It is character, however, not plot, that's at the heart of the proceedings. With collaborators like McDormand and costars Woody Harrelson and Sam Rockwell, McDonagh presents a film full of individuals who are so intensely imagined, and finely written, that they are simultaneously more extreme and more nuanced than we will be expecting.
In its verve, its flair and its precision, it's McDonagh's writing that makes all that possible, and using actors who often have worked with him before and directing his own work ensures there will be no slip-ups.
"By the time one of my scripts goes into production, I've been sitting with it for seven years, and every one of those lines is carefully chosen," McDonagh told Moviemaker Magazine. "If you signed on to do my script, you're doing my script, and that's the end of it."
Getting all the best lines as the film's furious and ferocious prime mover, the woman who put the billboards up and doesn't care who knows it, is grieving mother Mildred Hayes.
Played with convincing and uncompromising fierceness by McDormand, Hayes has been almost literally driven mad by her daughter Angela's unimaginably brutal death several months earlier as well as the local police's inability to come up with a suspect.
In a more conventional film, the police chief called out in those billboards would be Villain No. 1.
A terror both holy and unholy, a hardcore obsessive and unapologetic about it, Hayes pays for the billboards not so much with any specific purpose but because her daughter's fate has so taken over her mind that she can't think about anything else, not even what all this is doing to her son, Robbie (Lucas Hedges).
In a more conventional film, the police chief called out in those billboards would be Villain No. 1, but Harrelson's Chief Bill Willoughby, starched uniform and all, might be the most sane and reasonable person in the entire movie.
Not only does he have reasons why no suspects have been found, not only is he a fine husband and father (Abbie Cornish plays his wife), but he has a serious problem of his own to deal with.
This is not to say that all members of Ebbing's police force are men of similar mettle. Oh no. Look no further than Dixon, the chief's right hand (McDonagh veteran Sam Rockwell), to find an officer who is a racist hothead and small-minded momma's boy as well as an unswerving advocate of police brutality.