An idiom is a set phrase whose meaning you can't fully work out from the separate words, and its wording is often locked. All three below are informal-to-neutral: natural in conversation and semi-formal writing, but too casual for a formal report. Night and day means a dramatic, obvious difference between two things. To buy into an idea is to accept and believe in it. To have a hazy idea of something is to understand it only vaguely — an unclear, half-formed picture in your mind. Change one small part of an idiom and it stops sounding like English.
Idioms are fixed phrases
night and day /naɪt ənd deɪ/ — The two drafts are night and day; the second one is far clearer.
buy into /baɪ ˈɪntu/ — The team quickly bought into the new schedule once they saw the results.
a hazy idea /ə ˈheɪzi aɪˈdiə/ — I only had a hazy idea of what the report was asking for.
Not ""The results were night and days." (the idiom got pluralized)" — say ""The results were night and day." (fixed wording)". Night and day is frozen; you can't add an -s or swap a word. Idioms keep their exact shape or they stop meaning anything.
Try it: Which sentence uses the idiom in its correct fixed form? (We bought into the idea quickly. / We bought the idea quickly. / We buy in the idea quickly.) Answer: We bought into the idea quickly. — 'Buy into' is the fixed phrasal idiom meaning to accept or believe something, so 'bought into the idea' is right. 'Bought the idea' drops 'into' and sounds like a purchase, and 'buy in the idea' breaks the fixed wording and mixes up the tense.
Match the idiom to the setting
Idioms sound natural in speech and semi-formal writing, but a formal report usually wants the precise, neutral word instead. A game changer is something that dramatically changes a situation, usually for the better; in formal writing you'd say it had a profound impact — same idea, higher register. A deal-breaker is a single problem serious enough to end an agreement or make someone walk away. And to say a change barely moved the needle means it made almost no difference at all. All three are informal idioms, so swap in the plain formal wording when the setting calls for it.
a game changer /ə ˈɡeɪm ˌtʃeɪndʒər/ — For the small clinic, online booking was a game changer.
a deal-breaker /ə ˈdil ˌbreɪkər/ — A long commute would be a deal-breaker for most of the applicants.
barely moved the needle /ˈbɛrli muvd ðə ˈnidəl/ — The discount barely moved the needle on our monthly sales.
Not ""This is a deal breaker issue." (used as an adjective before a noun)" — say ""This is a deal-breaker." (used as a noun on its own)". A deal-breaker is a noun for the thing that ends an agreement; don't stretch it into an adjective in front of 'issue'.
Try it: In a formal written report, which phrasing fits best? (The new policy had a profound impact. / The new policy was a total game changer. / The new policy barely moved the needle.) Answer: The new policy had a profound impact. — A report calls for precise formal language, so 'had a profound impact' is the right register. 'A total game changer' is idiomatic and too conversational for a report, and 'barely moved the needle' is also an idiom and means the opposite of a big effect.
Idioms for scale and direction
A second group of idioms reports how big a change is, or which way it is heading. A huge step up is a clear improvement on what came before; formally, a significant improvement. A ton stands in for a large amount of money, time or effort — formally, a substantial amount. Heading the other way, if something is going downhill fast it is getting worse quickly (rapidly deteriorating), and if things could go south the situation may turn bad (dire consequences). All four are informal, so a report would use the plain wording instead.
a huge step up /ə hjudʒ stɛp ʌp/ — The new lab is a huge step up from the old one.
a ton /ə tʌn/ — They spent a ton on advertising last quarter.
going downhill fast /ˈgoʊɪŋ ˈdaʊnhɪl fæst/ — Sales have been going downhill fast since the recall.
things could go south /θɪŋz kʊd goʊ saʊθ/ — If we miss the deadline, things could go south quickly.
Not ""Revenue is going downhill fast." (in a report to shareholders)" — say ""Revenue is deteriorating rapidly." (in a report to shareholders)". The idiom is fine in conversation, but a formal report wants the neutral wording. Same meaning, different setting.
Try it: A colleague says the department spent a substantial amount on training. Which idiom says the same thing in conversation? (a ton / a huge step up / going downhill fast) Answer: a ton — A ton is the informal way to say a substantial amount. A huge step up is about improvement rather than quantity, and going downhill fast describes something getting worse.
Try it: In a casual team meeting, which sounds most natural for 'the change made almost no difference'? (It barely moved the needle. / It had negligible effect. / The results were night and day.) Answer: It barely moved the needle. — 'Barely moved the needle' is the idiom for almost no change and fits a casual meeting. 'Negligible effect' is correct in meaning but reads as formal report language, and 'night and day' means a dramatic difference, which is the opposite of what's intended.