How many autosomal DNA matches?

Earlier this week Blaine Bettinger posted a survey on Facebook asking how many 3rd cousin or closer matches you have on Ancestry DNA.  More than 1,200 people responded. While the most frequent answer was 1 - 5 matches there was a wide distribution. Some had none, some had more than 100 matches.

A simple way of looking at what to expect is by analogy to the urn problem -- coloured balls in an urn are either one colour or another, say black or white.  If you draw a certain number of balls how many of them are likely to be of each colour?

What you need to know is how many balls there are in the urn, how many are there of each colour and how many are drawn.

For the autosomal DNA matching you need to know how many there are in the population from which those who take the test are drawn, how many 3rd cousin or closer relatives you have, and how many tests there are in the company database. The more 3rd cousin or closer relatives you have, and the larger the company database the more likely you are to find a match.

The AncestryDNA test is sold in many countries, by far the largest proportion in the USA which has a population of 325 million. Ancestry advertize they have sold 6 million tests. Using those figures and either 100, 500 or 1,000  3rd cousin or closer relatives, the number will vary by family, the bar chart shows the probabilities of the test detecting the given number of 3rd cousin or closer relatives calculated using the binomial distribution.
The distribution found by Blaine Bettinger's survey combines respondents with different family sizes. Pedigree collapse and endogamy will make more distance cousins appear closer. Where people have deliberately tested known cousins (the equivalence of deliberately drawing the chosen colour ball from the urn) the number of matches will be greater.
Those of us without US ancestry are effectively drawing from a population with fewer or even no 3rd cousin or closer relatives. To increase the chances of finding a match remember to transfer your data to Family Tree DNA (another 10 per cent ot results), GEDmatch, MyHeritage, and especially for those of us with British ancestry LivingDNA when it become available.