'AA has an X% success rate' (some people say). The 'X' is often very low, sometimes in single digits.
The false analogy is the concept of success rate in terms of, say, pharmacotherapy.
If a medicine has a 5% success rate, that might mean that 5% of the people taking it in accordance with the regimen show a statistically significant improvement compared to the control group, whose members are not taking said drug but are taking a placebo, for instance.
The key is 'in accordance with the regimen'.
Let's look at a more suitable analogy.
Say state flood insurance is available. You have to pay your flood insurance premiums every week, for the insurance cover to apply. After a particularly bad flood, almost everyone, except for a few crazies, takes out the flood insurance. Proudly, they all display their insurance certificates on their walls, and if asked, they will report that they have indeed taken out flood insurance.
In fact, almost all of the townspeople take out the insurance.
However, over the course of the year, people miss payments. Some people miss a few payments but continue later, thinking they can get away with the gap in payments. Others drift away entirely from making their payments. A few miss payments altogether but make them up later. A tiny proportion make their payments dutifully every week.
After a year, a big flood comes. It turns out that only 5% of those with insurance policies townspeople are up to date with their payments, and only that 5% receive payouts.
This is a much closer analogy to AA. Almost everyone is thrilled with AA initially, but people do not keep up their payments. The Steps are not worked rapidly and thoroughly but slowly, fitfully, and incompletely, if at all. Fellowship comes and goes. Service is sparse. Then, Bang! A slip!
In the insurance example, the insurance is 100% effective, not 5% effective, even though only 5% of the people with the insurance receive payouts: the reason for the 5% lies with the individuals, not with the insurance.
Similarly, in AA: I have never seen someone drink who has completed a Steps Four and Five plus all the amends they can, who is attending regular meetings, who sponsors others, who engages consistently in Steps Ten and Eleven, and who performs regular service.
In fact, I have seen plenty of people stay sober (including myself) on rather less than 100% compliance with the programme as it is set out in the Big Book.
So, to extend the insurance analogy: 100% of people take up the insurance; 5% keep their payments up to date, and they receive payouts, but another good number of people who have made some but not all payments find their claims honoured when the flood comes. Pretty good deal, eh?
Are you fully paid up?