To be somewhat of a nitpick, there are two types of bounces. The more common type is when a visitor arrives who does not need a visa (e.g., Canadian, American) or already holds a visa. I wrote a very detailed description of this in an article which starts with...
Sometimes people arrive in the UK and do not perform well in their
landing interview; some people lie, some plan to abuse the system,
others exhibit strange behaviour, some appear to be incoherent. And
others do not have a convincing reason to be in the UK, for example
some people visit too often and other people appear to be a potential
A percentage of these visitors get 'bounced' (i.e., turned around,
denied entry, refused entry, sent home). This most frequently happens
to Americans, Canadians, Austrailians, and New Zealanders. Even
though these nationalities do not generally require visitor visas in
advance, they are required to have a convincing reason to visit the UK
and to exhibit that they are not a potential overstayer.
What happens when somebody gets bounced? Clearly many situations are
too hopelessly complex to even attempt explanation in an article like
this; but we can take a look at some common features.
Things begin with the Immigration Officer (IO), who may have observed
the person acting strangely (or stressed) in the queue, or who may not
be satisifed with the response to one of his questions (for example
lying or intending to break our laws); or worse, the person is flagged
up on the computer. At that point the IO will remove the person from
the rest of the traffic so that other travellers can be processed.
This is called 'being detained'. The first level of detention is a
segregated area in the arrivals hall. The person detained may be
escorted to the luggage collection area to collect their luggage and
to consign this to UKBA for inspection.
The complete article is here... http://www.londonelegance.com/transpondia/visitors/getting-bounced
The other type of bounce is when someone is transiting the UK and does not have the requisite DATV visa or fails to qualify for the concession. These are not very common because the Immigration Act 2000 stipulates fines for the airline and as a result the airlines will apply lots of diligence before take off. In the usual case, the person will not be allowed to board the flight.
The Office of National Statistics produces a report that indicates the OVERALL chance of a bounce is 1 in 3,000, and I think the bulk of those are of the first kind. If you subscribe to their publications you will get an email notification when new statistics are available.
Our laws mandate that the decision to admit or bounce lies solely upon the Immigration Officer who conducts the landing interview with the agreement of the duty CIO. I have never seen a case where a CIO has overruled an IO's decision, but the law allows for it to happen. You would be surprised at how many are American women coming over to see a guy they met on the net. It's fine to do that, but incredibly they lie about it and get caught in a lie. If an IO catches you in a lie, you are out of here.
So what goes through an IO's mind when they smell a bounce? What are they thinking? What signs are they looking for? Fortunately, the Home Office Research Unit has published two studies on exactly this topic. Don't ask me for the links because I make hard copies and save them on my hard drive, and the Home Office site gets reorganized at the drop of a hat anyway. Any link I posted would be rotted following the next election.
Basically the IO will suspect single women travelling alone, young men with lots of technical gear, people with lots of cash, people presenting brand new passports who have recently renewed their passport (you'll understand why), people with no peripatetic history, people who are stressed or acting nervous, and the list goes on. Business men and women, for example, get bounced frequently because they do not have a work permit.
Once you get bounced, you'll have your biometrics on file plus your passport will be recorded (changing passports does not help). And whether you like it or not, your biometrics will be sent to the USA.
So to answer the question: Yes, reports have been published on how the IO reaches a decision; and yes, statistics are available. Posting their links in SO invites quick rot. Having said that, you can use this link to get started. https://www.google.com/webhp?sourceid=chrome-instant&ion=1&espv=2&ie=UTF-8#q=home%20office%20research%20and%20statistics