It all depends on the period and the kind of science or art. Not easy to explain a profession in which people get PhDs in discussion note online. In the end, discovering connections comes down to documentation, but what counts as documentation varies by topic and period and region. Take the history of mathematics, which, beyond arithmetic, evolved early on mostly in application to astronomy. When sets of astronomical figures expressing the apparent motion of heavenly bodies in terms of degrees show up in one set of sources, and then the exact same figures, in the exact same units of measurement, which could not be hit upon coincidentally with the generally poor-quality or “blurry” measurements of astronomical instruments in premodern times, show up in some relatively distant place at a later time, the chances are about 100% that these numerical parameters were transmitted indirectly by sources and intermediaries that are now lost or not yet found. I don’t know if that makes sense, given my brief explanation, but basically when complex numbers line up exactly, you can be pretty sure there are connections. (An outdated but highly readable take on this kind of thing is Otto Neugebauer’s book The Exact Sciences in Antiquity.)
The same applies to game method lineages. As people in this discussion have pointed out, it’s likely that game-players in different places and times are going to come up with the same relatively finite number of things to do with 2d6, making 2d6 methods less meaningful as a marker of lineage (though not meaningless when most others are using 3d6 or 1d20 or 1d100). On the other hand, if you have a specific template, such as one in which each player is supposed to come up with one primary descriptive trait, two secondary descriptive traits, and one disadvantage, not measured with numbers but ranked as primary and secondary, converted to numbers of d6s just so… at that point, the chances are extremely good that the second one to appear was copying the first one, especially when the later one is just six years after the other one in a niche hobby where game designers scrutinize each others’ work. So that’s how we can see One Braincell riffing on Over the Edge, among other reasons.
In the skepticism expressed in the discussion so far, I didn’t see any specific examples of skepticism raised. I just saw a general skepticism. But I was asking if people had specific examples.
So I’ll give an example. In my blog post addendum, I threw out there that Tunnels & Trolls was at the root of Fighting Fantasy, which was behind Troika!. Maybe to some that seemed like a reach, but it’s easy to connect the dots. First of all, Troika! is obviously just the Advanced Fighting Fantasy rules cut and pasted and then tweaked a bit. The author, Dan Sell, doesn’t say so directly, so how can I be sure? He makes it perfectly clear indirectly in his intro to Troika! (in 2018, a date I had to look up because they didn’t even bother to put a date in the initial publication of that game):
I.e., he likes the Fighting Fantasy rules rather than D&D for his British brand of “old-school revival.”
As for Advanced Fighting Fantasy, probably a lot of people know that those rules were designed for solo gamebooks at first. But Ian Livingstone, one of the authors of the first Fighting Fantasy gamebook, The Warlock of Firetop Mountain, published in 1982, and of the whole FF system, was already writing in 1980 (White Dwarf 21) that spell points (used in FF and Troika!) made a better method than Vancian magic. (More here.) He cites RuneQuest there in White Dwarf magazine as one example of such a system.
But Tunnels & Trolls, along with D&D, was cited as one of the two inspirations of RuneQuest, from its first edition, through mention of its author, Ken St. Andre. This is the dedication of RuneQuest in 1978, three years after T&T and four after D&D. There were not a lot of role-playing games to take ideas from back then…
Tunnels & Trolls was the first published role-playing game to use spell points, derived from T&T by one route or another by most other magic systems outside of D&D. Any game designer in 1980 who read RuneQuest would know to look at T&T, which may be an obscure game now but was quite popular in the UK in that period.
You can also see the influence of T&T on FF with its Luck point system, not to mention the way it handles combat as a contest instead of alternating to-hit rolls.
Those interested in spell points may know that the Warlock variant of D&D rules, published in August of '75, just a few months after T&T, represented the CalTech variants of D&D developed within a year of D&D’s publication in '74, and they used “spell points” by that name. I can’t prove it, but I think it’s quite clear that Ken St. Andre in Arizona was introduced to D&D through a visitor for the LA area. The parallels between how Ken St. Andre describes his game in T&T1e and how we know players played D&D in the LA area are too great to be coincidental, such as the adoption of the name Dungeon Master before TSR did (TSR took “Dungeon Master” from California gamers). My point is that Ken St. Andre was probably not the inventor of spell points. It was one of the earliest schisms in fantasy rules design, less than a year before D&D was mass produced. These lineages are visible and documented.
So, basically, I was not making up the stuff I said out of thin air. That’s just one example. It just wasn’t the main point of my post. Often there are lines for every single dot. Not every line will be found in sources, but we can be pretty confident about a lot of them. And I don’t feel the need to recapitulate and cite all my sources every time I assert a connection. 
If others have questions about lineages you suspect or doubt, I’d be interested to hear your examples. This stuff can be fun.