[ColonelSandersLite]

So here's some preliminary results and a few notes:

sub 1 finished patrol
   0kts, Simple Stationary Baseline
   Radar, SJ-1 detections 15087/30000, 50.29%
   Radar, SJ detections 10269/30000, 34.23%
   Hydrophone, JP detections 9504/30000, 31.68%
   Visual, Day detections 6105/30000, 20.35%
   Hydrophone, WCA detections 5802/30000, 19.34%
   Visual, Night detections 3957/30000, 13.19%

sub 2 finished patrol
   10kts, Back and forth accross the whole lane
   Radar, SJ-1 detections 19939/30000, 66.46%
   Radar, SJ detections 14324/30000, 47.75%
   Hydrophone, JP detections 13301/30000, 44.34%
   Visual, Day detections 8757/30000, 29.19%
   Hydrophone, WCA detections 8347/30000, 27.82%
   Visual, Night detections 5688/30000, 18.96%

sub 3 finished patrol
   10kts, Back and forth accross the whole lane minus 13.5 miles on each side.
   Radar, SJ-1 detections 21707/30000, 72.36%
   Radar, SJ detections 15563/30000, 51.88%
   Hydrophone, JP detections 14502/30000, 48.34%
   Visual, Day detections 9719/30000, 32.40%
   Hydrophone, WCA detections 9271/30000, 30.90%
   Visual, Night detections 6399/30000, 21.33%

sub 4 finished patrol
   10kts, Back and forth 13.5 miles.
   Radar, SJ-1 detections 20659/30000, 68.86%
   Radar, SJ detections 14885/30000, 49.62%
   Hydrophone, JP detections 13859/30000, 46.20%
   Visual, Day detections 9322/30000, 31.07%
   Hydrophone, WCA detections 8880/30000, 29.60%
   Visual, Night detections 6220/30000, 20.73%

sub 5 finished patrol
   10kts, 13.5X13.5 mile box.
   Radar, SJ-1 detections 18074/30000, 60.25%
   Radar, SJ detections 12638/30000, 42.13%
   Hydrophone, JP detections 11600/30000, 38.67%
   Visual, Day detections 7528/30000, 25.09%
   Hydrophone, WCA detections 7124/30000, 23.75%
   Visual, Night detections 4737/30000, 15.79%

sub 6 finished patrol
   10kts, 13.5X13.5 mile upright hourglass.
   Radar, SJ-1 detections 18399/30000, 61.33%
   Radar, SJ detections 13084/30000, 43.61%
   Hydrophone, JP detections 12234/30000, 40.78%
   Visual, Day detections 8403/30000, 28.01%
   Hydrophone, WCA detections 8023/30000, 26.74%
   Visual, Night detections 5799/30000, 19.33%

sub 7 finished patrol
   10kts, 13.5X13.5 mile sideways hourglass.
   Radar, SJ-1 detections 18015/30000, 60.05%
   Radar, SJ detections 12295/30000, 40.98%
   Hydrophone, JP detections 11511/30000, 38.37%
   Visual, Day detections 7954/30000, 26.51%
   Hydrophone, WCA detections 7605/30000, 25.35%
   Visual, Night detections 5683/30000, 18.94%

sub 8 finished patrol
   10kts, wide box.
   Radar, SJ-1 detections 18654/30000, 62.18%
   Radar, SJ detections 13388/30000, 44.63%
   Hydrophone, JP detections 12504/30000, 41.68%
   Visual, Day detections 7978/30000, 26.59%
   Hydrophone, WCA detections 7202/30000, 24.01%
   Visual, Night detections 5037/30000, 16.79%

sub 9 finished patrol
   10kts, wide upright hourglass.
   Radar, SJ-1 detections 19759/30000, 65.86%
   Radar, SJ detections 14425/30000, 48.08%
   Hydrophone, JP detections 13558/30000, 45.19%
   Visual, Day detections 9774/30000, 32.58%
   Hydrophone, WCA detections 9407/30000, 31.36%
   Visual, Night detections 7244/30000, 24.15%

sub 10 finished patrol
   10kts, wide sideways hourglass.
   Radar, SJ-1 detections 20349/30000, 67.83%
   Radar, SJ detections 15110/30000, 50.37%
   Hydrophone, JP detections 13892/30000, 46.31%
   Visual, Day detections 8255/30000, 27.52%
   Hydrophone, WCA detections 7686/30000, 25.62%
   Visual, Night detections 4649/30000, 15.50%

While I haven't fully crunched the numbers yet, some preliminary notes:

I ran the simulation a few times and compared results. Maximum deviation seems to be 1% with about 0.5% being more typical. I will increase the number of tests by a couple of orders of magnitude when I'm fully happy with all of it to reduce error. That will take a while to run though.

There was a general trend for detection odds to go up with sub speed (multiple subspeeds not shown here) in a nonlinear fashion. For example, going from speed 0 to speed 1 might yield a 0.75% increase, but going from 15 to 16 might yield a 3% increase. There is certainly a point where decreased loiter time, causing a reduction in total targets to detect, will cut into total number of detection. I haven't done any math on this yet, but soon.

With shipping going both ways, adding a north/south component to the patrol has decreased odds of detection in all cases with one unusual exception. The upright hourglass pattern has better odds of detecting targets with some of the games more close range sensors. I ran it 3 times to be sure it wasn't some kind of statistical anomaly.

With the exception of a stationary submarine, Slower target speeds increase the odds of detection while faster target speeds decrease the odds of detection.

Movment perpendicular to the targets course seems to increase the odds of detection up to a point. Past this point, such movement seems to decrease odds of detection. I need to do more data sifting to be sure, but I suspect that each sensor and sub speed combination has an optimum distance that this occurs. Without diagraming it, it would seem to have something to do with the rate at which a target can traverse an area you have just searched. (I.E. knowing where targets cannot be, as mentioned above)

Originally Posted by CaptBones

There are many variables that we don't have in the game, such as multiple sensors with different detection probabilities for different types (sizes) of targets under various weather (signal propagation) conditions.

A lot of that actually is in the game but it tends to be subtle enough that its effects aren't noticed. The most obvious examples are hydrophones and how rough the sea is and watch crew and light level. Target aspect has an effect, and I have noticed that some targets can be detected further away than others.

Good posts though.