Během hry jsme viděli změnu skóre.

Because během requires the genitive case.

• hra = nominative singular
• hry = genitive singular

So:

• během hry = during the game

This is a fixed grammar pattern in Czech: během + genitive.

Other examples:

• během dne = during the day
• během týdne = during the week
• během zápasu = during the match

Během means during and focuses on something happening in the course of an event or time period.

So během hry means during the game.

By contrast, za can also sometimes relate to time, but it is used differently depending on context. For example:

• za hodinu = in an hour
• za války = during the war

For a straightforward phrase like during the game, během hry is the most transparent and common choice for learners.

Both are possible in Czech.

• Jsme viděli změnu skóre.
• Viděli jsme změnu skóre.

Both mean the same thing: we saw a change in the score.

Czech word order is more flexible than English word order. The choice often depends on rhythm, emphasis, or style rather than a strict rule.

Here, jsme viděli is perfectly natural.
But viděli jsme is also very common.

Because Czech past tense is formed with:

1. a past participle
2. a present-tense form of být (to be)

So:

• viděli = past participle, masculine animate plural / mixed plural form
• jsme = we are, used here as the auxiliary

Together:

• jsme viděli = we saw

This is normal Czech past tense formation.

Compare:

• viděl jsem = I saw
• viděla jsem = I saw (said by a woman)
• viděli jsme = we saw

The ending -i shows the plural past form used when the subject is:

• all masculine animate, or
• a mixed group that includes at least one masculine animate member

In many textbook examples, we is often given as viděli jsme by default.

Other possible plural past endings exist:

• viděly jsme would be used for an all-female group

So the sentence as written assumes a standard plural we form, typically understood as mixed or masculine animate.

Because změnu is in the accusative case, which is used for the direct object.

The verb vidět (to see) usually takes an object in the accusative.

• změna = nominative singular
• změnu = accusative singular

So:

• viděli jsme změnu = we saw a change

More examples:

• Vidím dům. = I see a house.
• Slyšíme hudbu. = We hear music.

Because skóre is one of those Czech nouns that is usually indeclinable, meaning its form does not change across cases.

So you can get structures like:

• změna skóre = a change of the score
• bez změny skóre = without a change in the score

The word skóre stays skóre.

This is common with some loanwords in Czech.

This is a noun phrase where:

• změnu = change in the accusative, because it is the object of viděli
• skóre = of the score / in the score

So změnu skóre literally works like a change of the score, though in natural English we would usually say a change in the score.

This is a very common Czech structure:

• konec hry = the end of the game
• výsledek zápasu = the result of the match
• změna plánu = a change of plan

Yes, změnu ve skóre is also possible, and it can sound a bit more explicit because it clearly means a change in the score.

So both of these can work:

• změnu skóre
• změnu ve skóre

The version in your sentence, změnu skóre, is compact and natural.

Very roughly:

• změna skóre = score change / change of the score
• změna ve skóre = change in the score

Vidět is a simple, common verb meaning to see, and it works well here.

• viděli jsme změnu skóre = we saw a change in the score

But Czech could use other verbs depending on nuance:

• zaznamenali jsme změnu skóre = we noticed / recorded a change in the score
• došlo ke změně skóre = there was a change in the score

So vidět is natural if the idea is that we observed it happening.

Yes, it is natural and correct.

A native speaker might also say:

• Během hry jsme viděli změnu skóre.
• Během hry jsme zaznamenali změnu skóre.
• V průběhu hry se skóre změnilo.
• Během hry došlo ke změně skóre.

Your sentence is straightforward, grammatical, and idiomatic.

Yes. Czech word order is flexible, though the emphasis may shift.

Possible alternatives:

• Během hry jsme viděli změnu skóre.
• Změnu skóre jsme viděli během hry.
• Během hry změnu skóre jsme viděli. — grammatically possible, but less natural in ordinary speech
• Viděli jsme během hry změnu skóre.

The original version is very natural because it starts with the time expression během hry, then gives the subject and verb, then the object.

Vidět is generally an imperfective verb.

In this sentence, aspect is not the main focus, because the sentence is simply reporting that we saw something during the game.

Czech aspect matters more strongly with pairs like:

• dělat / udělat
• psát / napsat

With vidět, the sentence is just a normal past statement about perception.

If you changed the verb, you could change the nuance:

• viděli jsme = we saw
• uviděli jsme = we caught sight of / we came to see

So viděli jsme sounds like straightforward observation, while uviděli jsme could sound more like we suddenly noticed.

In Czech, the subject is often built into the verb form.

Here, jsme already tells you the subject is we.

So Czech does not need a separate pronoun my unless you want emphasis.

• Jsme viděli změnu skóre. = We saw a change in the score.
• My jsme viděli změnu skóre. = We saw a change in the score.
  This sounds more emphatic, as if contrasting we with someone else.

That is why Czech often omits subject pronouns that English normally requires.