One of the hardest things to understand about yDNA matches is whether the match means anything. People really want it to be simple. If life were fair, you could look at the number of markers that match and get a good idea of how back the common ancestor lived. Instead, the analysis is just a confusing jumble of probabilities.
First, it depends on how many markers match. That's easy. The further back you go, the more likely some of the markers have changed. The more markers that match, the more likely it's close relationship.
Second, it depends on which markers match. That's not too difficult. Some markers change faster than others. A difference on one marker might be more significant than a difference on another marker.
Third, the answer isn't a "real" answer. It's a probability. You want to know that you and another person had a common ancestor who lived about 20-24 generations ago, but DNA can't tell you that. The only thing the DNA can tell you is that there is, say an 87 percent chance your common ancestor lived 24 generations ago. This is where many people throw up their hands, but it's really not that much harder than the first two ideas. Think about it this way. If there is a 0.2% chance every generation that a marker will change, then we have to be content with knowing there's a 20 percent chance the change happened some time in the past 100 generations. Now imagine 25 markers, or 37 markers, or 67 markers, all changing at different rates (and for some of them the rate of change is different in different groups). There are no exact answers, just probabilities.
Finally, the math gets really weird. Most people assume that the odds of a common ancestor get better every generation back. Not true. In fact, it's just the opposite. Of course, if you go back far enough we are all descendants of Genetic Adam, but it doesn't work that way in on a smaller scale. The further back you go without finding the common ancestor, the less likely it is that your common ancestor will be in the next few generations back. This is so counter-intuitive that I've been looking for a good Internet source to explain it. Here it is:
http://www.legalgenealogist.com/blog/2014/01/26/understanding-the-y...
Quoting from this article: "Assuming that we know [two men with a 37/37 match] don’t share a common father (one generation), the chances are 89.48% that they share a common ancestor within five generations. Assuming that we know they don’t share a common grandfather (two generations), the chances drop to 83.49% that they share a common ancestor within five generations. And assuming that we know they don’t share a common great grandfather (three generations), the chances are only 74.10% that they share a common ancestor within five generations."
What the article doesn't say is that if you keep going back, say 24 generations, the probabilities start to climb again. For example, I compared one of my 35/37 matches. We share a common ancestor 8 generations ago. If I don't prompt the FTDNA calculator, there is a 70.87 percent chance we share a common ancestor 8 generations ago and a 99.82 percent chance we share a common ancestor 24 generations ago.
If I tell the calculator we don't share a common ancestor in the last 5 generations, the chance that we share a common ancestor 8 generations ago drops to 57.98 percent and the chance we share a common ancestor 24 generations drops slightly, to 99.74 percent.
If I push a little harder, and say we don't share a common ancestor within the past 7 generations, the chance that we share a common ancestor 8 generations ago falls to 37.85 percent, but the chance we share a common ancestor 24 generations ago starts to climb a bit, to 99.62 percent.
In other words, the probabilities always favor a recent common ancestor. If you know you don't have a recent common ancestor, the probability starts to fall for the generations just beyond what you know, but the probability remains high for much more distant generations.
