What if I told you that you can simulate an NBA game (say, tonight’s Finals Game 4) just by flipping a coin? If it’s heads, chalk two points for the Cavs, if it’s tails, two points for the Warriors. Repeat a hundred times or so and presto! Game simulated.


You can even see the narrative of the game unfolding: the balanced start, the Dubs offense making a run, the short-lived comeback, and the final run to victory. But the results were completely random: just coin flips (virtual ones: I had a computer do this for me). A paper published last year on Physical Review E proved that, statistically speaking, this approach isn’t all that wrong. The study even compared upwards of 10 thousand NBA games with the theoretical model to confirm it.

The researchers treated the score as a random walk. The basic concept is the same we used for our “game”: move step by step one way or the other according to a coin flip.

Basketball is obviously more complex than that, but it turns out complications can easily be added in the model. For example, we could use some fancy statistical model to estimate if one team is better than the other, and take it into account using an unfair coin, that gives heads or tails with different probabilities. So it will be more likely that the stronger side comes out on top, but it won’t always.

Even within a single game, theory can give us some pretty cool insights, like decide when a lead is sufficiently large to guarantee the victory (within reason).

Players, coaches and analysts all have their systems, and the scientists used the large theoretical body on random walks to find out one of their own. They collected the lead size and the time left in the game in one parameter and found a formula that widely outperformed even the popular Bill James method.


The probability that a lead is safe. The black line is the result based on random walks, the blue one is the Bill James prediction and the red triangles are real data measured from actual NBA games. © 2015 American Physical Society, All rights reserved. Reproduced under license from http://dx.doi.org/10.1103/PhysRevE.91.062815.

Even armed with this understanding, sports remain intrinsically unpredictable. Our team could win against all odds (as Leicester fans know well), a good team could turn out to be historically good (as Warriors prove). As the researchers say, this is what makes us love sports. Sometimes to the point of coming up with embarrassing songs about our heroes.


Cover photo: Stephen Curry, CC-BY-SA Keith Allison, via Flickr. Some rights reserved.

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