There is no threshold number of rejections above which a writer, who wishes to find an agent, shall then get a 'yes' from any agent.
It is not a numbers game.
To increase the chances of not getting a rejection, such a writer must know their genre in and out by knowing most, if not all, of what there is to know about it. They must search for and find the agent that is the best fit for their work, and then they must write a 'perfect' query letter.
unless that writer is fortunate to have an agent contact them out of the blue because that agent saw their previous work, liked it, and wanted to represent that writer, Margaret Atwood coming to mind, or during a serendipitous encounter—perhaps at a writers' conference—that writer comes across an agent, or they find an agent because of another author's personal recommendation, a query letter is often the only chance to make an agent interested in reading and, with hope, signing on that writer.
Such a writer must therefore put as much care and attention into crafting and polishing a query as they should do the manuscript.
If one's pitch does not hit its mark, one's book will most likely not be given the chance. Do not forget that it is all about what the publishing industry experts believe will sell.
Though no agent or publisher has a crystal ball on which work will be a hit, the agent, who has to present the writer's work to potential publishers and convince them of its marketability, will like to get the impression, off the bat, that a work will be successful during the submission process. So, the writer must take care of that submission process extremely well.
"Agents like to see signs that you're a savvy writer who is deliberate about the submission process—that bodes well for your working style, should we partner with you in the future," said Mary Kole (book editor and former literary agent).
An example of a perfect query letter is one that:
(1) individualizes the process (i.e., starting out the introduction like this: according to information on your agency's website, I understand that you are seeking this type of fiction ...)
(2) adds writing accolades if one has any.
(3) sets up one's story (a story that is not cliché-filled or trite; a story that is unique; a story that even if based on an old idea is given a new twist), conveying what the main character wants most, and what is standing in their way.
(4) shows the agent who one's characters are.
(5) shows that one's story is driven by strong character motivations with strong actions, strong ramifications, and lots of emotions tied to each.
(6) includes attributes of the manuscript (genre, word count, setting, target audience, unique selling point etc.)
(7) includes any comparative titles in the market (without comparing oneself with any other author). The purpose of this is for the agent to get an accurate picture of one's story style.
(8) includes a concise biography of oneself and rounds off with the essence of one's story and why it is a good fit for that particular agent.
A good number of agents believe that a query written this way gives the writer the best chance of getting them to request their full manuscript. At this stage, the manuscript must then begin to speak for itself. If after an agent reads the manuscript, that agent rejects the writer, it is usually due to one or both of two main reasons:
(1) Poor writing - this is boring writing that makes the reader feel dumb (instead of smart), is hard to get through, does not speed the reader along, and tends to:
-Employ mostly passive voice rather than mostly active voice.
-Mix tenses inappropriately.
-Consist of much more telling than showing instead of balancing them out.
-Inform the reader of nothing they did not already know.
-Lack distinctive tone or style.
-Have point of view problems.
-Have clichéd storytelling that lacks originality, using a lot of frequently repeated phrases or opinions.
In the end, good writing boils down to the voice and the quality of the language on the page. Apart from the big-five publishing houses who look for profitability more than anything else, a good number of agents and/or publishers look for strong, vibrant, and unique voices as well as stories that are different from what has already been told.
(2) Poor plotting - in summary, a good plot must always have the following elements:
-Characters that are relatable (because they are flawed and have problems), and fully developed as the story arcs.
-Conflict; which is something that upsets a particular character (usually the main character) as well as the reader through the character's reaction. It is always good to introduce internal conflict(s) not just the external one(s).
-Complications; which are unforeseen troubles and challenges for the character in question. By creating suspense and introducing twists, complications keep the reader interested and gets them to care more about what might happen to the said character.
-Climax; where the opposing forces in external conflict are brought together to cause an explosion.
-Conclusion; in which the result of the explosion is known, the conflict is over, the character(s) in question have either won or lost and no major questions are left unanswered unless the work is part of a series).