Learn Hardcore Finnish: He puhuvat häviäjälle ystävällisesti ottelun jälkeen. - They talk kindly to the loser after the match.

It just happens to look like the English word he, but it is unrelated. It’s also capitalized only because it starts the sentence, not because it’s a pronoun (Finnish does not normally capitalize pronouns).

Why does the verb appear as puhuvat and not just puhua?

Puhua is the basic dictionary form (the infinitive) meaning to speak.

Finnish verbs must agree with the subject in person and number. For the 3rd person plural (they), puhua is conjugated as:

minä puhun – I speak
sinä puhut – you (sg) speak
hän puhuu – he/she speaks
he puhuvat – they speak

So -vat is the ending that marks 3rd person plural for many verb types. You cannot use the bare infinitive puhua as the main verb in a normal finite sentence like this.

Could you leave out He and just say Puhuvat häviäjälle…?

Yes, you can drop He:

Puhuvat häviäjälle ystävällisesti ottelun jälkeen.

This is still grammatical. Finnish is a subject-dropping language: when the verb ending clearly shows the subject (here -vat = they), the pronoun is often omitted, especially if the subject is already known from context.

However, using He is also fine, and it can sound a bit clearer or slightly more emphatic, depending on the context.

What case is häviäjälle and what does it literally mean?

Häviäjälle is in the allative case.

Basic form (nominative): häviäjä – loser
Allative: häviäjä
- -lle → häviäjälle – to the loser / onto the loser

The allative -lle often means:

to (a person or thing)
onto (a surface)
towards / onto (a goal)

Here it corresponds to to in English:
puhua jollekin = to speak to someone
So puhuvat häviäjälle ≈ (they) speak to the loser.

Why does puhua use häviäjälle (allative) and not some other case for the person you speak to?

With puhua in the sense of speaking to someone, standard Finnish uses the allative:

puhua jollekin – to speak to someone
puhua opettajalle – to speak to the teacher
puhua yleisölle – to speak to the audience

Other patterns exist but have different nuances:

puhua jonkun kanssa (genitive + kanssa) – speak with someone (more like have a conversation with)
puhua jostakusta / jostakin (elative) – speak about someone / something

So for speak to X, allative is the normal choice.

How is häviäjälle built morphologically? Why the j and the double l?

Base word: häviäjä (loser)

The j is already part of the stem: häviäjä.
The allative ending is -lle.
You simply attach -lle:
häviäjä + lle → häviäjälle.

The double l is just the ending -lle itself; Finnish commonly has double consonants in endings (like -ssa, -lla, -tta). There is no extra spelling trick here—just stem häviäjä + ending -lle.

What exactly is ystävällisesti, and how is it related to ystävällinen?

Ystävällisesti is an adverb meaning kindly / in a friendly way.

It is formed from the adjective:

ystävällinen – friendly, kind (adjective)
ystävällisesti – friendly, kindly (adverb)

In general, many Finnish adverbs of manner are made with -sti:

hidas (slow) → hitaasti (slowly)
selvä (clear) → selvästi (clearly)
ystävällinen (friendly) → ystävällisesti (in a friendly way)

So puhuvat… ystävällisesti = (they) speak kindly / in a friendly manner.

Can ystävällisesti appear in a different position in the sentence?

Yes. Finnish word order is fairly flexible. Common options here include:

He puhuvat häviäjälle ystävällisesti ottelun jälkeen.
He puhuvat häviäjälle ottelun jälkeen ystävällisesti.
He puhuvat ystävällisesti häviäjälle ottelun jälkeen.

All are grammatical. The differences are about emphasis and rhythm, not basic meaning. Placing ystävällisesti earlier can slightly highlight the manner of speaking; placing it later can make it feel more like an afterthought or clarification.

Why is it ottelun and not ottelu before jälkeen?

Postpositions like jälkeen require the preceding noun to be in the genitive.

Basic form: ottelu – match
Genitive: ottelu + n → ottelun

Jälkeen means after. The pattern is:

genitive + jälkeen – after something

Examples:

tunnin jälkeen – after the lesson
ruoan jälkeen – after the meal
ottelun jälkeen – after the match

Using plain ottelu jälkeen would be incorrect.

Is jälkeen a preposition or a postposition, and what does that mean?

In this sentence, jälkeen is a postposition.

A preposition comes before its complement (like English after the game).
A postposition comes after its complement.

Finnish commonly uses postpositions:

talon takana – behind the house (literally: house-GEN behind)
talon edessä – in front of the house
ottelun jälkeen – after the match

So ottelun jälkeen literally has the order match’s after.

Could ottelun jälkeen be moved elsewhere in the sentence?

Yes. You can rearrange it without changing the core meaning:

He puhuvat häviäjälle ystävällisesti ottelun jälkeen.
Ottelun jälkeen he puhuvat häviäjälle ystävällisesti.
He ottelun jälkeen puhuvat häviäjälle ystävällisesti.

All are grammatical. Starting with Ottelun jälkeen emphasizes the time frame: After the match, they…

Are there other natural ways to say They speak kindly to the loser after the match in Finnish?

Yes, for example:

He puhuvat ystävällisesti häviäjälle ottelun jälkeen.
(Just a slightly different word order.)
He puhuvat häviäjälle ystävällisesti pelin jälkeen.
(peli = game; more informal than ottelu.)
He juttelevat ystävällisesti häviäjän kanssa ottelun jälkeen.
(jutella = chat; häviäjän kanssa = with the loser. This stresses chatting with rather than speaking to.)

Your original sentence is fully correct and natural; these are just stylistic variations.