"I thought she might have had a problem with alcohol" versus "I thought she might have a problem with alcohol"

Question

Here in the following sentences why are we using "I thought she might have had" with 'had', why not simply "I thought she might have"?

1) Vincent remembered Eddie’s wife, “I knew Naedine very well; she was very nice to me. I felt I had a great rapport with her".

Vincent said, “Eddie didn’t talk much about it, but I thought she might have had a problem with alcohol. One New Year’s Eve I caught on right away. We were at the Inn at Jefferson Square. I was sitting at the table with my date, some friends and Naedine. She took a glass of wine and Eddie came over and told her she wasn’t supposed to be drinking."

2) “I thought she had a good chance to get on the medal stand,” Dunn said Monday. “And if she got a good jump, I thought she might have had a chance to win it. That one girl just got an amazing jump in. Tanae jumped better than she had ever jumped in her life. You can’t do much better than that. When you jump the best you’ve ever jumped at the state meet, that’s all you can ask for.”

In both of the sentences above why can't we say "....might have..." like here:

The big woman's face was bright red. For a minute I thought she might have a stroke. It was 100 degrees in the shade. (Ref)

Although I know about tenses (past tense and past perfect), this seems to always confuse me. Also it is always very easy to understand without 'thought' but with 'thought' it looks confusing.

Please elaborate this point.

Answer 1

You ask: In both of the sentences above, why can't we say "....might have..."?

I'll answer: Who says you can't? Let's try it, and see what happens:

“I thought she had a good chance to get on the medal stand,” Dunn said Monday. “Andif she got a good jump, I thought she might have a chance to win it".

That version seems grammatical, too.

Essentially, the speaker is saying:

If she had a good jump, she might have won.

There are many ways to say that, and you may not hear the most straightforward way of saying it the moment a microphone is thrust into a coach's face. So, the coach says,

If she got a good jump, I thought she might have had a chance to win [the race].

In this original, the words "if...", "I thought...", "might have...", and "a chance...," we are pretty well-nested in conjecture and conditional language. The result is a sentence where the word had could be omitted or included, and the sentence pretty much means the same thing, especially if you change the punctuation around:

"With a good jump," I thought, "She might have a chance to win the race."

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The same holds for your first example:

Eddie didn’t talk much about it, but I thought she might have had a problem with alcohol.

Eddie didn’t talk much about it, but I thought she might have a problem with alcohol.

The phrase "I thought she might" puts the sentence in the past tense, so the had can be removed. If I remove that phrase, though, the had needs to stay in place:

Eddie didn’t talk much about it, but she had a problem with alcohol.

Remember, we are dealing with spoken words that were written down, not an author's polished work. A writer may have revised the sentence to read something more like this:

Eddie didn’t talk much about it, but I thought she had a drinking problem.

Once again, after the conditional language has been removed, the had is required. Also, just like last time, I can remove the had, particularly with a change in punctuation:

Eddie didn’t talk much about it, but I thought, "She might have a problem with alcohol."

Answer 2

When you say "I thought she might have had a chance to win it." it seems (at least to me) that she's not won! Indeed you've used the PP to stress the result. However, when you say "I thought she might have a chance", it's possible that you're still in the middle of the action, that is not possible or so idiomatic with the PP.

Answer 3

… she might have is present tense. The verb is have. Might is a modal auxiliary verb.

… she might have had is present perfect tense. Had is a past participle. Have is the auxiliary verb for forming the present perfect. Might is a modal auxiliary verb, as before.