For some years, statistics have suggested that New York City was getting safer, cleaner and more expensive. Now there are numbers that suggest the city may not be home to as many rats as New Yorkers might have thought — or liked to boast about to visitors.

Jonathan Auerbach, a 26-year-old statistician studying for a doctorate at Columbia University, recently won a competition sponsored by the 180-year-old Royal Statistical Society of London. Mr. Auerbach claimed the prize with a paper in which he made the case that there are far fewer rats in the city than almost anyone had assumed.

About six million fewer.

By Mr. Auerbach’s calculations, the rat population is a mere two million, give or take 150,000.

In arriving at that total, he debunked the long-perpetuated idea that there was one rat for every person in the city. New York’s population stood at 8,405,837 as of July 2013, according to the Planning Department. But in his paper — published in the statistical journal Significance under the title “Does New York City Really Have as Many Rats as People?” — he called the one-person, one-rat idea “an urban myth.”