Our culture is needlessly obsessed with declaring ultimate champions — in sports, where it’s an appropriately objective measure, but in everything else now, too. We are constantly keeping score. We rank, list and wager over any activity that can produce a winner or a loser, to our collective detriment.

This urge finally came calling, inevitably and sort of sadly, for the friendliest of all modern competitions: the long-running TV game show “Jeopardy!,” which ABC took to prime time over the last week to determine, from a group of its winningest contestants, the rightful holder of the title “Greatest of All Time” — or GOAT, in overused lingo.

Tuesday night’s episode (the fourth round of special episodes that began last week) ended with Ken Jennings claiming the trophy and the $1 million prize — correctly responding “Who is Iago?” to the answer requiring the name of a non-titular character in Shakespeare’s tragedies who gave the most speeches.

Jennings’s nearly sweatless performance reminded fans of his preternatural ability to still win at “Jeopardy!” 15 years after he first made history on the show with a 74-game streak. The 45-year-old author, podcaster and general smarty-pants online influencer defeated his nearest competitors, James Holzhauer and Brad Rutter.

It was exciting stuff. ABC hyped up the stakes, not for the money but for the glory of it all. Those ­of us who long ago gave up the dinner-hour habit of watching “Jeopardy!” each weekday evening (or who never truly acquired it) could once again admire the show’s purest pleasures: difficult facts, across a breadth of knowledge, answered in the form of questions, as quickly as humanly possible, as politely as anyone behaves anymore.

The prime-time specials also offered the welcome opportunity to once more marvel at the unflappable composure of the show’s host of 35 years and counting, Alex Trebek, who continues to battle pancreatic cancer and proves each day that he was born to do this job.

Trebek’s viewers long ago realized that he is more to them than just a game-show host. Their devotion, and their need to see him on their screens, has transcended the usual boundaries of the format. If ever there was a time to declare a GOAT, it would be now, while Trebek can be the one to declare it, reading the answers so we at home can shout out the questions.

What is “The Fairy Queen”? What is Palm Beach? Who is Edward Jenner? Who is Edvard Munch? Who is Imhotep? What is a stethoscope? What is tarnish? Who is Adam Smith? What is cedar? What is Biafra? Who is Courtney Love? Who is Diane Arbus? What is “Combat Rock”?

As for those questions-as-­answers, they didn’t seem any more or less challenging than any episode of “Jeopardy!” that came before. We all know someone who could answer them quite handily (maybe that someone is you), but, in our years of playing “Jeopardy!” at home, we have at least learned there’s a big difference between sitting in the recliner and being on the show’s set, clicking madly while keeping calm.

As Rutter fell further behind each night, Jennings and Holzhauer dazzled viewers with their knowledge and speed — intensified by Jennings’s ability to keep up with the unnerving way Holzhauer, a professional gambler, treats “Jeopardy!” like a numbers game.

Now that Jennings is indeed the Greatest of All Time, does “Jeopardy!” change? Do its viewers? Probably not — it’s nearly a meaningless distinction, and there will never be a reason to stop playing. But what we have done is drag another of our shared institutions into the space reserved for more-serious showdowns, where it doesn’t belong.

Elsewhere, we carp, battle and grind one another down for bragging rights and total triumph. Sports culture and champion-making have seeped into nearly every aspect of life. It’s all just a little (or a lot) more elbowy and contentious — primary campaigns, award show nominations, lists of the decade’s best albums.

Most ruinously, America’s ultimate-throwdown mentality took over political leadership, where the most benign decisions are now treated as partisan deathmatches between the red team and the blue team.

“Jeopardy!” didn’t need to go there, but in so doing, it at least kept its manners and mood in check. GOAT or not, Jennings is a suitable wearer of such a crown — self-effacing, self-assured, good on TV. It’s too soon and probably too indecorous to speak of it, but perhaps “Jeopardy’s!” quest for its all-time champion produced something else instead: its next host?