Tenses and modals. Must have been vs. had to be

Question

I have a question regarding modals: must have/had to.

When an author of a book, that's written in past tense, chooses to use modal "must" he has to use its past tense form:

The car crashed. The roads had to be slippery. (The roads were slippery)

When he writes about something that happened even before, he'd write:

The car had crashed. The roads had to have been slippery. (The roads had been slippery)

Why does it look so different in present tense(?), "had to" and "must have" even mean slightly different things. Why one cannot replace:

That game must have been really bad. (The game was bad)

With:

That game really had to be bad. (The game was bad, in past tense. A weird sounding assumption, when used in present tense.)

What is the difference?

Thank you

Answer 1

Modal verb must denotes obligation as its most primary role.

You must finish the project till tomorrow. - It is obligatory for you to finish the project till tomorrow.

Past obligation is usually denoted by the equivalent modal phrase had to.

The task was urgent and I had to finish it as soon as possible.

In both examples, the action expressed by modal verbs will happen after the time of speech.

Now consider the following examples where the modal verbs must id used to denote deduction.

His lights are off. He must be out. - The action denoted by the modal verbs is simultaneous to the time of speech and it deduces new information from the current situation.

Must have been is used to denote the past experience of the same kind.

You must have worked a lot to be such a successful scientist.