La aleatoriedad cambia el desempate.

In Spanish, abstract nouns often take the definite article when speaking about a concept in a general way.

So:

• La aleatoriedad = randomness, random variation, randomness as a concept

This is very common in Spanish, even where English often drops the:

• La paciencia es importante. = Patience is important.
• La información cambia rápido. = Information changes quickly.

You can sometimes omit the article in certain styles or contexts, but here la aleatoriedad sounds much more natural.

Because nouns ending in -dad are normally feminine in Spanish.

Examples:

• la ciudad
• la posibilidad
• la libertad
• la aleatoriedad

So it takes feminine agreement:

• la aleatoriedad
• mucha aleatoriedad
• esta aleatoriedad

Aleatoriedad means randomness or random character/quality.

It is a correct and useful word, especially in:

• mathematics
• statistics
• computing
• technical writing
• formal analysis

In everyday speech, Spanish speakers often prefer azar in many contexts:

• el azar = chance
• Lo decidió el azar. = Chance decided it.
• El azar cambió el resultado. = Chance changed the result.

So aleatoriedad is perfectly fine, but it sounds more technical or formal than azar.

Because the subject is la aleatoriedad, which is singular.

• la aleatoriedad = singular
• therefore the verb must be singular: cambia

Compare:

• La aleatoriedad cambia el desempate.
• Los factores aleatorios cambian el desempate.

In the second sentence, los factores aleatorios is plural, so the verb becomes cambian.

Desempate is a noun. It usually means:

• tie-break
• tie-breaker
• tie-breaking stage/procedure
• sometimes the act of breaking a tie

It comes from the verb desempatar = to break a tie.

So:

• empate = tie, draw
• desempate = tie-break / tie-breaking result or method

Depending on context, el desempate could refer to:

• the tie-breaking rule
• the tie-breaking round
• the final decision when there is a tie

Because desempate is a masculine noun.

Its gender is lexical: you simply learn it as el desempate.

Examples:

• el empate = the tie
• el desempate = the tie-break

Even though it ends in -e, that does not automatically make it masculine or feminine. Nouns ending in -e can be either:

• el empate
• el desemapte
• la clase
• la noche

So the article tells you the gender.

Because el desempate is a direct object, but it is not a person.

Spanish uses the personal a mainly with specific human direct objects:

• Veo a María.
• Ayudo a mi hermano.

But with things, ideas, or events, there is normally no a:

• Cambio el sistema.
• La aleatoriedad cambia el desempate.

So the sentence correctly uses cambia el desempate, not cambia al desempate.

Normally, no.

Cambia al desempate would sound wrong in this context because desempate is not a person and is not the kind of noun that would usually take the personal a.

Also, cambiar a can mean something different, like to switch to:

• Cambió al plan B. = He/She switched to plan B.

That is not what is happening in La aleatoriedad cambia el desempate.

This is the normal Spanish order:

• subject + verb + object

So:

• La aleatoriedad = subject
• cambia = verb
• el desempate = direct object

Spanish is more flexible than English, so other word orders are possible for emphasis, but this version is the most neutral and straightforward.

If you changed the order, you might change the emphasis or even the meaning. For example:

• El desempate cambia = The tie-break changes.
• Cambia el desempate = The tie-break changes / The tie-break is changing.

Those do not clearly mean the same thing as the original sentence.

Yes. The exact English choice depends on context.

Desempate can refer to:

• the tie-break itself
• the tie-breaking rule
• the tie-breaker
• the deciding stage or criterion

For example, in sports, rankings, games, or algorithms, desempate might mean different but related things.

So if you are trying to understand the Spanish grammar, the important point is that desempate is a masculine noun meaning something like tie-break / tie-breaker / tie-breaking decision depending on context.

Yes.

Here cambiar takes a direct object:

• La aleatoriedad cambia el desempate.

That means something changes something.

Spanish cambiar can be used in different ways:

1. Intransitive: something changes

   • El sistema cambia. = The system changes.

2. Transitive: something changes something

   • La aleatoriedad cambia el desempate.

3. Reflexive: to change oneself / to change

   • El sistema se cambia fácilmente. or Me cambié de ropa.

So in your sentence, it is the transitive use.

Sometimes yes, especially in less technical Spanish.

Compare:

• La aleatoriedad cambia el desempate.
• El azar cambia el desempate.

Both are possible, but they feel slightly different:

• aleatoriedad = randomness, more formal/technical
• azar = chance, luck, randomness in a more everyday or idiomatic way

So if the sentence comes from a technical context such as statistics, game theory, or computing, aleatoriedad may be exactly the right word.

A simple pronunciation guide:

• aleatoriedad ≈ ah-leh-ah-toh-ree-eh-DAD
• desempate ≈ deh-sehm-PAH-teh

Stress:

• aleatorieDAD → stress on the last syllable because it ends in -d
• desemPAte → stress on pa, because words ending in a vowel usually stress the second-to-last syllable

Not in normal Spanish.

That version sounds unnatural and incomplete. Spanish usually needs the articles here:

• La aleatoriedad cambia el desempate.

Dropping both articles would sound like a headline fragment, bad machine translation, or very unnatural telegraphic language.

So for normal grammar, keep both:

• la
• el