Learn English – ‘might be’ vs ‘might have been’

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."

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."

Lost opportunities

The meanings of these are indistinguishable, except for a subtlety that I'll explain later:

We may have been able to save the victims.

We might have been able to save the victims.

The words "would" and "could" suggest both the past tense and the consequence of some imagined hypothesis, with either or both meanings being activated when suitable to the context. To use "would" here, you need to establish an imagined hypothesis. Then "would" indicates the consequence:

If only we had the antidote yesterday! We would have been able to save the victims.

It's possible to say "could have been able to", but "could" is the past tense of "can", so it already indicates ability. So, "could have been able to save the victims" is awkward. However, you could say:

If only we had the antidote yesterday! We could have saved the victims.

"Would have" and "could have" imply that the opportunity is now lost.

"May have", "might have", and "could have" don't require context to set up an imaginary hypothesis, but they do suggest that you have such a hypothesis in mind:

"We might have been able to save the victims."

"How?"

"The most recent antidote has been sitting in the refrigerator since yesterday."

"What? And no one tested it?"

An important difference

A very big difference between the may/might and would/could sentences is that the would/could sentences claim a high level of certainty about the hypothetical situation: the antidote is assumed to work. The may/might sentences lack that certainty. They suggest only that in the hypothetical situation (which might not even be stated yet), the antidote might have worked. "Would" corresponds to "will", and says that the antidote will work (in the imagined situation, which occurred yesterday). "Could" corresponds to "can", and suggests that the antidote can work (in the imagined situation, which occurred yesterday).

A subtle difference

"May have" mainly indicates uncertainty about what we could have done. "Might have" suggests both uncertainty and that the opportunity, if it even existed, is now lost.

This is English, so don't take that as a rule. Instead, memorize this well-known couplet (by John Greenleaf Whittier, 1856):

For of all sad words of tongue or pen,

The saddest are these: "It might have been!"

One more power of might

There's one more possibility with "might", which illustrates the flexibility of these words. "Might" can suggest that the victims actually were saved, or are actually in the process of being saved:

We might have been able to save the victims. I just read an article in a medical journal, which says that the antidote we tried yesterday was proven to work on mice in a recent experiment.

In other words, the antidote we tried yesterday might be working, right now. Since the uncertainty of the word "might" applies to our ability to save the victims, if we had that ability yesterday, then our efforts yesterday were successful, or are on the way to succeeding. Currently, we don't know (that's the uncertainty of "might"). Obviously, your listener will hear this meaning only if the victims are still alive.

You can also do this with "may have" and "could have", but those don't make the pun in the title of this section. Since "may have" has the least connotation of lost opportunity, it provides the clearest way to express optimistic uncertainty about the effects of yesterday's action: "We may have saved the victims."