Q. Would “Depending on” count as a dangler in “Depending on the weather, the play will be performed outdoors”? If not, why not?
A. We don’t think that’s a true dangler. It is a bit dangly looking; the play itself doesn’t depend on the weather—as a literal reading might suggest.
But consider that the introductory phrase is a sort of idiomatic shorthand for “Depending on how the weather turns out.” Idioms are expressions that are generally understood but don’t necessarily stand up to grammatical analysis. A true dangler is more likely to occur when the participial phrase has a more direct connection to the rest of the sentence:
Acting in the rain, the play showcased the resilience of the performers.
In that sentence, “Acting in the rain” appears (illogically) to modify the play directly rather than the performers. To fix this, rewrite: “Acting in the rain, the play’s performers displayed their resilience.” For more examples, see CMOS 5.115.