The probability of a response depends on how likely the recipient is to believe your message has utility for them. That's why people researching rare surnames are more likely to get a response than those researching common ones. For example, if I received a message from someone who was trying to find descendants of a Jacob Cohen, I might not even open it because the odds that his Jacob Cohen and mine were the same person are fairly low.
By contrast, I have the good fortune to be researching fairly rare surnames; I'll list them here in case a reader is looking for them as well: AINGOR(E)N, AKABAS, CRISS, EISENDORFF, FIZYK, KARDONSKY, SWIG, and ZUSSELMAN/ZISSELMAN. Finding these people takes work, but when I find someone who has one of them, they are usually aware that these names are rare and recognize the odds of a breakthrough for them are fairly high, and thus get replies.
To avoid the "Geni" problem of concatenating unconnected trees, I usually leave out something that I know and would likely be known by someone who actually was a relative. Early on, I wrote to a potential CRISS cousin and included a sequence of fathers and sons. I got an answer, that the sequence agreed with her father-in-law's family, but back in Ukraine, the family had been known as ZISSELMAN. My reply to her began, "Dear Cousin." In response, she sent a photo of her husband's father with his employer; the employer was my grandfather. Case closed.