Po pierwszej połowie był remis, ale trener powiedział, że nadal możemy walczyć o zwycięstwo.

Because the preposition po in the sense of after requires the locative case.

So:

• pierwsza połowa = the first half (dictionary/basic form)
• po pierwszej połowie = after the first half

Both words change:

• pierwsza → pierwszej
• połowa → połowie

This is a very common pattern in Polish:

• po meczu = after the match
• po przerwie = after the break
• po pierwszej połowie = after the first half

It is the locative singular.

More specifically:

• połowa is a feminine noun
• after po meaning after, it goes into the locative
• the adjective must match the noun, so pierwsza also becomes locative feminine singular

So:

• nominative: pierwsza połowa
• locative: pierwszej połowie

Polish does not use articles like a or the, so remis appears by itself.

Był remis literally means something like:

• there was a draw
• it was a tie

In Polish, this kind of structure is very natural for describing the score or situation:

• Była cisza. = There was silence.
• Był problem. = There was a problem.
• Był remis. = It was a draw / The score was tied.

You do not need an equivalent of English a/the.

Because remis is a masculine noun in Polish.

In the past tense, the verb agrees with the grammatical gender of the subject:

• był = masculine singular
• była = feminine singular
• było = neuter singular

Since remis is masculine, you say:

• był remis

Compare:

• była przerwa = there was a break/intermission
• było zwycięstwo = there was a victory

Because Polish usually drops subject pronouns when they are clear from the verb ending.

możemy already means we can.

So:

• możemy = we can
• walczymy = we fight / are fighting
• powiedział = he said

You could add my for emphasis:

• że nadal my możemy walczyć...

But that would sound marked or contrastive, like we can still fight, not someone else.

Normally, the pronoun is unnecessary.

Że means that and introduces a subordinate clause.

So:

• trener powiedział, że... = the coach said that...

This is one of the most common structures in Polish:

• Wiem, że... = I know that...
• Myślę, że... = I think that...
• Powiedział, że... = He said that...

Also, in Polish punctuation, you normally put a comma before że when it introduces a clause:

• trener powiedział, że nadal możemy...

This is a very important difference between Polish and English.

In English, after a past reporting verb, you often backshift:

• He said that we could still fight for victory.

In Polish, you usually do not backshift in the same way. You keep the tense that fits the meaning inside the reported statement.

So Polish says:

• powiedział, że nadal możemy walczyć...
• literally: he said that we still can fight...

This is completely normal Polish.

If you translate naturally into English, you will often say:

• the coach said that we could still fight for the win

So don’t expect Polish to copy English tense sequence rules.

Yes, but it changes the feel.

• że nadal możemy walczyć o zwycięstwo = that we can still fight for victory
• że nadal mogliśmy walczyć o zwycięstwo = that we could still fight for victory

The version with możemy reflects the content of what the coach said more directly, and it is very natural in Polish reported speech.

The version with mogliśmy is also possible, but it sounds a bit more shifted into the narrator’s past perspective.

In many everyday contexts, Polish prefers the present here.

Yes, Polish word order is flexible.

Nadal means still. In this sentence, nadal możemy is the most neutral and natural order.

You may also hear:

• możemy nadal walczyć
• nadal walczyć możemy — much less neutral, more stylistic/emphatic

The most standard version here is:

• że nadal możemy walczyć o zwycięstwo

That places nadal before the verb phrase and clearly means we can still fight.

Here o means for in the sense of striving for / competing for / fighting for.

The verb walczyć often combines with o + accusative:

• walczyć o życie = fight for life
• walczyć o wolność = fight for freedom
• walczyć o zwycięstwo = fight for victory

So the whole phrase means:

• to fight for victory
• in sports English, often more naturally: to keep fighting for the win

It is in the accusative case.

The preposition o has different meanings and can take different cases, but with walczyć o it takes the accusative.

Here, zwycięstwo is a neuter noun, and its accusative singular looks the same as the nominative singular:

• nominative: zwycięstwo
• accusative: zwycięstwo

So the form does not change visibly, but grammatically it is accusative because of o.

Because walczyć o zwycięstwo emphasizes the idea of continuing the struggle / continuing to compete, not the final result itself.

• walczyć o zwycięstwo = fight for victory / keep battling for the win
• wygrać = to win

The coach is saying that the team still has a chance and should keep trying. So walczyć is a very natural choice in a sports context.

It suggests effort, determination, and that the result is not decided yet.

Powiedział is perfective.

Its imperfective partner is mówił.

Very roughly:

• powiedział = he said, he stated, he told us once/completely
• mówił = he was saying, he used to say, he spoke

In this sentence, the coach made a specific statement at a particular moment, so the perfective verb powiedział is the natural choice.

Compare:

• Trener powiedział, że... = The coach said that...
• Trener mówił, że... = The coach was saying / used to say that...

Yes, Polish word order is flexible, and that version is grammatically possible.

But the original:

• Po pierwszej połowie był remis

is the most natural if you want to set the scene first: After the first half, it was a draw.

If you say:

• Remis był po pierwszej połowie

it sounds more marked, as if you are emphasizing the draw.

Polish often puts time expressions early in the sentence when they provide the context:

• Po meczu...
• Po przerwie...
• Po pierwszej połowie...

So the original order is very natural.

Very often, yes, but it depends on the sport.

• pierwsza połowa = first half
• druga połowa = second half

This works especially well for sports divided into two halves, like football.

For other sports or situations, Polish may use different words, for example:

• pierwsza część = first part
• pierwsza tercja = first period/third (in hockey)
• pierwsza kwarta = first quarter

So połowa is correct here because the match is being viewed as having two halves.

Ale means but and introduces a contrast.

The contrast is:

• the situation after the first half was only a draw
• despite that, the coach said the team could still fight for victory

So the logic is:

• Po pierwszej połowie był remis = After the first half, it was tied
• ale trener powiedział... = but the coach said...

It connects two ideas that pull in slightly different directions: the score was level, yet there was still hope and determination.

It is very natural and idiomatic.

A Polish speaker would easily understand it as a normal sports-related sentence. It has several very standard patterns:

• po + locative for after
• był remis for a tied score
• powiedział, że... for reported speech
• walczyć o + accusative for fight for

So it is a good example of natural Polish rather than a word-for-word translation from English.