Learn Hardcore Japanese: kuni ni yotte ninki no supootu ga tigaimasu. - Popular sports differ depending on the country.

人気 (にんき) is originally a noun meaning “popularity.”
Grammatically it can behave like a na-adjective, but in practice it is much more common to use it as a noun with の before another noun:

人気のスポーツ = sports of popularity / popular sports
人気の歌手 = singers with popularity / popular singers

You can see 人気な sometimes (e.g. 人気な商品), and it’s not wrong, but:

人気の + noun is more natural and common.
Many native speakers will intuitively prefer 人気のスポーツ over 人気なスポーツ in this exact sentence.

So the sentence uses the most natural, everyday pattern: noun (人気) + の + noun (スポーツ).

What exactly does によって mean in this sentence?

Here, 国によって means “depending on the country” or “from country to country / by country.”

General idea of ～によって:

It attaches to a noun: N + によって
It can mean:
- “by / through / via” (method, agent)
- “depending on / according to” (basis for variation)
- “because of / due to” (cause, in some contexts)

In this sentence:

国によって = “depending on the country / based on the country”
It sets up the condition that causes variation in what follows:
- 国によって　→　人気のスポーツが違います
- Depending on the country → the popular sports differ.

Could I replace によって with something like ごとに or で here?

You can, but the nuance changes.

国ごとに人気のスポーツが違います。
- 国ごとに = “each country, country by country”
- Emphasizes “each individual country” having its own popular sports.
- Very natural, close in meaning to the original.
国で人気のスポーツが違います。
- 国で literally: “in each country”
- Understandable, but feels a bit simpler / less natural than 国によって or 国ごとに for expressing systematic variation.
- Sounds more like “in different countries, popular sports are different,” not explicitly stressing “depending on.”
国によって人気のスポーツが違います。 (original)
- Stresses variation depending on the country as a factor.
- Very idiomatic for this “AによってBが違う” pattern:
  XによってYが違う = “Y is different depending on X.”

So, 国によって and 国ごとに are best; 国で is possible but less typical for this specific phrasing.

Why is it スポーツが違います with が, not スポーツは違います with は?

Both が and は are possible with 違う, but they have different feelings.

スポーツが違います。
- が marks the subject / the thing that is different.
- Neutral, factual statement:
  “The popular sports are different (depending on the country).”
スポーツは違います。
- は makes スポーツ the topic and often implies contrast:
- Could sound more like:
  “As for sports, they’re different (even if other things might not be).”

In this sentence, we’re simply stating what is different (popular sports), so が is the most straightforward and natural choice:

What is the subject and topic of this sentence? How is it structured?

Sentence: 国によって　人気のスポーツが　違います。

国によって
- Adverbial phrase = “depending on the country”
- Sets the condition / basis for comparison.
- It’s not the subject; it’s like “by country / from country to country.”
人気のスポーツが
- Subject (marked by が)
- “The popular sports”
違います
- Predicate verb: “are different”

So the logical structure is:

(Depending on country) + (popular sports) + (are different).

There is no explicit topic は here; the entire sentence is just one fact statement about how popular sports differ by country.

Why do we translate 違います as “are different” when it literally looks like “is different”?

Japanese verbs don’t change form based on singular/plural like English verbs do.

違います just means “is/are different”; it doesn’t specify number.
Whether we translate it as “is different” or “are different” depends on the English subject.

In this sentence:

Subject: 人気のスポーツ = “popular sports” (plural in natural English)
So a natural English translation is:
- “The popular sports are different (depending on the country).”

If the subject were clearly singular, we’d translate 違います as “is different” instead.

Can I say スポーツの人気は国によって違います instead? What’s the difference?

Yes, that’s a very natural alternative:

スポーツの人気は国によって違います。
= “The popularity of sports differs depending on the country.”

Differences in focus:

国によって人気のスポーツが違います。
- Focuses on which sports are popular changing between countries.
- “The popular sports themselves differ.”
スポーツの人気は国によって違います。
- Focuses on the degree of popularity of sports varying.
- “The popularity (level) of sports differs from country to country.”

Both are correct; the original is more like “different sports are popular in different countries.”

Why is the verb in polite form (違います) and not plain form (違う)?

Japanese has levels of politeness in verb endings:

違います = polite (ます-form)
違う = plain (dictionary form)

You choose based on who you’re talking to and context:

In a textbook, classroom, news, or speaking to someone you don’t know well:
- 国によって人気のスポーツが違います。 (polite) is natural.
In casual speech with friends:
- 国によって人気のスポーツが違う。 (plain) is common.

The grammar is the same; only the politeness level changes.

Can 国によって come at the end, like 人気のスポーツが違います国によって?

No, that would be unnatural in standard Japanese.

The pattern N + によって works like an adverbial phrase and normally comes:

At the beginning:
国によって人気のスポーツが違います。
Or right before the part it modifies:
(In other sentences, e.g. 国によって違う, 会社によって給料が違う, etc.)

Putting 国によって at the very end would sound odd and ungrammatical in normal prose or speech. So keep it where it is (or near the verb if you shorten it to 国によって違います).

How would you say just “It depends on the country” using this pattern?

You can omit the obvious part (“what” is different) and just say:

国によって違います。

In context, this means:

“It depends on the country.”
Literally: “(It) is different depending on the country.”

Japanese often omits subjects and objects when they are clear from context, so once the topic (e.g. food, holidays, rules, etc.) is understood, 国によって違います is a perfectly natural standalone sentence.