ED Astrometrics: Maps and Visualizations

It's not perfect of course, since there's no way to estimate how many more stars may have numbering higher than those that are known. But I figure that will mostly average out, and I just need a ballpark estimate of how thoroughly explored each area is.
In fact this is a well-studied statistical problem, known since WW2 as the German Tank Problem. For these purposes you can get away with the simple unbiased estimator for the maximum value in an unknown sequence, N̂ ≈ m + m/k - 1, where m is the highest number seen in the sequence, and k is the number of samples. So e.g. if a given boxel has 5 systems in the database, and the highest number is 20, then you can estimate that there are about (20 + 20/5 - 1) = 23 systems in that boxel.

Of course the estimate is fairly meaningless if you have only one or two systems seen (the linked article talks about confidence intervals, which get quite large for very small k), but the nice thing about it being an unbiased estimate is that the errors really will wash out when averaged over a bunch of sparsely sampled boxels.

Even so, I can already say that the saturation map you're producing feels generally correct. At least the places I've been that are red were places where it felt like there were very few untagged systems - e.g. when I was there after DW2 I was surprised at how thoroughly the far western Abyss was already explored.

Instead maybe I should assume exploration is 100% at Sol, and average in a gradient from there, fading out to zero effect at around 600 ly or so. Everything within 500ly seems pretty reliably tagged these days.
Agreed, it's extra headache for no gain to even try the calculation in the Bubble. It's a royal jumble of hand-placed systems and sectors, and it's all fully tagged anyway. I'd probably not bother doing the computation within 500 ly of Sol, and then kick in a gradient that falls to zero at about 1000 ly. That would keep the vast majority of the weird boundary issues and non-procgen systems safely out of consideration.
 
Yeah, it's really simple actually. I'm working out the combination of boxel system number sequences and looking for gaps. For instance, if we know of system numbers up to 100 within a given boxel (of whatever size/masscode), I can scan from 0-100 and see how many of those names are missing, and give an approximate percentage that way. It's not perfect of course, since there's no way to estimate how many more stars may have numbering higher than those that are known. But I figure that will mostly average out, and I just need a ballpark estimate of how thoroughly explored each area is.

Where this completely breaks down is in the sectors where only a handful of people passed through. We don't have data on most of the boxels there, and this results in very "grainy" (noisy) results in the map. There are many arm gaps that look this way. It will improve over time as more people explore out there.

EDIT: So it's not a separate "density" calculation at all. Rather it automatically takes that into account by estimating a percentage of exploration, unlike the other maps that just plot a direct count of systems known.
Ok, that makes sense.

If it helps, Jackie Silver and I did a big survey of Phleedgoea recently, and more specifically made sure to scan the final numbered system of every boxel E and above. I did the same in Scaulua. Might be useful to have some hard numbers on stellar density just to see how they compare.

Some interesting tidbits to come out of all this. Most system numbering follows a pretty regular pattern, I believe depending on where you are in relation to the Core and the galactic plane. So in the case of Phleedgoea the number of systems in a boxel would decrease by around 3.5% as you moved 'west' (Eg. VZ-O e6 ends in 884, UZ-O in 851, TZ-O in 792, etc.) and by increasingly larger percentages as you go 'south' starting at around 6.5% from e6 to e5 and dropping as much as 32.25% from e1 to e. However there were also a significant number of boxels (around 63 I think) that had numbers 12-14x higher than expected.
 
Ah, the German Tank Problem! I knew there was a historical example that I couldn't quite think of. Awesome. But yeah, I was only going to go down that rabbit hole if it proved necessary, but the early tests of the map were showing that the concept was working as-is. As long as it gets the general point across about where it's extremely difficult to find pristine untagged systems, than I've done my job. :)
 
Some interesting tidbits to come out of all this. Most system numbering follows a pretty regular pattern, I believe depending on where you are in relation to the Core and the galactic plane. So in the case of Phleedgoea the number of systems in a boxel would decrease by around 3.5% as you moved 'west' (Eg. VZ-O e6 ends in 884, UZ-O in 851, TZ-O in 792, etc.) and by increasingly larger percentages as you go 'south' starting at around 6.5% from e6 to e5 and dropping as much as 32.25% from e1 to e. However there were also a significant number of boxels (around 63 I think) that had numbers 12-14x higher than expected.
Can confirm this (though without having calculated exact percentages) based on an ongoing D-boxel survey not far from there.
 
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