Originally Posted by db_ggmm
2x8 reps in 5 minutes with my 1rm vs 10x5 in 30 seconds body weight squats. I assume this must be what you are suggesting. To make the example more clear, I would suggest 3x8 reps in 4 minute 30 seconds body weight squats as the "high rep" set and yes, you've broken the example. The example has to assume some additional caveat, such as "in general, when working at or near *capacity*". A handful of body weight squats in 5 minutes are far removed from capacity, which explains why they break the example, however, it is possible that enough body weight squats / minute can fit.
I definitely agree with a lot of what you've posted in the longer explanation, except I would argue one minor point. You are attributing your performance improvements from the widowmaker to an increase in 1rm capacity, while I would suggest again as I did a few posts ago that the widowmaker primarily trains squatting endurance which greatly assists in removing the glass ceiling from your 3, 5, and 8 rep training which most directly influences your 1rm. I don't know if there is any way to prove the benefit is endurance or strength, but the effect is real. This is generally what I suggested to the "why widowmaker" question.
Endurance and strength, in absolute terms, are not so different, and both contribute to the overarching concept of power. Increases in either strength or endurance will increase power, and people often see benefits in one by becoming better at the other.
Power is a function of force, distance, and time; proportional to the first two, inversely-so to the last. Training exclusively in any one of those three may be limiting, while training in all three modalities will provide a well-rounded increase in overall power. Low rep training really focuses on force, while keeping distance and time relatively constant; a widowmaker brings into focus the latter two as well, slightly diminishing the force component.
Is not someone who squats 315 for 20 reps stronger than someone who can do it for 5? Endurance sees a benefit from strength in that a stronger athlete will not have to fully exert himself to accomplish one task and so can perform that task repeatedly before becoming exhausted. For instance, if you're playing basketball, a stronger player may not exert himself as much to grab a rebound as a weaker player, and therefor should be able to preserve energy in the long run and increase his ability to jump repeatedly throughout the game.
Things get a little blurry when discussing endurance, specifically between cardiovascular and muscular. Many weightlifters ignore their cardiovascular strength to focus on muscular strength, since they operate in exertion ranges where the heart and lungs aren't required to exceed their typical capacity. Same with sprinters vs long distance runners. I was considering to go full-on bio nerd here in describing how different exercise activates different metabolic pathways and how that requires the muscular and cardiovascular systems to adapt to the circumstances, but I'll refrain.