doing something vs by doing something

[hardworker]

I would like to make up a few pairs of similar sentences.

(1a) By working in shifts, we finished our big project in three days.
(1b) Working in shifts, we finished our big project in three days.

(2a) By looking back, you realize that a very important person passed briefly through your life.
(2b) Looking back, you realize that a very important person passed briefly through your life.

(3a) By scoring the hundredth goal in tonight's game, the young hockey player was elected as Player of the Year.
(3b) Scoring the hundredth goal in tonight's game, the young hockey player was elected as Player of the Year.

(4a) By walking through the woods, we could feel an air of mystery.
(4b) Walking through the woods, we could feel an air of mystery.

How can I figure out when to add the preposition, by? Which sentence in each pair requires this preposition? Thank you for your help.

[Joe]

"By" implies the method or "how" you achieved something.

I would say "By" is fine in 1 and possibly 3 though it needs rewording:

By scoring the hundredth goal in tonight's game, the young hockey player became eligible for election as Player of the Year.