Efforts to screen high-definition broadcasts of Broadway shows in movie theaters have been random, halting and frustrating. Yet, in little more than a month, a filmed-live version of the recent Broadway production of “Of Mice and Men” came together and, beginning in November, will be beamed into about 1,400 theaters around the world.

It required an unlikely series of coincidences and a measure of sheer doggedness: a seemingly offhand comment to the lead producer from the play’s star James Franco; a long-shot phone call to an executive with the National Theater of London; a race against a forbidding deadline to secure union agreements; and an extremely rare decision by the creative team to stick around past the end of the run.

“Of Mice and Men” represents the first Broadway offering from the successful National Theater Live series, which, to date, has featured marquee events in British theater. Arriving in the same season as the announcement of a joint venture between Broadway Worldwide, a production company, and a Chinese entertainment and media conglomerate to capture live-in-performance Broadway musicals, it could augur a boost in HD broadcasts of commercial theater.

The National Theater, the Royal Opera, the Bolshoi and, most successfully, the Metropolitan Opera have heavily marketed HD broadcasts, earning money and attracting international audiences along the way. But Broadway offerings have been few, the most notable being “Memphis” and “Jekyll and Hyde,” largely because separate deals need to be cut with various unions and members of the creative team.