DNA Cousin Matching

Below is the AncestryDNA summary for my wife's DNA matches

188 4th-6th cousin matches

Below is the AncestryDNA summary for my DNA matches

1025 4th-6th cousin matches

I suspect a number of readers who have had their DNA tested will look at my wife's numbers, and feel they are similar to their own. And then look at mine and be surprised. "You're so lucky!" they'll think.

Except...I'm sure there's a large number of false positive matches. Back in 2014 Ancestry changed their formula to reduce the number of false positives in general, but I think it's still high for Ashkenazic Jews. It's definitely still high for me.

• I have 437 pages of matches, 50 matches each, or a total of 21,850 matches. This obviously includes a lot of ancestors Ancestry categorizes as "Distant" or 5th-8th cousins.
• My wife has 163 pages, or 8,150 matches

The situation is similar at FamilyTreeDNA. I have a total of 5,728 matches, my wife has 876, and my mother has 3,374.

So if I assume the number of matches everyone gets, in a purely random environment, should be approximately similar...It's possible between 4/5 and 5/6 of my "4th Cousins or closer" matches are wrong.

So if the match doesn't have a family tree, and their Ethnicity information suggests we connect on my Jewish ancestry, why should I bother emailing them, when there's over an 80% chance of a false positive? [Unfortunately, even those with family trees don't include generations beyond the 'immigrant ancestor' which would be necessary to make a connection.]

Another situation I have -- several years ago, I came into contact with another researcher on one of my paternal lines who had done a lot of research in Polish archives, and his research took back that surname for me a couple generations providing many cousins. Yay! However, the name he had for my second great grandmother was wrong, the date of birth for my second great grandfather didn't match family records, and the birth record for my great-grandmother hasn't been discovered yet, leading me to wonder if there wasn't a second person with my second great grandfather's name. Well, this person has been declared a cousin of mine by FamilyTreeDNA, and the distance corresponds to the research I was given. However, is this proof?

Well, no. I can assume that I am related to all people of that surname from that Polish town. In some manner. However, the DNA match in no way confirms what generation we really have a shared ancestor. And the less accurate the matching is, the more this is the case. [But it is still nice to see his name pop up in my matches at FamilyTreeDNA.]