Mein Rateversuch liegt völlig daneben.

Rateversuch is a compound noun:

• raten = to guess
• der Versuch = attempt, try

So Rateversuch literally means attempt at guessing or guessing attempt.

It is understandable German, but it is not the most everyday word. Depending on context, native speakers might also say:

• mein Tipp = my guess
• meine Schätzung = my estimate
• meine Vermutung = my assumption / guess

So the word is clear, but it can sound a bit more deliberate or constructed than a simple Tipp.

Because Rateversuch is:

• masculine: der Rateversuch / der Versuch
• singular
• in the nominative case here, because it is the subject of the sentence

With a masculine singular noun in the nominative, the possessive article is mein:

• mein Rateversuch

Compare:

• mein Rateversuch = nominative masculine
• meinen Rateversuch = accusative masculine
• meine Vermutung = nominative feminine
• meiner would not fit before this noun here

So mein is the correct form because it matches the grammatical role and gender of the noun.

Yes, liegen literally means to lie or to be lying, but in this sentence it is part of the idiomatic expression danebenliegen.

danebenliegen means:

• to be wrong
• to be off
• to miss the mark

So liegt ... daneben is not about physically lying somewhere. It is an idiom.

German often uses verbs in idiomatic ways that do not match English literally. Here, the idea is that the guess is off to the side, not hitting the correct answer.

Because the full verb is danebenliegen, and in a main clause German splits this kind of verb apart.

So:

• infinitive: danebenliegen
• main clause: liegt ... daneben

That is why you get:

• Mein Rateversuch liegt völlig daneben.

This is very common in German with separable verbs or verb expressions of this kind.

Compare:

• Ich stehe auf. = I get up.
• Er kommt mit. = He comes along.
• Mein Tipp liegt daneben. = My guess is off.

Literally, daneben means something like:

• beside it
• next to it

But in idiomatic use, especially with guesses, estimates, and judgments, daneben means:

• wrong
• off
• off the mark

So here it does not mean physical location. It means the guess is incorrect.

A useful thing to know: daneben can also be used in other contexts to say someone is acting inappropriately, absurdly, or strangely. So its meaning depends a lot on context.

völlig is an adverb meaning:

• completely
• totally
• entirely

It intensifies daneben.

So the difference is roughly:

• Mein Rateversuch liegt daneben. = My guess is off.
• Mein Rateversuch liegt völlig daneben. = My guess is completely off.

You can leave völlig out, but keeping it makes the statement stronger.

It is understandable and grammatical, but many native speakers would probably choose a simpler noun in everyday speech.

More natural alternatives might be:

• Mein Tipp liegt völlig daneben.
• Meine Schätzung liegt völlig daneben.
• Meine Vermutung war völlig falsch.

So the structure liegt völlig daneben is very natural, while Rateversuch is the part that sounds a bit less common.

Yes, that is grammatical and natural.

The difference is mainly one of style and nuance:

• liegt völlig daneben is more idiomatic and vivid
• ist völlig falsch is more direct and plain

So:

• Mein Rateversuch liegt völlig daneben.
• Mein Rateversuch ist völlig falsch.

Both work, but danebenliegen is a very common expression for guesses, estimates, or predictions that miss the mark.

The infinitive is danebenliegen.

So you would say:

• Mein Rateversuch liegt völlig daneben.
  main clause

but:

• ..., weil mein Rateversuch völlig danebenliegt.
  subordinate clause

and:

• Es ist ärgerlich, danebenzuliegen.
  infinitive construction

This is an important pattern in German: the split form appears in main clauses, but the full verb comes together in infinitives and subordinate clauses.

Because all nouns are capitalized in German.

Here the nouns are:

• Rateversuch
• and, inside the compound, Versuch is also a noun

Even though English only capitalizes nouns in special cases, German capitalizes every noun, including compound nouns. So Rateversuch must begin with a capital letter.