Like with shields, we have spent decades researching and developing the safest gear possible for sports reenactment. From the oldest dowel rods and swing set parts, to the modern Class 4 gear, much thought and study has gone into learning what makes weapons safer than others.
For the longest time, 5/8ths was the gold standard for padding. Why was this the standard in so many groups? The answer is more pragmatic than scientific. The padding we could purchase came with a 5/8 inch wall so it was just law.
Over time we experimented, and found that simplifying to 1/2 inch exterior padding on a striking surface was not only just as safe, but often more accurate as weapons often were compressed below the 5/8 inch rule anyway. Likewise we found that 1/3 inch was sufficient for non striking surfaces as a minimum.
Other considerations such as tip padding have been unparalleled in research. How to make the strongest 'horse pill' while maintaining structural integrity and safety. Ultimately the 1 inch compressed pill on non-striking tips proved to be the safest around. This was contrary to the popular belief that a longer, softer tips were best. The science showed that the longer the tip, the greater chance of it bending and breaking the core through.
Other considerations that we improved upon were things like points and eyesocket safety. The truth of the matter is that no weapon is going to be 100% safe in the hands of an unsafe combatant. When all of the factors were equalled out, 95% of the time injury was not due to negligence or unsafe weaponry but unsafe and uncontrolled people. To this end we focus more on teaching control first, and it was no surprise to discover that injury diminished with better control. Thus, the weapons were never the problem at all.