Fun Fact: Lebron James Plays Basketball

Between building airplanes and playfully destroying everyone else in my apartment at Super Smash Brothers, my roommate Nathan brought up an interesting recent fact about LeBron James. He told me that LeBron scored 11 consecutive field goals (not in football... you know who you are) in one game. Apparently this was a pretty special event, but how rare is it for a player of LeBron's caliber? TO THE SCIENCE-MOBILE!

Benford's Law

Given a large set of data (bank accounts, river lengths, populations, etc) what is the probability that the first non-zero digit is a one?  My first thought was that it would be 1/9.  There are nine non-zero numbers to choose from and they should be uniformly distributed, right?

Turns out that for almost all data sets naturally collected, this is not the case.  In most cases, one occurs as the first digit most frequently, then two, then three, etc.  That this seemingly paradoxical result should be the case is the essence of Benford's Law.