If someone gives you a present, you might exclaim either:
- How would you have known it was my birthday?!
- How could you have known it was my birthday?!
There is probable agreement among English speakers that "how+could" is the more fitting pair when there is something unlikely to happen--that did happen--and you are expressing surprise about it.
Consider:
- I don't know how the killer would have known the key code, but he did!
- I don't know how the killer could have known the key code, but he did!
My preference is for "could" as a more natural way of conveying surprise about the improbable event that happened. To my eyes it's more congruous with "...but he did!"
By corollary, this case:
- I don't know how the killer would have known the key code, so he must not have!
- I don't know how the killer could have known the key code, so he must not have!
I'm not sure if there's much to remark on the difference. What if the alliteration of "killer could" was reversed?
- I don't know how the walrus would have known the key code, so he must not have!
- I don't know how the walrus could have known the key code, so he must not have!
It seems less a clear winner, in any case. :-)
Tom is the best expert ...
Assertion of a fact. Where there are agreed criteria then there's no need to hedge an statement.
Djokavic is the current number one male tennis player in the world
When criteria are less certain, or we ourselves are not sure of our facts, or we wish to be modest by appearing to be uncertain of our facts we may use I think
I think Djokavic is the best male tennis played of all time
I think that the population of the UK is 50 million (actually 65 million)
This formulation implies that we are open to correction and discussion
Adding would softens this further, emphasises that we are uncertain
I would think that the population of the UK is greater than 50 million
The I would have thought formulation is normally used in a context where some information has recently been given. Depending upon the context it may imply that we are actually contradicting the information, or that we are expressing surprised acceptance.
I think Tendulakar is the best batsman of all time
I would have thought Bradman had a better record
that was disagreeing, suggesting that by some criteria Bradman is better
The current UK population is 65 million
Oh, I would have thought it was only 50 million
but now I've changed my opinion (this implied but not said)
that was agreeing, I thought it was 50 million, but I accept your statement of 60 million is correct. We could just say
Oh, I thought it was only 50 million
With pretty much the same meaning, the slight difference being that the second case implies it was actively in my mind, whereas the would form could imply that I hadn't really formed a solid opinion until now, but I would probably have guessed 50 million.
As your comment indicates we are indeed into shades of meaning and idioms. In these cases the tone of voice will often differentiate the meaning.
I would have thought Bradman had a better record
Would probably said with a questioning or challenging tone and raised eyebrow.
Best Answer
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:
That version seems grammatical, too.
Essentially, the speaker is saying:
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,
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:
The same holds for your first example:
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:
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:
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: