Two issues with your paradigm.

(1) What you are plugging into the function really changes the results. Are you plugging in the entire mythos, or only parts?

For example, in your Ceaser and Augustus examples you are selectively choosing a ‘factual’ picture of them, presumably leaving out stories like a baby Augustus climbing a tower when no one was looking to be found at its top staring at the sky.

If we pick and choose, something like Josephus’s story looks very close to an identity function to the events at the end of the 19th dynasty with some extremely specific details. We just need to ignore things like the claim of getting the Hyskos in Jerusalem to attack Egypt, as that detail is almost certainly false.

Presumably given the way you are discussing it, you see it necessary to evaluate the stories as a whole, which I do not (and despite that not being the convention you chose when it is convenient to what you are trying to prove vs disprove).

(2) This then feeds into the second issue, which is your sense that a greater distance between overall stories means we can’t trust sub-detail matches to be anything more than historical coincidence.

These texts are very heavily edited along the lines of “history is written by the victors.” But details that are left can be highly specific in matching against details elsewhere and help reveal what’s really going on under the layers of BS.

As a modern example, we can look at 9/11 conspiracy theories. Even though a bunch of crazy BS has been added to the history, while it in aggregate dilutes the identity between overall sets of claims and history, the part of the claims of “the two tallest towers in the US fell on Sept 11th” is very much grounded in truth and not coincidence.

There’s added benefit in taking a partial look as well, as it’s one of the only ways you can end up with testable predictions in this field.

So as an example, in the above comment regarding the Denyen being the tribe of Dan, we had two ‘coincidences’ - Dan are referred to as staying on their ships in Judges 5 and there’s Aegean style pottery made with local clay in early Iron Age Tel Dan. These might be happenstance coincidences, but if we consider the bubble of these details, we can hypothesize that if there’s something more to this identification, we might expect to find additional details in line with such an identification outside that bubble.

And indeed, in Ezekiel 27:19, the only other place the same form of Dan is used outside Judges 5, it’s in reference to Dan and the Greeks together trading with Tyre. Which fits pretty well with identifying Dan as the Denyen in Adana given the Denyen were right next to the Ahhiyawa (pre-Greeks) and the mentioned trade goods are in line with what would have been coming from that area of Anatolia.

But there’s a ton of historical inaccuracies surrounding these sections, so if we collect the Bible together in aggregate it’s not going to match pretty much anything as a historical “identity function”.

So there’s value in looking at the overlaps between multiple sources piecemeal, as if things are only random coincidence there shouldn’t be a collection of similar piecemeal details across multiple sources including emerging archeological details.

In the other direction too. If you look at the Noah story in the Bible in its entirety you might conclude that it’s a flood myth like other flood myths, much like in your comment. And yet if you look at the piecemeal details, instead it looks like a famine mythos that was reworked into a flood myth due to Babylonian influence.

So it’s more productive to look at details over the overall stories.

Make sense?