SHANGHAI—The definition of a China “bull” used to be those who saw the Chinese economy rushing full speed ahead into the distant future.

Their vision wasn’t so far-fetched. Remember: Annual growth was still hitting double digits until 2010. As recently as 2014, Justin Lin Yifu, a former World Bank chief economist, was publicly confident that growth could roll along at 8% a year for another 20 years, with the right mix of economic overhauls to oil the wheels.

The minority “bear” proposition was for a severe slowdown, somewhere in the mid-to-low single digits. An even rarer breed of “permabears” warned of collapse.

How quickly calculations have changed. We haven’t yet reached the point where the former bear case has become the bull case, but we’re getting close.

At a recent workshop hosted by the Council on Foreign Relations, a nonpartisan U.S. think tank, participants—35 or so academic economists, Wall Street professionals and geopolitical strategists—lined up around three different growth scenarios for China. Only 31% chose the optimistic one, defined as 4% to 6% annual growth, dependent on leaders successfully implementing reforms; 61% foresaw a “lost decade” of 1% to 3% growth; the rest thought a so-called hard-landing, or contraction, was most likely.

Of course it wasn’t a scientific survey, but what’s interesting is that apparently nobody considered the possibility that the Chinese government could deliver on its promise of “medium to fast” growth, meaning 6.5% or higher.

If the old-style bulls are virtually extinct as a species, a major reason is widespread skepticism that the Chinese leadership under President Xi Jinping is focused on economic transformation.

Instead, Mr. Xi’s attention seems to be fixated on his anticorruption drive, cracking down on internal dissent, bringing the media to heel, firming up his control over the security forces and challenging the U.S. for dominance in the South China Sea.

Ironically, those predicting a hard landing in the Council on Foreign Relations workshop might have had the best rationale for optimism. Michael Levi, a council fellow and one of the organizers, says this crowd thought that the economy hitting rock-bottom would galvanize the leadership into action and that China would “come out better on the other side.”

All this matters because, as former U.S. Treasury Secretary Larry Summers wrote recently, China for the first time in centuries “affects the global economy as much as it is affected by the global economy.” Mr. Summers thinks that after decades of extraordinary growth China will inevitably experience a “reversion to the mean.” In other words, it will become merely average, crawling ahead at around 2% along with its peers.

Beijing itself has targeted 6.5% to 7% growth this year after claiming 6.9% expansion last year—an almost certainly inflated figure, according to economists, even as it was the slowest in a quarter century.

Now, having absorbed the shock of a collapse in global commodity and energy prices linked to China’s slowdown, everyone from Wall Street hedge funds to international lending agencies and multinational businesses are trying to figure out the effects on the world when—not if—Chinese growth downshifts further.

The International Monetary Fund, which has been steadily revising lower its China forecasts, sees growth slipping to 6% next year.

On one level, a cooling economy is a blessing; China can no longer live with the damage to the environment and human health that comes from its old pattern of high-speed development spearheaded by heavy industry and manufacturing. Nor can it afford the continued rapid buildup of corporate debt to keep that economic model going.

And as economists keep pointing out, even modest growth in a $10 trillion economy—the world’s second largest—packs a big punch. China now delivers about one-third of global growth.

A critical question, though, is whether Beijing can manage the slowdown that is accompanying its transition to services and consumption-led growth without a crisis of some kind that could tip an already fragile global economy into recession.

Janet Yellen, the Chairwoman of the U.S. Federal Reserve, is among those clearly worried. In making the case for slower interest-rate increases, she has specifically cited the dangers posed by China’s fading growth.

Other American think-tanks are equally concerned. Although continued sluggish growth is still the most likely scenario “the world can no longer ignore the risk of a hard landing,” write Matthew P. Goodman, David A. Parker, and Daniel Remler of the Center for Strategic and International Studies.

Amid political tensions in China, they add, “the safest bet is that growth in the world’s second-largest economy will continue to disappoint.”

In the West, at least, pessimism about China’s outlook has become the mainstream sentiment. Or as Mr. Levi of the Council on Foreign Relations says, 4%-6% growth has become “code for doing well.”

The bears have come in from the cold. And the growling of the permabears keeps Ms. Yellen and other central bankers awake at night.