A battle of the backrooms: old, grey matron takes on snappy western upstart for sorting supremacy, down to the last Dewey decimal.

On Tuesday, Salvatore Magaddino will crank up the “Rocky” theme song and deliver a pep talk. His crew will then have one hour to defend the city’s title as home to “the world’s fastest library-sorting system” (at least according to the trophy) and to break its 2-2 tie with a squad from the King County Library System, which serves the area around Seattle.

“The adrenaline is outta control,” Mr. Magaddino said.

Mr. Magaddino, a former captain in the New York Police Department, once investigated major crimes and coordinated security for the World Series. Now that he is deputy director of BookOps, a 191-person unit, his job includes finding high-tech ways to manage old-fashioned materials.

Mechanized sorters like New York’s are relatively rare in the library universe. Seattle, hometown of Amazon, had the first.

They call it the Tin Man.

Anthony Miranda is manager of materials distribution services for the King County system, one of the country’s busiest. Last year, 21 million items circulated through its 48 branches. (The Seattle Public Library, which serves the city, is a separate system.)...