Let’s say it’s a home game for the Golden State Warriors and Steph Curry shows he’s still got it, sinking back-to-back three-pointers minutes into the first quarter. The fans at Chase Center take notice, and so do the betting markets, where the odds move in the Warriors’ favor.

Yet it’s a long game. The away team comes back, and with just 10 seconds to go, the Warriors are down by two and have just missed a shot. A victory is unlikely, and the betting odds should have shifted to reflect that near-certainty. But they don’t.

“If you look at the history of NBA games, the probability that a team with the ball, up by two with 10 seconds left, wins is north of 90%,” says Eben Lazarus, an assistant professor of finance at UC Berkeley’s Haas School of Business. “But what shows up in the betting markets is that people treat baskets as too similar over the course of the game. They overreact to information that’s not very important—early baskets—and underreact to strong signals at the end.”

This interesting pattern in how people interpret new information holds true across a range of settings, from sports betting to financial markets, according to a paper published in the Quarterly Journal of Economics.

Lazarus and co-authors Ned Augenblick from UC Berkeley Haas and Michael Thaler of University College London conducted three experiments and analyzed millions of betting transactions and prices on options contracts, and found that people consistently overreact to weak information and underreact to strong information.

“There are all kinds of situations where I might know whether a piece of news is good or bad, but struggle to judge exactly how important it is,” Lazarus says. “We saw this pattern everywhere we looked, which was surprising to us given the stakes involved in betting and financial markets.”

Building on decades of behavioral science and economics research

Lazarus and his co-authors wanted a way to unify different theories about how people act in ways that aren’t quite rational when processing new information.

The study builds on decades of behavioral psychology and economics research about how people update their beliefs given new information, dating back to a classic 1966 paper arguing people are overly cautious in updating, and a 1992 paper by Dale Griffin and Amos Tversky showing people tend to overfocus on information that seems dramatic but gives less weight to how reliable it is.

More recent papers have shown that people make systematic errors as a result of mistakes in calculating probabilities, and when people are uncertain about what decision to make they tend to pick a middle-ground option. The paper also connects to studies looking at how financial markets sometimes overreact and sometimes underreact to news.

“We think that we have a simple framework for thinking systematically through a lot of situations in the financial markets and the real world,” he says.

As humans, we take in information all the time, whether it’s a new poll that favors our preferred candidate or feedback from a boss. The researchers theorized that most of the time we don’t have the information to accurately judge just how important that information is, so we tend to default to a middle ground.

“In cases where it’s easy to figure out which direction to update your beliefs, but not quite how much you should update, people will tend to treat all ‘good’ information somewhat similarly,” he says. “Given this difficulty, you’re going to see people overreacting to news that’s fairly weak and underreacting to news that should move you close to certainty.”

Experimental evidence

The research team first tested their theory in lab experiments, including both a classic experiment involving determining which deck a particular card came from and a novel sports-related experiment where they recruited 500 NBA fans and presented them with sequences of events in a simulated basketball game.

The simulations started with 2:40 left in each quarter, and participants then saw a sequence of four possessions. After each possession, participants had to predict the probability of each team winning (they could earn a $50 bonus based on their accuracy).

The researchers established the “correct” probabilities of wins in each scenario using data from the website inpredictable.com. But they found that while people understood that late-game baskets were more important than those scored early in the game, they still overreacted to first-quarter baskets—giving them 60% more importance than they should—and underweighted fourth-quarter baskets by 33%.

“This gave us a good sense that people were over- or under-reacting to information in experiments, but we needed to come up with some ways to test this in higher-stakes settings in the real world,” Lazarus says.

Sports betting data from Betfair

To do that, the research team turned to sports prediction market Betfair, analyzing over 5 million betting transactions across 260,000 basketball, soccer, football, and ice hockey games. Since the researchers had no way to determine the “correct” probability of a win with certainty, they developed a new empirical method to measure whether prices were over- or underreacting to information.

Again, they found that early in games, events like scores created bigger shifts in betting odds than they should have, given the high uncertainty about the outcome. Meanwhile, important events like fourth-quarter goals caused smaller shifts in the market than is justified.

Data from options markets

Lazarus and his co-authors also tested their theory in a sophisticated financial market, using option price quotes for S&P index options traded on the Chicago Board Options Exchange from 1996 to 2018. After applying multiple filters, they had over 4 million option prices corresponding to 955 expiration dates. To give a clear time horizon, they focused on those expiring in 100 trading days (~4.5 months).

They found the same pattern they observed in the sports betting market.

“…News today appears to hold relatively little information about the value of the S&P in multiple months, but the market acts as if it (does),” the authors write. “However, within two weeks of a contract’s resolution, the relationship reverses…as signals become stronger, the market begins to underreact.”

Real-world implications

While the research explains some puzzling patterns in how people and markets respond to news, Lazarus cautions that being aware of these patterns does not remove all risk.

“It’s still not a free lunch if you know that on average markets are underreacting or overreacting at different points in time,” he says. “You can still lose a lot of money if you bet against these moves.”

Still, the findings suggest that it’s wise to pay attention to how much weight to give different pieces of information, even in situations that are far more ambiguous.

“Let’s say I have a negative interaction with my boss and I’ve spent all week fretting about it,” he says. “How important is it really for my future at this company? I think people would do well to take that step back and think about how much to react.”