you miss a day you need to make up all that you missed plus what you owe for that day
And anyone could "buy in" at any time by doing all the pull ups that you missed on that day (so buy in early)
Then take a few days off and go hard for your max!
ps grip strength and filing off calluses is important as well. For a lot of people grip goes or calluses cause a person to stop/drop before they actually need to.
variance is important