I would believe that 40% of the NASS attendees go on to complete their applications for nominations....but I doubt that 40% attend the Academy.
My son mentioned that the admissions briefing at West Point SLS this summer made the statement that about 40-50% of each SLS session would "receive offers". My guess is they are referring to LOA's or similar, not actual appointments.
This does not automatically translate into filling the class, as there will many receiving multiple offers. Especially recruited athletes.
That's not because they went to SS/SLS, it's just appears that way due to selection bias. Core academic stats (and maybe EC's depending on who you believe) have to be pretty good to get picked for SS/SLS unless a recruited athlete. So it's not surprising that the success rate is a bit higher, as there are very few there that are not well qualified. And recruited athlete's also have higher odds of receiving an offer.
So it sounds like the stats could be valid if applied to "offer" percentage, not a plebe class percentage.
Factor in that there is an opportunity to pass the CFA early and the numbers skew even more. And you have to have medical clearance to attend. Not anything like DODMERB, but there are probably some screened even in that process.
As many have stated, it appears the converse is not true: Not attending SS/SLS does not reduce the odds of making it into the class if you look at the total applicant pool.
It's just tough in competitive states. EX: My son was initially declined for one of the seminars even with reading+math SAT in the mid 1400's, 3.9 unweighted GPA, several AP/Honors classes, etc. Was added late for two of the seminars.
So like everyone says.... if you don't get picked just get ready for when the apps open. you are in control of completing that!