How long to get a 200 rating point increase from serious chess study alone according to this academic paper? In the academic journal article "The Role of Deliberate Practice in Chess Expertise" from APPLIED COGNITIVE PSYCHOLOGY Appl. Cognit. Psychol. 19: 151– 165 (2005)

At the top of page 162, the authors state that


  "...each log unit of serious study alone yields about 200 rating
  points compared to 33 rating points for log tournament play. Hence,
  players ought to devote the majority of their time to that activity."


I have gone over this academic paper several times, but I cannot decipher what "each log unit" represents. What time span is a "log unit" in this context where studying chess alone gave the chess players in this academic paper 200 ratings points vs 33 ratings points from playing in tournaments? Is it 6 months, 10 months, a year?
The first paragraph of the RESULTS section on p. 155 says


  We applied log-10 transformations to three variables (cumulative study alone, cumulative tournament play, and chess book library size) prior to correlation and regression analyses.


The log-10 (logarithm base 10) of a number is what power you have to raise 10 to in order to produce that number; e.g. log 100 = 2, log 1000 = 3, etc.

So the sentence


  each log unit of serious study alone yields about 200 rating points


means that, all other things being equal, if player A studies ten times as long as player B, his rating will be about 200 points higher. (Another student who studies a hundred times as long as player B will have a rating of about 200 points higher than player A.) So there is no constant time span per 200-point gain; the required time to gain a particular amount of rating improvement gets larger and larger as you improve. (Another way to put this is that chess study produces diminishing returns.)

(In a sense, the Elo rating system is logarithmic as well, so you could claim that the relationship between study time and playing skill is actually linear. But since everybody measures playing skill by Elo rating, that's not so productive.)