Strange But True: The math behind a winning team


Q: Suppose your favorite NBA team plays above average, with a win rate of 0.750, or about three games out of every four. What's the probability that they will beat another 0.750 team? How about just an average team, a really bad one, or a really good one, like the Golden State Warriors? As fans of the Cleveland Cavaliers (whose average is around 0.750), we wanted to know.

A: If two teams of the same strength play, each has an equal chance of winning. So the Cavs facing another 0.750 team have a 50 percent probability of winning (or losing). Facing a lesser opponent pushes the probability of winning above 50 percent, while against an average team you'd expect to prevail at about your overall win rate, 0.750. With a stronger team, obviously, the probability drops down.

Estimating the win probability for other match-ups is more difficult. But based on a simple mathematical model developed by the authors and win-rate data from the 2015 2016 NBA season, a 0.750 team like the Cavs will win only about 27 percent of the time against a 0.900 team like the Warriors.

Q: When "money talks," where is it apt to be heard these days?

A: University of Pennsylvania researcher Daniel Preotiuc-Pietro and colleagues used a machine-learning model to analyze some 10 million tweets posted by more than 5,000 network users, reports Rachel Nuwer in "Scientific American" magazine. They found that in about 90 percent of cases, the tweeters inadvertently tipped off their socioeconomic status, largely by referencing their work. Earlier studies had also uncovered users' gender, age, political leaning, even postpartum depression and post-traumatic stress.

Postings from those with higher incomes tended to involve business, politics and nonprofit work and were primarily used to disseminate information. However, lower-income people focused mainly on personal subjects and social communication. Interestingly, "the analysis also revealed that tweets from those who make more money are likelier to express fear or anger" (from the "PLOS ONE" journal).

As Preotiuc-Pietro concludes, "People should be aware of how much they inadvertently disclose about themselves."

Q: Humans have an impressive technological toolkit compared to other species. Is this because we're very smart or because we're very social?

A: In his book, "The Secret of Our Success: How Culture Is Driving Human Evolution, Domesticating Our Species and Making Us Smarter," Harvard professor Joseph Henrich uses a simple mathematical model to investigate how inventions spread through a population. Consider some invention (such as a stone tool) and imagine two different proto-human species, the Geniuses—who are very smart (inventive) but not too social—and the Butterflies—who are very social but not too smart.

Suppose each Genius has a 10 percent chance of independently inventing the tool, while each Butterfly has only a 0.1 percent chance. But also suppose each Butterfly has (on average) 10 friends from which he/she might learn how to make the tool, while each Genius has only one friend. If there's a 50 percent chance that a person who knows how to make the tool passes this knowledge on to a friend, then a simple calculation reveals that, in the long run, only 18 percent of Geniuses will have the tool while 99.9 percent of Butterflies will.

"Keep in mind that the Geniuses were 100 times smarter than the Butterflies whereas the Butterflies were only 10 times more social. Bottom line: if you want to have cool technology, it's better to be social than smart."

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