Strategy. Innovation. Brand.

Braess’s Paradox and The Super Bowl


Of course they'll win.

Of course they’ll win.

Braess’s paradox posits that adding capacity to a network can reduce the network’s performance. Conversely, removing links in the network can improve its performance.

Dietrich Braess, a German mathematician, originally identified the phenomenon in traffic flows. As new roads open up, overall traffic flows sometimes slow down. That’s certainly unexpected behavior.

The paradox illuminates the result of selfish choices in self-organizing networks. Let’s say you have a crowded network of roads. A new road opens up that appears to offer a faster route. Driver makes selfish choices and head to the new road, making it more crowded while not appreciably alleviating the rest of the network. The result: on average, it takes longer to get to the destination. (Conceptually, this seems similar to the paradox known as the tragedy of the commons).

Does it work? Well, in 1990 New York City temporarily closed 42nd Street, a major thoroughfare. People predicted disaster but traffic actually flowed more smoothly. In 2011, Los Angeles closed a ten-mile stretch of freeway for construction and predicted a traffic “jam of biblical proportions” (known sardonically as Carmaggedon). It turned out to be not so bad.

The paradox may also happen in other self-organizing networks, like your brain. New Scientist reports that certain brain injuries can result in loss of vision. Surprisingly, creating another lesion in another part of the brain can help restore partial vision. Nobody understands exactly why but, apparently, the new lesion removes links in the network and helps the overall network improve its performance.

The same phenomenon can affect your ability to make optimal choices. Let’s say you’re going to by a new car. To find the best one for your needs, you decide to closely review 1,000 makes and models. The result? You’re quickly overwhelmed. To improve performance, it’s better to winnow the field and evaluate fewer options rather than more.

Sports analysts believe that the paradox may also pertain to team sports. Some teams play better when their star player(s) is removed from the game. Why would that be? Think of a team as a network. The ball often moves to (and sometimes from) the star player in the network. The path to and from the star is the most heavily travelled link in the network. Removing that link means the network has to reorganize and redistribute. That can result in improved performance.

I think we saw Braess’s paradox in the Denver Broncos’ defense this past season. Many observers consider Von Miller the best player on the Broncos’ defense. Miller was suspended for the first six games of the season. When Miller did not play, the Broncos actually recorded more sacks per game (a key defensive statistic) than they did when Miller played. In other words, the network reorganized itself and performed better.

Braess’s paradox may be very good news for the Broncos in the upcoming Super Bowl. The team has lost a number of key defensive players (including Miller) to injury. As the defensive network reorganizes itself, its performance may well improve. We already know that the Broncos have an unstoppable offense. As Braess’s paradox works its magic on the defense, the team is almost guaranteed a victory.

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