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I was speaking to a parent's friend at dinner, and when he asked me a question I replied by saying:

正しく推測しました

to which he then corrected me by saying that the correct response would have been

正しく推測していました

because my version would be interpreted as "I guessed correctly" rather than the second version which would be "(someone who is not the speaker) guessed correctly".

I tried to do more research regarding the uses of 〜ている when referring to third parties, but the closest thing I've found to an answer is the usage of 言っていた (reported speech) and outside that, I don't think I've seen any mentions of this function of 〜ている before. Could someone explain this to me? Is it always a must to use the 〜ている form of a verb when describing something someone else did when the topic is omitted?

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First of all, I would never say either 正しく推測しました or 正しく推測していました under any circumstances. They sound very odd.

If I have to use the word 推測, I would use it as a noun.

推測が正しかったです。

You can use の to specify whose guess it was, and it can be anyone.

(私/あなた/彼の)推測が正しかったです。

If I have to use 推測 in its verb form, I would still nominalize it with こと.

  1. (私/あなた/彼の)推測したことが正しかったです。
  2. (私/あなた/彼の)推測していたことが正しかったです。

(正しかった can be replaced with 正しい but let’s leave it aside in this discussion.)

In everyday conversation, it is more common to use a plainer verb like 思う.

  1. (私/あなた/彼の)思ったことが正しかったです。
  2. (私/あなた/彼の)思っていたことが正しかったです。

These two are different in that the former describes a change of state of mind that happened at one point of time, while the latter refers to a state of mind that lasted for some period. This difference is not that important when you are talking about yourself. However, since you cannot tell when exactly some change occurred to another person’s inner state (unless they express it somehow), the first form is not usually used for anyone other than the speaker.

The same difference applies when a verb is used as the predicate.

  1. そう(だろうと)思いました。
  2. そう(だろうと)思っていました。

Both are good if you are talking about yourself, while only the second is appropriate if you are talking about a third person, except in a novel or a voice-over where the narrator describes the state of mind of a character objectively. One thing you need to be careful with here is that neither sentence is appropriate if you are talking about the second person. This is for a different reason than what we have discussed so far: you don’t tell someone what they thought as if you know better.

It is OK to ask that person using either form.

  1. そう(だろうと)思いましたか。
  2. そう(だろうと)思っていましたか。
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First, let's not use 推測 ("to conjecture") casually in a daily conversation unless you want to speak like a mad scientist or a robot in an 80's movie. It's a stiff technical word.

Next, the implied subject will always be inferred from the context. Generally speaking, 正しく推測しました can be about a third person, and 正しく推測していました can be about the first person ("I"). Without understanding the entire flow of the conversation, I cannot tell why someone explained to you like that. Still, 推測しました tends to refer to something that just happened, while 推測していました tends to refer to a guess made in the past. If someone ("you", "I" or "he") made some guess in the past and it turned out to be correct just now, one may say 正しく推測していた (or more casually 当たって(い)た or 正しかった), but not 正しく推測した.

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