And yet, instead of dismissing VaR as worthless, most of the experts I talked to defended it. The issue, it seemed to me, was less what VaR did and did not do, but how you thought about it. Taleb says that because VaR didn’t measure the 1 percent, it was worse than useless — it was downright harmful. But most of the risk experts said there was a great deal to be said for being able to manage risk 99 percent of the time, however imperfectly, even though it meant you couldn’t account for the last 1 percent.

“If you say that all risk is unknowable,” Gregg Berman said, “you don’t have the basis of any sort of a bet or a trade. You cannot buy and sell anything unless you have some idea of the expectation of how it will move.” In other words, if you spend all your time thinking about black swans, you’ll be so risk averse you’ll never do a trade. Brown put it this way: “NT” — that is how he refers to Nassim Nicholas Taleb — “says that 1 percent will dominate your outcomes. I think the other 99 percent does matter. There are things you can do to control your risk. To not use VaR is to say that I won’t care about the 99 percent, in which case you won’t have a business. That is true even though you know the fate of the firm is going to be determined by some huge event. When you think about disasters, all you can rely on is the disasters of the past. And yet you know that it will be different in the future. How do you plan for that?”

One risk-model critic, Richard Bookstaber, a hedge-fund risk manager and author of “A Demon of Our Own Design,” ranted about VaR for a half-hour over dinner one night. Then he finally said, “If you put a gun to my head and asked me what my firm’s risk was, I would use VaR.” VaR may have been a flawed number, but it was the best number anyone had come up with.

Of course, the experts I was speaking to were, well, experts. They had a deep understanding of risk modeling and all its inherent limitations. They thought about it all the time. Brown even thought VaR was good when the numbers seemed “off,” or when it started to “miss” on a regular basis — it either meant that there was something wrong with the way VaR was being calculated, or it meant the market was no longer acting “normally.” Either way, he said, it told you something useful.

“When I teach it,” Christopher Donohue, the managing director of the research group at the Global Association of Risk Professionals, said, “I immediately go into the shortcomings. You can’t calculate a VaR number and think you know everything you need. On a day-to-day basis I don’t care so much that the VaR is 42. I care about where it was yesterday and where it is going tomorrow. What direction is the risk going?” Then he added, “That is probably another danger: because we put a dollar number to it, they attach a meaning to it.”

By “they,” Donohue meant everyone who wasn’t a risk manager or a risk expert. There were the investors who saw the VaR numbers in the annual reports but didn’t pay them the least bit of attention. There were the regulators who slept soundly in the knowledge that, thanks to VaR, they had the whole risk thing under control. There were the boards who heard a VaR number once or twice a year and thought it sounded good. There were chief executives like O’Neal and Prince. There was everyone, really, who, over time, forgot that the VaR number was only meant to describe what happened 99 percent of the time. That $50 million wasn’t just the most you could lose 99 percent of the time. It was the least you could lose 1 percent of the time. In the bubble, with easy profits being made and risk having been transformed into mathematical conceit, the real meaning of risk had been forgotten. Instead of scrutinizing VaR for signs of impending trouble, they took comfort in a number and doubled down, putting more money at risk in the expectation of bigger gains. “It has to do with the human condition,” said one former risk manager. “People like to have one number they can believe in.”

Brown told me: “You absolutely could see it coming. You could see the risks rising. However, in the two years before the crisis hit, instead of preparing for it, the opposite took place to an extreme degree. The real trouble we got into today is because of things that took place in the two years before, when the risk measures were saying that things were getting bad.”