There are so many factors you are ignoring in your analysis... No offense but I have to say that your understanding of recruitment is lacking a lot of depth. Recruitment strategies and practices vary quite a bit but below I tried to give some ideas to the shortcomings (IMHO) of your analysis.
TL;DR: Recruitment is a complex procedure that typically has many factors that are asymmetrically known to different parties. Writing applications, personal letters etc is almost an art in itself. Thus it's important to get a better understanding of the system before jumping into conclusions with misleading statistics.
Outcomes
You seem to take the outcome as a binary variable, while for a single application it might be a valid way to see it, for a single applicant it might be misleading. Based on the project at hand and the candidates in question, the fact that you didn't make it for that particular application isn't necessarily independent of any future incidents, or rather the other way around; your future applications will most likely not be independent of the previous one(s).
It's quite the contrary, actually. You might have significantly increased, or decreased, your chances for a future position with the same group, or at another group associated with the one you applied to. That's practically based on the competition (to which you are will be in the dark) for the project you applied to, and to the impression you have left on the admission committee or the individual PI/group leader. It's important to keep in mind that people talk. In other words, your reputation will most likely proceed you, whether that is positive or negative that's a different story.
Fairness
One might like to think otherwise, but life isn't always fair and recruitment is typically one of those scenarios. In most respectable universities, all open positions need to be publicly announced, which means that anyone in the world can practically apply to them. Furthermore, there are usually laws and regulations that are put in place to work against discrimination of any kind.
What might get forgotten, however, is that the projects aren't really randomly devised. It is not that uncommon for a position to be announced so specifically that it's essentially tailor-made for a candidate; practical examples of this case could be the continuation of a master thesis work, or any similar project work. Such a position could be de facto filled months in advance.
If you are applying to a position at a group with no prior knowledge of the place, you might actually be applying to a position that is already filled. However, many PIs use the public application procedure to "scout talent". In other words, you might not be an interesting target for the project/position you have applied to, but you might still be very interesting for an upcoming project (see previous section "Outcomes").
Spamming
If you are looking at numbers only, you might be mislead on accessing the real number of feasible candidates. I might be insensitive, or even offensive to a certain degree, but there are people who do not even read the job description and mass-apply (especially if it's free to apply). I work with bioinformatics, and among the other candidates there were some who apparently: "... always dreamed of the chance to be a radio engineer, and thus would gladly take the opportunity to ..." (I have not seen the application myself, as it'd be a conflict of interests. I heard about this much later at a pub gathering with my colleagues and boss)
You would be muddying the statistics if you count with people that would be sorted out almost immediately.
Hype
Word gets around, quickly... So more and more people want the same thing; "Did you hear {insert_famous_professor} group has announced a new position?!" While that is a normal human behavior, it also points out a fundamental defect in the way we reason; just because something is famous it's not necessarily better than something else that isn't as reknown. At this point it's also worth noting that a successful senior scientist isn't necessarily a good teacher of doing science. The distinction might not be very apparent prior to doing a PhD but a couple of years into academia, you start noticing the difference.
In other words, while most people swarm over a few number of positions, very few apply to many positions elsewhere. Ask any head-hunter (recruitment professionals) and they'll even give you statistics.
Suitability
Call me a snob if you will, but doing a PhD isn't a god-given right to all humans. It's a job, a career path and thus not suitable for everyone. Please note that I do not, in any way, mean that you are not suitable to do a PhD (it would not be my place to make a judgement, even if I knew you in person). I am merely stating that if a person is consistently getting a rejection, the chances are highly likely that the person is being unrealistic, or stronly under/over-valuing his/her skills. The negative effect of over-valuing is obvious, I suppose, but modesty or humility to the extreme could also impair one's chances of getting an acceptance.
Hope it helps!
