差点 (almost / nearly)

That was close

• You slipped on the ice outside your building but grabbed the railing just in time.
• I我wǒnearly差点儿chà diǎnrto fall down摔倒shuāi dǎo。 — "I nearly fell." It almost happened, but didn't.

almost差点chà diǎn(non-syllabic diminutive…儿ér) + Verb = nearly happened

• almost差点chà diǎn(non-syllabic diminutive…儿ér) + Verb = something almost happened but did not: nearly差点儿chà diǎnrto arrive late迟到chí dào, nearly差点儿chà diǎnrforget忘wàng(completed / change)了le.
• It goes before the verb, after the subject; (completed / change)了le often closes the sentence: I我wǒnearly差点儿chà diǎnrforget忘wàng(completed / change)了le.

I我wǒnearly差点儿chà diǎnrforget忘wàng了le。

With not没méi: the tricky part

• For something unwanted, nearly差点儿chà diǎnr and nearly差点儿chà diǎnrnot没méi mean the same: nearly差点儿chà diǎnrto fall down摔倒shuāi dǎo = nearly差点儿chà diǎnrnot没méito fall down摔倒shuāi dǎo — "nearly fell (but didn't)".
• For something wanted, not没méi flips the meaning: I我wǒnearly差点儿chà diǎnrnot没méicatch赶上gǎn shàngthe train火车huǒ chē。 — "I nearly missed the train (but caught it)."

I我wǒnearly差点儿chà diǎnrnot没méicatch赶上gǎn shàngthe train火车huǒ chē。

Wanted or unwanted?

nearly差点儿chà diǎnr versus about the same差不多chà bu duō

• nearly差点儿chà diǎnr = "nearly happened": he他tānearly差点儿chà diǎnrcry哭kū(completed / change)了le — "He nearly cried."
• about the same差不多chà bu duō = "about, almost (in amount)": about the same差不多chà bu duō十点shí diǎn(completed / change)了le. They are not interchangeable.

he他tānearly差点儿chà diǎnrcry哭kū了le。

Recap

Read the full reference: HSK 4 grammar — Adverbs.