Learn Hardcore German: Die Statistik hilft ihr zu verstehen, wie der Algorithmus auf verschiedene Kommentare und Likes reagiert. - The statistic helps her understand how the algorithm reacts to different comments and likes.

If you wrote hilft sie, sie would be nominative, so it could only be a subject, not an object. That would change the meaning to something like She helps the statistics, which is not intended here.

What exactly does ihr mean here? It seems to have many meanings.

In this sentence, ihr = to her (3rd person singular, feminine, dative).

The word ihr can be confusing because it has several uses:

Dative singular, feminine (to her):
- Ich helfe ihr. – I help her.
  That’s the use in your sentence: Die Statistik hilft ihr …
Possessive determiner (her / their):
- ihr Auto – her car
- ihr Auto – their car (context decides)
Pronoun, nominative plural (they):
- Ihr seid nett. – You (plural, informal) are nice.

In this context the only one that fits grammatically is the dative “to her” meaning.

Why do we need zu verstehen after hilft ihr? Could we just say hilft ihr verstehen?

German normally uses zu + infinitive for “to + verb” when it’s not a modal verb or a few special verbs.

hilft ihr zu verstehen = helps her to understand

With helfen, the usual patterns are:

jemandem helfen, etwas zu tun
Die Statistik hilft ihr, etwas zu verstehen.
or a noun form:
Die Statistik hilft ihr beim Verstehen.

Without zu, hilft ihr verstehen sounds wrong/unfinished in standard German because helfen is not a modal verb like können, müssen, etc. Modal verbs can be followed directly by an infinitive without zu:

Sie kann den Algorithmus verstehen. – She can understand the algorithm.
But: Die Statistik hilft ihr, den Algorithmus zu verstehen. – The statistics help her to understand the algorithm.

Where exactly does zu go in a phrase like hilft ihr zu verstehen? Could it be hilft ihr verstehen zu?

In German, zu goes directly in front of the infinitive verb at the end of that clause or phrase:

Correct: ... hilft ihr zu verstehen ...
Incorrect: ... hilft ihr verstehen zu ...

With more than one verb element, zu often appears inside the verb cluster:

anzufangen, weiterzuarbeiten, kennenzulernen, etc.
- Sie versucht, ihn kennenzulernen.

But in your sentence there’s just one infinitive (verstehen), so it’s simply:

zu verstehen at the end of the infinitive phrase.

Why is there a comma before wie der Algorithmus auf verschiedene Kommentare und Likes reagiert?

Because wie der Algorithmus auf verschiedene Kommentare und Likes reagiert is a subordinate clause introduced by wie.

Structure:

Main clause / infinitive clause:
Die Statistik hilft ihr zu verstehen, …
Subordinate clause:
wie der Algorithmus auf verschiedene Kommentare und Likes reagiert.

In German, all subordinate clauses (introduced by words like dass, weil, wenn, wie, ob etc.) are normally separated from the main clause by a comma.

So the comma marks the boundary between:

what the statistics help her to do (zu verstehen)
and what exactly she understands (wie der Algorithmus … reagiert).

Why is the verb reagiert at the very end of wie der Algorithmus auf verschiedene Kommentare und Likes reagiert?

In German, subordinate clauses send the finite verb (the conjugated verb) to the end of the clause.

The clause is:

wie – subordinator (“how”)
der Algorithmus – subject
auf verschiedene Kommentare und Likes – prepositional object/adverbial
reagiert – finite verb (goes to the end)

So word order rule:

Main clause: verb is in second position
Die Statistik hilft ihr …
Subordinate clause: verb is in final position
…, wie der Algorithmus … reagiert.

Why do we use auf with reagieren and not another preposition? And why are Kommentare and Likes in the accusative?

In German, reagieren is almost always used with auf + accusative when you mean react to something.

auf etwas reagieren – to react to something

So:

auf verschiedene Kommentare und Likes
auf – preposition fixed with reagieren in this meaning
verschiedene Kommentare und Likes – its object in the accusative case

You can see it if you replace the nouns with a pronoun:

auf sie reagieren – react to them (sie = accusative plural)

Other cases would be wrong here:

auf verschiedenen Kommentaren (dative) → wrong for this verb pattern
The correct pattern is always: auf + Akkusativ with reagieren.

Why is it verschiedene Kommentare and not verschiedenen Kommentare or verschiedener Kommentare?

Because verschiedene is an adjective describing a plural noun without an article in the accusative.

Case: accusative (after auf with reagieren)
Number: plural (Kommentare, Likes)
Article: none (indefinite plural)
Adjective: verschieden-

In this pattern (no article, plural, accusative), the adjective ending is -e:

verschiedene Kommentare
verschiedene Likes

If there were a definite article, the ending would change:

auf die verschiedenen Kommentare – on the various comments
(here verschiedenen because die already marks case/number/gender)

But because there is no article, the adjective itself takes the -e ending for plural accusative: verschiedene.

Why is there no article in verschiedene Kommentare und Likes? Why not die verschiedenen Kommentare?

Both are possible, but they mean slightly different things.

verschiedene Kommentare und Likes – various comments and likes in a general, indefinite sense. We don’t know or care which specific ones.
die verschiedenen Kommentare und Likes – the various comments and likes that are already known or specific in the context.

In your sentence, we are talking about how the algorithm reacts in general to different comments and likes. That’s why an indefinite plural without article fits well:

auf verschiedene Kommentare und Likes reagiert
= reacts to various / different comments and likes (in general).

Why are Statistik, Algorithmus, Kommentare, and Likes all capitalized?

In German, all nouns are capitalized, regardless of their position in the sentence. So:

die Statistik – noun (statistic(s))
der Algorithmus – noun (algorithm)
Kommentare, Likes – plural nouns

This includes loanwords from English, like Like (internet “like” on a post). Once used as a noun in German, they follow the same capitalization rule:

ein Like, zwei Likes
Likes is just the normal German plural of the loanword Like.

Is there any difference in meaning between wie der Algorithmus reagiert and dass der Algorithmus reagiert?

Yes, there is a clear difference:

wie der Algorithmus reagiert – how the algorithm reacts (the manner / pattern of reaction)
dass der Algorithmus reagiert – that the algorithm reacts (the mere fact that it reacts)

Your sentence is about understanding the way in which the algorithm responds to different comments and likes, so wie is the correct choice:

… zu verstehen, wie der Algorithmus … reagiert.
= to understand how it reacts, not just that it reacts.