How does Watson's habit of embellishing both help and hinder a reader's attempt to solve the mystery before Holmes does in "The Red-Headed League"?
Any embellishment on Watson’s part would likely take the form of leaving out information so that the reader could not guess the solution and Holmes would seem all the more brilliant. Indeed, Watson often seems to be pretty far behind Holmes in terms of deduction. Using Watson as a narrator keeps the reader in the dark, because Watson cannot keep up with Holmes.
It creates suspense, since readers—along with the sidekick narrator—do not have access to the detective's innermost thoughts until he finally chooses to reveal them after the mystery is solved. (enotes style)
Holmes declares that Watson shares his “love of all that is bizarre and outside the conventions and humdrum routine of everyday life” (p. 4). This is why Watson chronicles his cases. However, he has also shown an enthusiasm also “somewhat to embellish” the cases. However, we cannot necessarily take him at his word because he said this in front of a client. He might be just playing with Watson. Although Holmes has quite a high opinion of himself, he also seems to avoid taking credit.
In the end, Holmes paraphrases Flaubert to say:
‘L'homme c'est rien—l'oeuvre c'est tout’ (p. 18)
The man is nothing, the work is everything. (trussel)
Therefore, Watson may not be embellishing at all. In fact, you could argue that Watson dumbs down his own role in order to help the reader understand what happened. He often asks Holmes questions the reader might ask.
“And how could you tell that they would make their attempt to-night?” I asked. (p. 18)
In the long run, the reader simply may not have enough information to solve the crime before Holmes because Watson embellishes Holmes’s glory by withholding facts from the reader to make Holmes’s cases more interesting.