The study conclusion was somewhat different in this respect. Their belief was that the majority not committing crimes weren't behaving that way out of fear of detection since they are well aware of how ineffectual the police are. Their belief was that it was the innate decency of the majority coupled with their fear of the possible anarchy that leads to their good behaviour.
They further concluded that their estimated total of all crimes, which is very much greater than those reported of course, was already about as many as can be committed by the remainder. Those two conclusions meant the police presence was largely superfluous.
There's some supporting circumstantial evidence too. For example, for a few years now police numbers have been falling due to cutbacks, while crime levels have been falling at the same rate. Police traffic patrolling has fallen very dramatically too over many years now, but road death and accident rates have been falling throughout the same long period. Both inevitably lead to the conclusion that the police make very little difference.
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