Woman of the Hour marks the directing debut of actor Anna Kendrick, and it shows off a hugely promising knack for character and atmosphere. It seems based on a killer premise (no pun intended), and exploits its story inspiration and broader themes extremely well. If it has a fault – and it does – it is that the potential of this based-on-a-true-story idea is hamstrung by the true story that occurred. It is often said that true stories can be more remarkable than the made-up ones, but in this case the truth squandered a lot of potential.

Kendrick plays Sheryl Bradshaw, an aspiring actress in 1970s Los Angeles. On the recommendation of her agent she reluctantly agrees to appear on the popular game show The Dating Game, despite loathing it and everything it culturally represents. She is asked to choose between three romantic suitors, with her and everyone else unaware that one of them is a serial killer.

Rodney Alcala (played here by Daniel Zovatto) was a real serial killer, and in 1978 actually appeared on The Dating Game opposite the real-life Bradshaw. A year later he was arrested and convicted of five murders – while incarcerated he was conclusively linked to another three. The actual number of victims is likely much, much higher. Woman of the Hour expands its exploration of Alcala’s crimes by including scenes both before and after his game show appearance, and thus adopts a non-linear structure. It is solidly written and insightful, but – and here’s the key problem – fails to link Alcala to Bradshaw, the protagonist, in any close or meaningful fashion. In real terms coming so close to a murderer is terrifying. In narrative terms it is unavoidably unsatisfying.

It is also a deep shame, as the central story of Woman of the Hour does a superb job of surrounding Bradshaw with all manner of sexist and patriarchal monsters: the neighbour (Pete Holmes) that refuses to leave her alone, or the sleazy contestant #2 (Jedidiah Goodacre) whose braggadocio hides some toxic beliefs about women, or even dismissive TV host (Tony Hale) with a slick presentation and brittle ego. By story’s end it is pretty clear that, while abhorrent, the serial killer is just the sharpest edge of an entire patriarchal environment. Kendrick does not identify a solution, but one can hardly imagine there is one. The film may be set in 1978, but the situation hardly seems to have significantly improved.

Ultimately Woman of the Hour is a decent film, but it is also one that has struggled to find a defining through-line in terms of story, character, or theme. It has hit on a winning premise, but failed to find a narrative to match. In many respects it feels like two separate films, one about a woman immersed in micro-aggressions and another that focuses on a serial killer at the expense of his victims (co-star Autumn Best deserved better). The two approaches struggle to fit together, despite strong performances and an impressive directing debut from Kendrick.