Studies on how people really improve at chess? How do people really improve at chess?

I often hear people say that any of the following will improve a player's ability:


Doing tactics puzzles
Playing more games
Playing bullet games
Playing longer games
Playing correspondence games
Memorizing openings
Analyzing own games
Reading chess books


Sometimes I hear a specific example like "I've been doing tactics puzzles since last year and it has improved my understanding significantly", and then I ask for their lichess name, and I check it, and their rating has been extremely steady for the last 3 years.

Often these kinds of suggestions seem at first to be anecdotal, but even anecdotes would be true. These are worse than anecdotes because they are not based in reality.

Is there some scientific study of GMs and their history to find out exactly the key points that made them great? Or some study of kids over time with different training techniques and comparison of rating changes to see what works and what doesn't?

As far as I can tell, the thing GMs have in common is that they all had strong chess coaches when they were kids and became very strong players by the time they were 15 or younger.
The closest thing there is to a long term study from child to gm of training techniques would be the polgar sisters. I'd advise searching for information on them to answer your question. Also I'm sure old soviet literature is full of ways to train chess GMs, they specialized in that for many years and had quite a few methods they thought optimally trained young players.

Anecdotally I can tell you from 2000 to 2200 I trained 2 hr 45 minutes on average each day, studying at minimum 10 chess tempo tactics, 3 recent gm games, a gm game of guess the move on chesstempo, and 1 15+ minute game on ICC a day with about an hour spent afterwards studying related games and opening lines. I also participated in an endgame club for about 4 months that year, read through Dvoretskys Endgame Manual, and Endgame Strategy by Mikhail Shereshevsky. At the beginning of that year (first 3 months) I also read through Winning Chess Middlegames by Ivan Sokolov. 

For the first 10 months I gained maybe 50 rating points over 3 tournaments. I gained 150 points in 2 tournaments in the last two months. 

I think this level of training could probably net 400 points in a year at lower levels, so long as young trainees were given optimum resources to practice with. Often times people use books that are either not suited to their level, don't address their weaknesses, or simple aren't very good. Also people have a tendency to play a lot of blitz or do things they find easy, but not the optimal things for improving their strength.

/end anecdote