Learn Hardcore Finnish: Valmentaja sanoi, että päivän tulos ei ole yhtä tärkeä kuin hyvä strategia. - The coach said that today’s result is not as important as a good strategy.

The base form (dictionary form) is valmentaja.
In this sentence it is in the nominative singular, functioning as the subject of the verb sanoi.
Literally: Valmentaja sanoi… = The coach said…

How is sanoi formed, and what tense is it?

Sanoi is:

The past tense (imperfect) of the verb sanoa (to say).
3rd person singular form: hän sanoi = he/she said.

The personal ending -i marks past tense, and the 3rd person singular has no extra ending (unlike sanoin = I said, sanoit = you said).

What is the role of että here, and why is there a comma before it?

Että is the conjunction that introducing a subordinate clause (a content/statement clause) reported by sanoi.

Valmentaja sanoi, että … = The coach said that …

In Finnish, you normally put a comma before että when it starts a subordinate clause. This is standard punctuation, even though English often omits the comma before that.

Why is päivän in the form päivän and not just päivä?

Päivän is the genitive singular of päivä (day).

In päivän tulos, the genitive päivän modifies tulos (result), creating a possessive or specifying relationship, much like:

päivän tulos = the day’s result / the result of the day

So päivän answers “whose result / what kind of result?”.

What exactly does päivän tulos mean as a phrase?

Literally:

päivän = of the day / the day’s
tulos = result, outcome

Together päivän tulos is a compound-like noun phrase: the result of the day, often understood as today’s result (e.g. the score or outcome achieved today).

How does ei ole work? Why is there a separate word ei instead of just a negative verb form?

Finnish uses a special negative verb ei that is conjugated, and the main verb appears in a non-finite form (here: the basic form olla → ole).

In 3rd person singular:

on = is
ei ole = is not

So:

tulos on tärkeä = the result is important
tulos ei ole tärkeä = the result is not important

In this sentence we have ei ole yhtä tärkeä = is not as important.

What does the structure yhtä tärkeä kuin mean? How does this comparison work?

Yhtä … kuin is the standard Finnish way to say as … as in comparisons of equality.

Pattern:

yhtä + adjective (in basic form) + kuin + comparison term

So:

yhtä tärkeä kuin = as important as
yhtä iso kuin = as big as
yhtä kallis kuin = as expensive as

Here:

ei ole yhtä tärkeä kuin hyvä strategia
= is not as important as a good strategy

Why is it tärkeä and not tärkeämpi? What’s the difference?

tärkeä = important
tärkeämpi = more important (comparative form)

With yhtä … kuin, you must use the basic (positive) form of the adjective:

yhtä tärkeä kuin = as important as
(equality: same level of importance)

If you used tärkeämpi kuin, you would get:

tärkeämpi kuin = more important than
(inequality: greater importance)

The meaning of the sentence would then change: instead of saying “is not as important as…”, you would be saying “is more important than…”.

Why are tulos and tärkeä in the same form (both look like nominative singular)? What is their relationship?

Yes, both are in nominative singular and they are linked by olla (to be):

päivän tulos = noun phrase (subject)
tärkeä = predicate adjective (complement of olla)

In Finnish, a predicate adjective describing a singular subject in the nominative also appears in the nominative:

Tulos on tärkeä. = The result is important.
Päätös on vaikea. = The decision is difficult.

Negation doesn’t change that:

Tulos ei ole tärkeä. = The result is not important.

What case is hyvä strategia in, and why is there no article like “a” or “the”?

Hyvä strategia is:

hyvä = good, adjective in basic form
strategia = strategy, noun in nominative singular

Together they form a nominative noun phrase functioning as the comparison target after kuin.

Finnish has no articles (a/an/the). Whether you translate it as a good strategy or the good strategy depends on context in English; Finnish leaves that to context and doesn’t mark it grammatically.

Could the order be reversed, like “Hyvä strategia on tärkeämpi kuin päivän tulos”? Is that still correct?

Yes, you can say:

Hyvä strategia on tärkeämpi kuin päivän tulos.

That means:

A good strategy is more important than the day’s result.

Differences:

The order is reversed (good strategy now the subject).
The comparative form tärkeämpi (more important) is used instead of ei ole yhtä tärkeä (is not as important).

So it’s not a direct word-for-word reorder of the original; it’s a slightly stronger statement, but conceptually very close in meaning.

Is että always required after sanoi in this type of sentence, or can it be omitted like “The coach said the result is not …”?

In Finnish, when you report a full clause as content of sanoa, using että is normal and usually required:

Valmentaja sanoi, että päivän tulos ei ole yhtä tärkeä kuin hyvä strategia.

Omitting että here would sound unnatural or ungrammatical in standard Finnish.

You can omit että in some more colloquial or different-type structures, but for reported statements like this, keep että.