Everybody loves a winner. But two British researchers have published a host of mathematical reasons why those at the top shouldn't be admired so much and why trying to imitate them rarely works. It's all because exceptional performance rarely comes from exceptional skill. Instead it tends to come from exceptional circumstances, often luck.

This may sound like sour grapes and class warfare. But it's based on solid math.

High performers, people just below the top, are often more skilled than those at the very top.

In one study, five million subjects played a 50-round game where each round was a success or a failure. The game was set up so that success in one round made success in the next round more likely, while failure in one round made failure in the next round more likely, what the researchers called get rich quick dynamics. Each player drew a specific skill rating and dependency (how much one round affected the next) before the game started, so the researchers could tell just how much skill affected outcome.

The results? People with 50 successes were not the most skilled. The most skilled tended to average about 40 successes. After that, skill level dropped as the number of successes rose.

The researchers liken this to the story of Bill Gates' success. Gates is often said to be the richest man in the world. And while they don't deny his talent, they claim what elevated him from merely being successful to the top was circumstances, including his mother's social connections with IBM's chairman, which allowed Gates to gain an initial contract with the PC company, generating a lock-in effect that was a crucial step in Gate's success, much as success in the early rounds of the researchers' game was a crucial step on the road to 50 successes. Take away the initial boost Gates' got from his mother and other early boosts and he probably never gets to 50.

Try to imitate Bill Gates and you're unlikely to get the same results unless you can imitate his circumstances, too. This also applies to business books, courses and gurus that aim to teach you how to go from good to great by learning from the experts.

Unless you can separate out the noise (luck) from the skill, top performance is not an indication of topnotch skill. High performers, people just below the top, are often more skilled than those at the very top.

This has many social implications, from setting CEO salaries to deciding who's a proper role model or worthy of admiration to determining the top national tax rate.

It's not a plea for mediocrity, just a recognition that those at the very top are rarely any better than those in the tier just below. Sometimes they're a lot worse. Enron was once a highly admired business model. Today it's an epithet.

Even baseball is full of examples. Baltimore Oriole and Chicago Cub fans are all too familiar with the names Jeffrey Maier and Steve Bartman, two fans who played a major role in determining the World Series winners of 1996 and 2003. Ultimately, it was the Yankees and Marlins who were greeted as champions at the White House those two years. But they couldn't have gotten there without a little luck.

People at the top should remember how they got there. And so should their fans.

An article on the study appears in the Proceedings of the National Academy of Sciences (PNAS).