Since Daniel Boggs mentioned that the Saving Throw categories are actually in one of the manuscripts Dave sent to Gary, and the fact that it actually contains a category for lasers (I hadn't realized what I saw, when reading "death ray"), I guess it's not unlikely that Dave Arneson invented the concept. Still, why did he do it like he did?
In OD&D, there is a "Death Ray", or possibly "Death, Ray" category, and a "Stone". Those are gone in AD&D, and also "Rod, Staff or Wand" have been harmonized into one, in contrast to OD&D where "Staves & Spells" and "All Wands" are different. Some of these I find puzzling.
In AD&D it feels like the categories could be described as "Physical Transformation", "Transformation again", "Magic Items", "Area Effects" and "The rest". While The first two are slightly overlapping, it at least makes more sense than OD&D.
I have a heard time figuring out how anyone could have been thinking when staves are one category and wands another. Even if these once were stat checks, it's now impossible to see which stat covered which one. In the comments I got the suggestion that when a PC encounter he should probably save vs "Rock Slide" or something to that effect, and it will be up to the DM to base it off a sensible number. I wonder if the categories are different things Dave had encountered in his Blackmoor campaign, and had noted down numbers for?
Considering Arneson and his friends had been playing wargames, I think about how saves are used in the rules I know. Often you roll morale for your troops in the same way as you roll a save in D&D or T&T, to avoid something bad happening. Also, cohesion and acceptance of orders is some mechanics I've seen. I see here at least a small suggestion the idea could have come from that background. Still no hint on if there are any system to the categories.
There are two things that bug me about all this. I would like to know what kind of thinking lies behind the original edition of D&D, and how the idea of rpg evolved. Lost knowledge is so sad. The other thing is my thirst for symmetry, rationalizing and shaving off rough edges on rules to make them run smoothly not only from familiarity. Both these annoy me in this case.
Having been reminded that T&T actually reinvented the idea of basing "saves" of the stats I'm inclined to put it back into D&D like I think of it. It can't really stop me from turn and poke those saves a bit more, though.