Sports fans have cried foul for 25 years as scientists have dumped statistical ice water on basketball players’ “hot hands.” It seems obvious to even casual spectators that competitors occasionally score a bunch of baskets in a row and need to keep shooting while they’re in the zone.
Sorry, b-ball buffs. Researchers have yet to document any chance-defying scoring runs among even the best players. Kobe Bryant may well sink shot after shot, game in and game out, but even this all-star’s season-long pattern of hits and misses fits within the mathematical definition of a random sequence, scientists say. Kobe’s chances of hitting a shot are no greater following a swish than a miss.
Still, it’s perfectly natural to assume that if a sharpshooter sinks one basket — or if a jockey rides a winning horse in the first race of the day, or if a stock goes up in value on Monday, to name a few — it boosts the probability of the same thing happening with the next shot, race or trading session, says psychologist Benjamin Scheibehenne of the University of Basel in Switzerland. In his view, effective thinkers are primed to expect streaks of the same outcome in basketball scoring and other sequences of events — the laws of probability be damned.
A hair-trigger sensitivity for perceiving clumps of events makes sense because most animal species — including people — search for food and other vital resources that are typically found in patches, he asserts. Human ancestors did so. And in the modern world, information foragers on the Internet and snack seekers in the supermarket also find what they want in clusters. So a tendency to look for clumpy patterns in sequences of events pays off when it counts, even if it distorts judgments about basketball scoring and the stock market.
“People seem to be tuned in to detecting streaky patterns,” says Scheibehenne. “Detecting actual randomness doesn’t buy you much, since there would be nothing to predict anyway.”
Evolutionary forces and learned expectations jointly produce streak-seeking minds, proposes psychologist Andreas Wilke of Clarkson University in Potsdam, N.Y. In the distant past and in the present moment, in stands of trees dotting a savanna and in shopping malls punctuating an urban sprawl, desirable stuff clusters together.
A gambler’s dilemma
In support of the idea that human thinking — not just brain activity but also how the brain reads the environment — is attuned to streaks, Scheibehenne and his colleagues have found that volunteers prefer betting on the next symbol to appear on a computerized slot machine if they have seen one or both of its two symbols (cherries and a peach, for example) come up several consecutive times on a regular basis, rather than in a random succession that includes a few clusters here and there. That makes sense for gamblers, since a streaky machine is more predictable than a random one.
In contrast, bettors trying to decide whether cherries or a peach would turn up next tended to do poorly and to give up on machines with symbols that frequently alternate, apparently overlooking the predictable back-and-forth pattern, the scientists report in an upcoming Evolution and Human Behavior.
Betting patterns of the 238 participants in the slot machine study — who were vying for $50 awards given to the top two gamblers — signaled an intuitive preference for streaky sequences, says Scheibehenne. Slot machines elicited a foraging strategy used by animals that seek food distributed in patches, whether icons were programmed to appear randomly or regularly in long strings. Foraging for slot machine successes in this way worked best on streaky machines and worst on alternating machines.
Finding clumps of anything depends on a simple rule of thumb: Keep searching in the same place after a successful choice, such as finding a berry in a bush, and move to another spot after a failed attempt or two. For alternating sequences, the opposite approach works better: Look elsewhere after a correct choice and stay put after an error, because the situation will reverse quickly.
For random sequences anything goes, because all strategies do equally poorly.
In Scheibehenne’s study, volunteers saw two slot machines on a computer screen. Participants didn’t know which machine generated a random sequence of icons and which one produced a sequence that alternated icons or clustered them together to varying extents. Overall, players continued to bet on streaky machines 70 percent of the time after making winning choices. And players used the patch-finding strategy on about half of their alternating-machine bets and a bit more often than that when wagering on random machines.
“Participants may have had a general tendency to use the appropriate choice strategy for streaky environments as a default strategy in all cases, which could explain their inferior performance on alternating sequences,” Scheibehenne says.
Consistent with that possibility, participants made progressively more losing bets on slightly and moderately alternating sequences over 250 trials, appearing to become increasingly confused, rather than learning to predict back-and-forth swings.
These findings build on evidence of hot-hand thinking across cultures that was reported in 2009 by Wilke and anthropologist Clark Barrett of the University of California, Los Angeles.
Wilke and Barrett developed a computer game that simulates a search for fruit trees in a forest and for modern resources such as parking spaces. In 100 trials, each player decides whether to stay in the same spot or move to a new spot to find what they want. In each case, resources are randomly distributed.
Among 32 UCLA students and 32 Shuar hunter-gatherers living in an Amazonian village, most said that they expected fruit trees in the computer game to occur in patches. Both students and villagers usually continued to forage in the same place after finding a piece of fruit, in line with that expectation.
In another exercise, the students and hunter-gatherers tried to predict 100 random coin flips. Half the students, who knew about the concept of randomness, usually assumed incorrectly that getting heads meant that the next flip would yield another heads, and getting tails would lead to another tails. So did nearly all Shuar.
“This supports the idea that hot-hand thinking is an evolved default, which, in cases of true randomness, must be learned out of,” Wilke says.
Hunting and gathering
Even in a video game where players roam huge domes searching for chests that contain glowing green spheres, a foraging tactic that evolution has honed for finding patches of berries and other good eats looms large, says biologist Philippe Louâpre of the University of Rennes in France.
With each discovery of a sphere, 92 volunteers reported becoming increasingly motivated to open more chests in the same dome. As empty chests accumulated, the volunteers reported a growing desire to move their search to a new dome. Players reacted more strongly to finding a sphere than to opening an empty chest, enabling them to zero in on clumps of orb-bearing containers but also leading them astray if they found the only orb in one part of a dome first.
Participants searched domes in this way whether spheres were distributed randomly, evenly or in clusters, Louâpre and his colleagues report in a paper published December 8 in PLoS ONE.
Other evidence indicates that bumblebees searching for pollen-bearing flowers and parasitic insects seeking host animals take the same simple approach in deciding whether to keep looking in the same place or go elsewhere, Louâpre says.
“There may be an ancient motivational mechanism tailored by natural selection for deciding when to leave a patch,” he says.
Such findings are intriguing but don’t confirm that people have evolved to expect sequences to be streaky, remarks psychologist Thomas Gilovich of Cornell University. Slot machine and video game players may simply reason that clusters of icons or green orbs in a small, random sample represent the pattern that can be expected in a much longer sequence, Gilovich argues. A biased sample could prevent players from recognizing that icon and orb distributions would eventually even out.
Gilovich first proposed this explanation in an influential 1985 paper. Using shooting and free throw records over one to two seasons of play for two professional basketball teams, he and his colleagues found no chance-busting sequences. Yet 91 of 100 basketball fans surveyed by the researchers believed that players get hot hands, defined in the study as a player having a better chance of making a shot after making his last two or three shots than he does after missing his last two or three shots.
Some hot hands do appear to be real. Studies have found hot hands in individual sports — such as golf putting, bowling and horseshoes — in which players largely avoid the influences on one another that affect performance on a team. And a 2000 computer simulation of basketball shots over a season suggests that the statistical tools employed by Gilovich may have missed some genuine hot-hand scoring runs among hoops players, Wilke says.
Just remember: Casino slot machines are called one-armed bandits for a reason. The only streak to expect by feeding them money is a losing one.
Famous sports streaks
In professional sports, amazing streaks get celebrated as demonstrations of athletic prowess and heroism. Whether these grand acts of sustained achievement surpass mathematical standards of randomness or not, each one inspires new generations of players and fans alike with a story of almost unbelievable achievement.
56-game hitting streak
Where have you gone, Joe DiMaggio? Look in the record books. Joltin’ Joe got at least one base hit in every game from May 15 to July 16 during the 1941 season. During his streak, the Yankee Clipper had a batting average of .408 and added a hit in the All-Star Game. Pete Rose comes in a distant second to DiMaggio, with hits in 44 consecutive games in 1978.
Pitched 59 scoreless innings in a row
The right-handed pitcher, nicknamed Bulldog, finished the 1988 major league season with an amazing streak, leading the Los Angeles Dodgers to a World Series win over the Oakland A’s. He bested by one-third of an inning a record set in 1968 by the Dodgers’ Don Drysdale. During Hershiser’s streak, he allowed 30 hits, walked nine batters and struck out 34.
51 consecutive games with a point
Known as The Great One, Gretzky tallied either a goal or an assist in each of the Edmonton Oilers’ first 51 games in the 1983–84 hockey season. In doing so, Gretzky broke his own record from the previous season of 30 straight games with a goal or assist. The streak, which included 61 goals and 92 assists, set a record that has lasted more than a quarter century.
47 consecutive games with a touchdown pass
From 1956 to 1960, the Baltimore Colts quarterback threw a touchdown pass in 47 straight games. Unitas established a streak that has held up even against today’s elite quarterbacks, such as Peyton Manning and Tom Brady. Unitas dismissed his record as unimportant and said that he cared only about winning games. — Bruce Bower
Image credit, from top: Harris & Ewing/Library of Congress; Lenny Ignelzi/Associated Press; IrisKawling/Wikimedia Commons; NFL/Associated Press