Monday, September 17, 2012

Chance and explanation

In Game 2, of the 2011 NBA Finals, the Dallas Mavericks came roaring back from a 15-point deficit in the fourth quarter to win the game.  Dirk Nowitzky, who had shot poorly for most of the game, suddenly started making shots.  This exciting rally evened the playoff series at 1-1.
For the next few days, newspapers, bloggers, and people standing by water coolers across the country swapped theories about this remarkable turnaround.  Did Dallas respond to taunting by the Miami Heat stars?  Did they realize their backs were up against the wall and that they would have great difficulty coming back to win the series after losing the first two games?  Did the Heat choke under pressure?
The one thing I didn’t hear in any of this discussion was the most likely explanation for the sharp change in fortunes of the two teams in the final quarter of the game:  chance.  That’s right.  Pure randomness.  Not an enthralling explanation, but most likely the correct one.
In game situations, NBA ballplayers make about 40-50% of their shots.  Dirk Nowitzky has been hovering around that 50% mark all season.  That means that over the course of a season, he makes about half his shots.  Just for fun, pull out a coin and flip it 20 times and write down the sequence.  A good coin will land on heads about half the time, but over any small sequence of (say) 5 flips, you might get 4 or even 5 heads in a row.  That doesn’t mean that the coin is on a hot streak.  It is just chance. 
Even so, back in 1971, Amos Tversky and Daniel Kahneman pointed out that people expect things to even out in the short run.  If a coin comes up heads three times in a row, we expect there to be a few more tails later to even things out.  We are surprised when a fair coin flips heads 5 times in a row, although it is fairly common for that to happen. 
What makes a coin flip fair is that in the long run it comes up heads 50% of the time.  People extend this belief to assume that it will commonly come up heads even for a few coin flips.  Tversky and Kahneman called this a belief in the law of small numbers.
The second factor at play here is that people love to give explanations for things.  I have written about the importance of explanation for people often in this blog.  Whenever something differs from people’s expectations, they want to give some reason why this situation was different from what they anticipated.  People are highly skilled at coming up with explanations for things.
Putting these together, then, think about the end of Game 2.  Dallas made a few shots in a row.  At the same time, the Miami Heat missed some shots.  If this had happened in the middle of the second quarter, nobody would have noticed.  In fact, these streaks happen all the time in the middle of games.  But, when it happens at the end of the game, everybody takes note.  It is surprising and it demands an explanation.  That’s when all of the speculation begins.
And that is fine.  In a world where there is violence, unemployment, crime, and illness, it is fun to spend a few minutes chatting with friends about the NBA Finals.  The best explanation for what actually happened in the game may be chance, but that doesn’t make it a good conversation starter.