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On FamilyTreeDNA, they have their TiP Report that gives the probability that two matching members shared a common ancestor within the last number of generations. E.g., for a yDNA-37 match with 4 variations it suggests 90.6% within the last 12 generations. Now for this yDNA test on my side of the match, we know the paternal line with a very high level of confidence back to the 1600s and ten generations due to yDNA triangulation of the paper trails.

Therefore, I'm wondering, could it be this is a false positive? It seems to me that you could have two separate lines that go back many hundreds of years that just happened to mutate and by coincidence end up in the same general area of yDNA and thus appear as a match. I know a NPE is also a possibility, but perhaps this type of coincidence is too? If so, what is the probability of a yDNA match where surnames do not come close to each other being a false positive?

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It seems to me that you could have two separate lines that go back many hundreds of years that just happened to mutate and by coincidence end up in the same general area of yDNA and thus appear as a match.

You are totally right! The yDNA test from FTDNA looks for so-called STR markers. The more markers - more precision. Each haplogroup has it's own more common values of markers but as time pass the markers mutate in random way. Also markers can mutate with change of value to greater or lesser. And more - there are back mutations too!!! So when a lot of time pass we will see values very close to each other set's of markers. You can imagine it as overlapping circles on water from stone thrown there. It the reason because clustering of people based on STRs failed. But Y-STRs are good for predicting haplogroup, and, sometimes - (sub)clade.

Besides it we can guess the TMRCA because statistically markers mutate uniformly. But it works only for populations. For two particular people it doesn't work. For example, a father and a his son can be on great distance of 4 on Y-67. But it doesn't mean that they are not related in last time

The ONLY precise method to confirm relationship is to pass SNP test. Every SNP has each own year of forming. So one can say when MRCA lived for two people sharing the same SNP. The only problem left that we need not ANY SNP, but to find your so-called "terminal" SNP. And do to it one needs to pass full sequence of Y chr, what is rather expensive procedure.

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