SAN FRANCISCO — How crazy is the money sloshing around in start-up land right now?It’s so crazy that more than 900 tech start-ups are each worth more than $1 billion. In 2015, 80 seemed like a lot.It’s so crazy that hot start-ups no longer have to pitch investors for money. The investors are the ones pitching them.It’s so crazy that founders can start raising money on a Friday afternoon and have a deal closed by Sunday night.It’s so crazy that even sports metaphors fall short.“It’s not like one jump ball — it’s 10,000 jump balls at once,” said Roy Bahat, an investor with Bloomberg Beta, the start-up investment arm of Bloomberg. “You don’t even know which way to look, it’s all just wild.” He now carves out two hours a day for whatever “emergency deal of the day” pops up.The funding frenzy follows nearly two years of a pandemic when people and businesses increasingly relied on tech, creating bottomless opportunities for start-ups to exploit. It follows breakthroughs in artificial intelligence, nuclear technology, electric vehicles, space travel and other areas that investors say are poised to change the world. And it follows nearly a decade in which tech companies have dominated the stock market.The activity has crossed into even frothier territory in recent months, as tech start-ups offering food delivery, remote-work software and telehealth services realized that they not only would survive the pandemic but were in higher demand than ever. The money hit a fever pitch in the final months of 2021 as investors chased a limited pool of start-ups and as tech stocks like Apple, which topped a valuation of $3 trillion, reached new heights.When Roy Bahat, left, an investor with Bloomberg Beta, thought past tech bubbles would burst, “every single time it’s become the new normal,” he said.Andrew Spear for The New York TimesThe result is a booming ecosystem of highly valued, cash-rich start-ups in Silicon Valley and beyond that are expanding at breakneck speed and trying to unseat stalwart companies in all kinds of fields. Few in the industry see a limit to the growth.“The pot of gold at the end of the rainbow has become bigger than ever,” said Mike Ghaffary, an investor at Canvas Ventures. “You can invest in a company that could one day be a trillion-dollar company.”Astonishing data for 2021 tell the story. U.S. start-ups raised $330 billion, nearly double 2020’s record haul of $167 billion, according to PitchBook, which tracks private financing. More tech start-ups crossed the $1 billion valuation threshold than in the previous five years combined. The median amount of money raised for very young start-ups taking on their first major round of funding grew 30 percent, according to Crunchbase. And the value of start-up exits — a sale or public offering — spiked to $774 billion, nearly tripling the prior year’s returns, according to PitchBook.The big-money headlines have carried into this year. Over a few days this month, three private start-ups hit eye-popping valuations: Miro, a digital whiteboard company, was valued at $17.75 billion; Checkout.com, a payments company, was valued at $40 billion; and OpenSea, a 90-person start-up that lets people buy and sell nonfungible tokens, known as NFTs, was valued at $13.3 billion.Investors announced big hauls, too. Andreessen Horowitz, a venture capital firm, said it had raised $9 billion in new funds. Khosla Ventures and Kleiner Perkins, two other venture firms, each raised nearly $2 billion.The good times have been so good that warnings of a pullback inevitably bubble up. Rising interest rates, expected later this year, and uncertainty over the Omicron variant of the coronavirus have deflated tech stock prices. Shares of start-ups that went public through special purpose acquisition vehicles last year have slumped. One of the first start-up initial public offerings expected this year was postponed by Justworks, a provider of human resources software, which cited market conditions. The price of Bitcoin has sunk nearly 40 percent since its peak in November.But start-up investors said that had not yet affected funding for private companies. “I don’t know if I’ve ever seen a more competitive market,” said Ambar Bhattacharyya, an investor at Maverick Ventures.Even if things slow down momentarily, investors said, the big picture looks the same. Past moments of outrageous deal making — from Facebook’s acquisitions of Instagram and WhatsApp to the soaring private market valuations of start-ups like Uber and WeWork — have prompted heated debates about a tech bubble for the last decade. Each time, Mr. Bahat said, he thought the frenzy would eventually return to normal.Instead, he said, “every single time it’s become the new normal.”Investors and founders have adopted a seize-the-day mentality, believing the pandemic created a once-in-a-lifetime opportunity to shake things up. Phil Libin, an entrepreneur and investor, said the pandemic had changed every aspect of society so much that start-ups were accomplishing five years of progress in one year.“The basic fabric of the world is up for grabs,” he said, calling this time “the changiest the world has ever been.” In mid-2020, he started Mmhmm, a video communication provider for remote workers, and has landed $136 million in funding. Mr. Libin said he heard from interested investors a few times a week.Phil Libin has attracted $136 million in funding for Mmhmm, the video communication service he founded.Andrej Sokolow/picture alliance, via Getty ImagesIn less frothy times, young, fast-growing tech companies sought new investment every 18 months. Now they are re-upping multiple times a year.For Daniel Perez, a co-founder of Hinge Health, a provider of online physical therapy programs, the unsolicited emails from investors started in late 2020. They contained pitch decks packed with the elaborate research that the investment firms had done on Hinge, including interviews with dozens of its customers and data on its competitors.These “reverse pitches,” which numbered in the 20s, were meant to persuade Mr. Perez to take money from the investment firms. He also got several term sheets, or investment contracts, from investors he had never met before.“Often when we’re speaking to investors, they’d cut me off and say, ‘Let me show you what I already know about you,’” Mr. Perez said. The reverse pitch from Tiger Global, the firm that Hinge picked to help lead a $300 million funding round alongside the investment firm Coatue Management last January, was 90 pages.A few months after Hinge announced that funding, the reverse pitches started rolling in again. Three different investors sent Mr. Perez videos from celebrities they had hired on Cameo to make their case. One was from Andrei Kirilenko, a former Utah Jazz player whom Mr. Perez was a fan of.“It was a constant drumbeat that got a bit more feverish,” Ms. Perez said. In October, Hinge raised another $600 million led by Coatue and Tiger.Mr. Bhattacharyya said this kind of “pre-work” had become table stakes for firms looking to land a hot investment. The goal is to pre-empt the company’s formal fund-raising process and show how excited the firm is about the start-up, while possibly sharing some useful data.“It’s part of the selling process,” he said.Vijay Tella, founder of Workato, an automation software start-up in Mountain View, Calif., said the dossiers sent by prospective investors during his company’s latest round of funding in November were so elaborate that one firm had interviewed 30 of Workato’s customers. Afterward, Mr. Tella worried that his customers had been spammed by prospective investors and even apologized to some.Workato, which raised $310 million across two rounds of funding last year and is valued at $5.7 billion, is not currently seeking more money. But, Mr. Tella said, “I would bet right now that those calls are still happening.” More