## The Hot Hand

Are ‘Lucky Streaks’ Real? Science Says Yes

Maybe you’re not a gambler, but you probably have a grasp of the concept of a “hot hand” or a lucky streak. I’ve wondered before–is this a real phenomenon? My own experience suggests it could be, but one person’s anecdotes are just that. Luck-ily, a new study of online betting shows that the concept of a “hot hand” is real, but perhaps not for the reasons you might expect. The study found that when a person wins a bet, they become increasingly likely to succeed after each win. The converse is also true: Once you lose a bet, you become progressively more likely to keep losing.

The fascinating study looked at 565,915 sports bets made by 776 online gamblers in Europe and the United States, and found that, all things being equal, you’re likely to win or lose 48 percent of the time (draws presumably account for the remaining 4 percent). After a single winning bid, the chance of winning a second goes up ever so slightly to 49 percent. But here’s where things get interesting. After the second win, the chance of winning a third time increases to 57 percent. After that: 67 percent. Following a four-bet winning streak, the chances of scoring a fifth haul increase to 72 percent. The probability of a sixth win is then 75 percent, and finally, after six wins, bettors had a 76 percent chance of notching lucky No. 7.

What the heck is going on here? What probably explains this pattern is that after each win, people selected bets with better odds. Bettors appear to assume that after each win, they were more likely to lose–to regress to the mean, as they say–and so they compensate by making safer bets.

‘Winners worried their good luck was not going to continue, so they selected safer odds. By doing so, they became more likely to win.’
The study, published this month in the journal Cognition, also found that losses can breed more losses. After losing twice, the chances of winning decreased to 40 percent. After four losses, the chance of winning was 27 percent. After six duds, you have only a 23 percent chance of winning. The explanation: after each loss, gamblers on average choose bets that are less likely to turn out, apparently assuming that they are more likely to win than before–and perhaps to make up their losses (although, on average, people gamble less after each loss). As you probably know, bets with a lower chance of winning have higher payouts.

The idea that one is more likely to lose after winning, or more likely to win after losing, is known as the gambler’s fallacy (in reality, all things being equal, one is just as likely to lose or win on any given bet, assuming one is betting on independent events that don’t effect each other’s outcomes, as is the case with the vast majority of sports bets). This stands in contrast to the “hot hand fallacy”: that one is more likely to win while on a hot streak. Bettors apparently don’t generally believe this to be true, or at least their behavior suggests they don’t.

“The result is ironic: Winners worried their good luck was not going to continue, so they selected safer odds,” the researchers wrote. “By doing so, they became more likely to win. The losers expected the luck to turn, so they took riskier odds. However, this made them even more likely to lose. The gamblers’ fallacy created the hot hand.”

The researchers, Juemin Xu and Nigel Harvey at University College, London, conducted the study by examining the online betting activities of people on sports such as horse racing and soccer.

In Popular Science by Douglas Main

Below are the extended notes provided by cognitive psychologist and statistician Barbara Drescher for use in Skepticality Episode 235.  Take a look and leave your comments below. Also, please be sure to listen to the podcast for our own hilarious commentary. Also, visit Barbara’s blog. This phenomenon was discussed on Virtual Skeptics, #90. Listen, watch and enjoy: It’s like Meet the Press, but with chupacabras.

You’re perhaps not understanding what they studied.

They didn’t study something with a consistent bet. It’s more like craps. The subjects were able to choose from among different odds. After winning, people made more conservative bets–bets with better odds of winning (and presumably lower payouts). After losing, people make riskier bets, probably because those bets would pay more if they won.

So, overall, you wouldn’t win more money. You’d just win more often.

Here are links to references John Rael made in the Skepticality episode.

• A new study of online betting shows that the concept of a “hot hand” is real, but perhaps not for the reasons you might expect.
• ‘Winners worried their good luck was not going to continue, so they selected safer odds. By doing so, they became more likely to win.’ The study, published this month in the journalCognition, also found that losses can breed more losses.
• The idea that one is more likely to lose after winning, or more likely to win after losing, is known as the gambler’s fallacy  (in reality, all things being equal, one is just as likely to lose or win on any given bet, assuming one is betting on independent events that don’t affect each other’s outcomes, as is the case with the vast majority of sports bets).

## On The Luck Of The Irish And Taking Probability Personally

Millions of people around the world celebrate the 17th March in a variety of ways – from marching in a parade down Armagh Street in Dublin; dying the Chicago River green; partying in a number of pubs in downtown Reconquista, Argentina – or falling in front of my slow-moving car in central Perth, while wearing a green “St Patrick’s Drinking Club” shirt, Dr Seuss-style emerald hat and drunkenly texting on a phone.

Kylie Sturgess - Credit to Viva Life Photography

Despite the heart-stopping experience of checking on the well-being of craic-chasing pedestrians (who assure me that they’ve got the luck of the leprechauns as they laugh off tomorrow’s bumper-shaped bruises and hangover) – the day is usually a cheering one, filled with goodwill and Guinness Beer. Around 34 million people in the USA lay claim to Irish ancestry; even President Obama boasts of Irish cousins that he’s visited in the past. Cereal hiding lucky charms, the handing out of shamrocks, potential pots of gold at the end of rainbows – no matter where we are in the world, people are generally familiar with the claim that there must be something to the “luck of the Irish”… and I’m not just saying that because I graduated from a university that features a leprechaun as their football mascot.

The study of luck and how it is viewed is a familiar one to students of psychology and an important aspect of studying superstitions. Many of us may be familiar with the phrase “Luck is probability taken personally”, which I’ve read as being attributed to Chip Denman, manager of the Statistics Laboratory at the University of Maryland. So, how personally is luck taken and must it mean that it’s akin to any other “four letter word”? Can you really up the ante when it comes to being a lucky person and improve the statistical likelihood of having the “Luck of the Irish” (so to speak)?