I don't mean to sound like a naysayer but I'm wondering if those are actual tested maxes or "projected maxes" based off of a chart or something? Assuming those are actual gains, who is to say that another methodology wouldn't work just as well?
From what little I understand of the 5/3/1 system, it seems like a liberal adaptation of prilepin's chart
Wave 1: 65%x5, 75%x5, 85%x5 or more
Wave 2: 70%x3, 80%x3, 90%x3 or more
Wave 3: 75%x5, 85%x3, 95%x1 or more
Wave 4: 40%x5, 50%x5, 60%x5
Prilepin's chart has been tweaked for powerlifting, it was originally created by observing olympic lifters, but the powerlifting adaptation looks like this:
week/percentage/sets&reps/total reps/prilepin's recommendations
5 65% 6/3 18 18â??30
6 75% 6/2 12 12â??24
7 85% 6/1 6 4â??10
8 75% 5/3 15 12â??24
9 85% 5/2 10 10â??20
10 95% 4/1 4 4â??10
So one could argue or question whether doing Wendler's 65% & 75% lifts in week 1 are really beneficial. The 85% x 5 falls within prilepin's recommendations. In week 2 the 90%x3 is damn close to meeting prilepin's recommendations of 4 reps...and I can say from experience that I have made good gains not getting in 4 lifts at 90% or higher each week...and in week 3 we're shooting for 1 rep at 95% which is how I've always kind of tackled ME work...get in a solid 1-3 reps at 90%+ and things look good for the most part.
I don't know if this really answers your question. I see alot of people jumping on the 5/3/1 bandwagon and I wonder if it's just because it's something simple that people can stick with or if there really is something magical happening (I tend to think it's the former).
At the end of the day, if it works, it doesn't matter. Just SMASH FUCKING WEIGHTS and don't worry about the details.