One of the worst things that can happen when you’re watching a movie is when you just don’t believe a chance event, and your suspension of disbelief is knocked out of the window. You’re no longer being swept along by the story and you’re suddenly acutely aware that someone wrote that distracting moment you just witnessed.
If you’re a screenwriter, moments like that don’t just spoil the fun of the movie, they also make you wonder if you aren’t guilty of the same sin in your own writing.
It’s not that coincidence doesn’t work in movies, but you need to be aware of when you’re using coincidence as an integral part of the story rather than merely for convenience’s sake. Which is not as straightforward as it sounds. I’ve had discussions with my writing partner about events which to me seem ludicrously coincidental, whereas to him they seem like the kind of thing that “could happen.” And vice versa. To some extent it’s subjective, but there are some objective criteria:
Does the coincidence fit with the story world? It’s one thing for Charles Dickens to have characters bump into each other just in time to move the plot forward, but does it work in your screenplay? Different genres deal differently with coincidence too. In a comedy caper, a chance meeting with someone from a previous scene in a completely different context can be hilarious whereas the same event will feel contrived in a thriller.
Is it something you’ve experienced yourself or has it happened to someone you know? How many times have you bumped into a significant person in the rush hour bustle at a crowded railway station or at a busy airport terminal? How many times have you used your spouse’s/child’s mobile and forgotten to delete a revealing text message? What about going shopping to chase away post-divorce blues and being tapped on the shoulder by a former lover who emigrated to the other side of the world twenty years ago?
Does the coincidence harm your main character or help them? Generally, you have less credibility when it helps them (whatever that says about how our brains work). It feels like a cop-out, like the character is being let off the hook. Whereas if it makes things worse for them… the raised stakes can sometimes distract your attention from the coincidence. Sometimes.
Is the coincidence a pay-off of something that was set up in an earlier scene? If the coincidence is the result of something hinted at or established earlier in the script, it can feel less like a coincidence, even though it still is. If it comes right out of the blue, the same event can feel terribly contrived.
Is coincidence an integral part of your story’s theme? A movie like Magnolia can take liberties with coincidence because it’s part and parcel of what the film is exploring.
Some writers keep coincidence journals, noting down chance events that happen to them which seem somehow significant. Not a bad idea, I guess, even just to sharpen your sense of what you think qualifies as believable. And paying more attention to the phenomenon increases the likelihood of noticing coincidences when they occur.
In any case, I think coincidence as a tool in a screenplay should be handled with great care and integrity. For your own sake, if nothing else. After all, the last thing you want to do is throw a glass of cold water in the reader's/audience’s face and jolt them out of your story.