Scan probe mathematics

It appears I am in a mood for mathematics and spacetime geometry lately. This time, I try to answer my own curiosity as regards scanning down anomalies. Doing that in Sanctified Vidette has taught me a lot about the connection between scan probe strength, scan deviation and how fast one can scan down an anomaly. It is a long log entry, but it will serve me well to write down in detail what I learned.

1/ Astrometric pinpointing 

I believe an example works best to explain this. Let us stay that you start out as usual with your scan probes at 8AU, centered on the current guess for the anomaly's position. The scan will refine the position of the anomaly. The base number goes one notch down: so the maximum deviation between the indicated position after the scan and the real position goes down to at least 4AU.

The Anathema is one of the ships boosted for scan deviation, giving you a reduction factor of 0.75 , which brings the maximum deviation after scanning down to 4 ✕ 0.75 = 3AU. 

If you've installed a pinpointing array I, you get another factor 0.9 (it is 0.8 for the T2 version, but let us stick to T1). Combined with the Anathema, you now have 3AU ✕ 0.9 = 2.7AU maximum deviation.

You have trained astrometrics perhaps to level IV, it gives you another factor (1-0.05✕level) = 0.8, so now we're at 2.7AU ✕ 0.8 = 2.16AU 

Finally, say you have trained astrometric pinpointing to level III. This corresponds to yet another factor (1-0.05✕level) = 0.85, bringing the maximum deviation down to 2.16 ✕ 0.85 = 1.84AU. 

Hurray! You can skip right down to 2AU for your next scan, since the number dropped below 2. 

In all of the above, I assumed that the signal strength (the percentage shown each time you scan the signature) is still at 0%. If you get it to say, 55%, this gives you an additional factor (1-0.55)=0.45, and you get down to 1.84 ✕ 0.55 = 0.83 , which is great news because now you can skip three notches and go straight to 1AU for your next scan.

2/ Scan probe sensor strength

You need to bring the signal strength up to 100% before the anomaly becomes warpable. This is where your probe strength comes in - that is the number you see when you hover over the scan probe loaded in the probe launcher. It can be boosted by the astrometric rangefinding skill, a scan rangefinding array, a gravity capacitor rig, ship bonuses, some boosters and implants, and better core scanner probes. Note that for combat probes, the number is halved but for the table below, you should double it, as if it is a core scanner probe.

The table below gives you, for anomalies of class I to V, as a function of the probe strength, the deviation you need to get down to in order to get to 100% signal strength on your next scan and thus lock down the anomaly.

probe strength	Level I	Level II	Level III	Level IV	Level V
40	0.46976	0.23488	0.11744	0.05872	0.02936
50	0.5872	0.2936	0.1468	0.0734	0.0367
60	0.70464	0.35232	0.17616	0.08808	0.04404
70	0.82208	0.41104	0.20552	0.10276	0.05138
80	0.93952	0.46976	0.23488	0.11744	0.05872
90	1.05696	0.52848	0.26424	0.13212	0.06606
100	1.1744	0.5872	0.2936	0.1468	0.0734
110	1.29184	0.64592	0.32296	0.16148	0.08074
120	1.40928	0.70464	0.35232	0.17616	0.08808
130	1.52672	0.76336	0.38168	0.19084	0.09542
140	1.64416	0.82208	0.41104	0.20552	0.10276
150	1.7616	0.8808	0.4404	0.2202	0.1101
160	1.87904	0.93952	0.46976	0.23488	0.11744
170	1.99648	0.99824	0.49912	0.24956	0.12478
180	2.11392	1.05696	0.52848	0.26424	0.13212
190	2.23136	1.11568	0.55784	0.27892	0.13946
200	2.3488	1.1744	0.5872	0.2936	0.1468

So, what this means is that if you have a level I anomaly, and your scanner probes' strength is at 70, you need to bring down the probes to the 0.5AU notch to get to 100% signal strength with certainty - the 1AU notch will not be good enough. However, if you have 90 strength, you only need to be at 1AU resolution to get the anomaly with certainty. If you are all the way up to 180, you do not even need to get closer than 2AU before locking it down. Combining good pinpointing (as explained above) with probe strength of at least 170-180 is the "secret" to scanning down level I anomalies in just two rounds of scanning, first 8AU and then 2AU.

Now note that some numbers here are even smaller than your smallest 0.25AU resolution. You can get those by either getting lucky on your positioning, or by tightening the probe formation closer (control-scroll down in the solar system map).