ところを見ると details
Examples
judging from the fact that X — the speaker infers from something observed on the spot; the main clause is always a conjecture, never a flat assertion
電気が消えてるところを見ると、もう寝ちゃったのかな。
denki ga kieteru tokoro o miru to, mou nechatta no kana.
Going by the lights being out, I'd guess he's gone to bed already. casual
誰も文句を言わないところを見ると、この案で問題ないのだろう。
dare mo monku o iwanai tokoro o miru to, kono an de mondai nai no darou.
Judging from the fact that nobody is objecting, this proposal must be fine. neutral
出席者が半数に満たないところを見ると、周知が行き届いていなかったものと思われます。
shussekisha ga hansuu ni mitanai tokoro o miru to, shuuchi ga yukitodoite inakatta mono to omowaremasu.
Given that fewer than half attended, word evidently did not get around. formal
Formation
plain clause + ところを見るとattaches to plain clause
Notes
End it flat instead (〜ところを見ると、寝た) and the sentence reverts to
the literal "when I saw him…".
Related patterns
Similar
からすると takes a bare NOUN and is happy with abstract evidence the speaker never witnessed (統計からすると); ところを見ると takes a whole CLAUSE, and that clause has to report something observed on the spot (電気が消えているところを見ると) — ×統計ところを見ると has no frame to sit in, and からすると can only reach a clause via 〜ことからすると.
Lookalikes
The same ところ, and 〜ところを見る is also a perfectly literal sentence — 食べているところを見た is "I saw him in the act of eating", ところ as the phase of an action and 見る as an ordinary verb; the inferential reading needs both the と and a conjectural tail, so 食べているところを見ると、もう帰ってきたらしい infers rather than reports watching.