(January 24th, 2016)
I am not a WSJT expert and always wondered how that software was behaving under certain circumstances. For instance, what are the %decodes for ultra weak signals in the -28dB to -30dB range? What about the "shorthands", how more sensitive are they compared to complete callsign messages? What is the sensitivity penalty for not having a callsign in Call3? Does a sequence need to have a detectable signal for the "complete duration" of the sequence or a partial sequence suffices for WSJT to produce a decode? Is there any sensivity improvement if the callsign is "looked up" in the "To Radio" box? How does the average work and perform? These are the kinds of questions that have been haunted me for a while.
Since I could not find all the answers to my questions in the WSJT manual, and the info on the internet is either inexistent, incomplete or anecdotal, I decided to use an emperical approach to this issue and generate my own simulations and experiments in order to come up with some answers.
Joe Taylor has developed a very convenient simple software called "SimJT", which is specifically designed for computer-to-computer testing of the WSJT weak-signal communications program. SimJT allows to generate sequences of desired charateristics such as S/N, DT, DF, etc. and all that, in any mode such as JT65/A/B/C and CW. That is the main tool which I have employed in order to carry out the various simulations.  
The methodology employed for this experiment is simple:
1) Using SimJT, produce about "100 samples" of "CQ KK6FAH DM04" for each signal level (-19dB, -20dB, -21dB, ...... -28dB, -29dB, -30dB).
2) Feed the 100 samples of each signal level to WSJT-10 and calculate the %Decode. WSJT is set to "Aggressive Deep Search". 
3) Run the experiment above in 2 waves, the first "WITH" the callsign "KK6FAH" in Call3, and the second wave "WITHOUT" the callsign in Call3.
4) Run the same experiment but this time, with a "shorthand" message (RO in this example) instead of a message involving a callsign.
The results of the experiment described above are summarized in the graph above to the right.
If we start with the "red curve" on the graph to the right above, which is %decode recorded when the callsign is "IN" Call3.txt, we can see that WSJT-10 was able to produce decodes 100% of the time up to -26dB. The %decode drops to 94% at -27dB, and then drops sharply at -28, -29 and -30dB. At -30dB, out of the 100 samples fed to WSJT, only 4% of them produced a decode.  
The region from -27dB to -30dB is extremely interesting and provides a good demonstration that "1 dB" can make a significant difference in the probability of producing a successful decode in weak signal communications. In addition, the graph also shows that the operator "Patience" itself is also a big factor, where if an EME practitioner is patient enough, the chances of producing a decode will increase sharply. For instance, if a signal is consistently at -29dB, it will take in average 3 sequences before WSJT will produce a decode. Patience is everything in EME!
In addition, the typical variations in the EME signals due to libration and scintillation effects should yield a sequence or a portion of a sequence where the signal will get strong enough and for long enough to cross the "critical threshold" of low %decode probability and will eventually get in a signal strength territory that will be more likely to produce a decode. For instance, one can imagine that a signal incursion in the -25dB to -26dB range for several seconds due to libration would significantly increase the chances of producing a decode. If one is patient enough, that kind of incursion should occur at some point in time.     
The "gray" curve represents the shorthands. Not surprisingly, due to the simpler nature of the shorhand messages, the sensivity of these is far greater. Even at -30dB, shorthands were successfully decoded 96% of the time. This means that if a QSO succesfully passes the initial CQ and "OOO" phases, the QSO will get much easier during the RO and RRR phase and the back and forth is most likely going to result in a successful QSO.
The "blue curve" in the first graph on top of this webpage represents the exact same simulation, but this time, when the callsign (KK6FAH) is NOT in Call3.  
At -20dB, the 100 samples were decoded 100% of the time. This figure drops to 92% decodes at -21dB and down to only 22% decode at -22dB! At weaker signals, the %decodes drop to 0%!
One mitigation functionality to this massive loss in sensitivity is the "AVERAGE" feature in WSJT. It was observed that even if a serie of sequences did not produce an individual decode, the average information generated by the integration of multiple sequences will provide enough information to produce a decode which will show up in the "AVERAGE BOX".   
The number of sequences that are necessary to produce a decode in the average box is obviously dependant on the signal strength and is summarized in the graph to the right. For instance, in the experiment that was run, at -25dB, per the first graph on top, 0% individual decode was produced when the callsign was NOT in Call3, and per the graph to the right, after 5 individual sequnces, a decode finally registered in the average box.
The moral of the story is: do everything you can to have the most updated information in your Call3 file!
What is the impact and potential benefit of having the callsign of the station of interest "looked up" in the "TO RADIO" box? I reran the %decode experiment on the -29dB samples after the callsign had been looked up in the "to radio" box and NO decode advantage was recorded where the %decodes remain at 33%. As long as the callsign is in Call3, the probability of decode will stay the same.
This question had been puzzling me for a while. For this particular experiment, I fed WSJT with a sequence at -25dB for the first 35 seconds and then, I "cut" the feed for the remainder of the sequence and observed if a decode was produced. A video of the experiment in question is available to the right. If we count the 2.5 DT, the actual length of the signal feed was 35 sec-2.5sec = 32.5 sec.  
The results are unequivocal: YES, a decode can be obtained even with only a partial sequence. I also did the same experiment with a "shorthand" (RO) at -30dB and a feed of only 20 seconds. That was sufficient to produce a decode. 
The ramifications of this are very significant! That is, even if a signal is let's at -32dB and too weak to produce a decode, if the EME practioners attempting the QSO are patient enough, eventually, the impact of libration should produce a temporary strengthening of the signal that may be strong enough and may last long enough to produce a decode. In other words, with enough patience, it is possible to wait for a favorable "wave" and litterally ride on it!
Based on the initial results of the moon echo project, the typical fluctuation of an EME signal has a standard variation of about 2dB. Practically speaking, this means that the EME signal will vary by +/- 2dB 66% of the time, and 95% of the time (2 sigma), the signal will be contained within +/- 4dB. The 3 sigma value represents 99.7% of the time at +/- 6dB. Signal strengthening and weakening greater than 6 dB is possible but less frequent. The morale of the story is: with enough patience, a QSO that may seem impossible may become probable if the parties working on it show enough determination...
The serie of experiments described above really helped me better understand how WSJT behaves.
Stay tuned!
***WARNING: For Best Resolution, it is critical to select 720p HD resolution in the youtube "settings" at bottom right of the player. The 360p default setting won't yield good enough resolution to see the details. It will take several seconds before the High Resolution kicks in, so you will need to restart the video from the beginning when the High Resolution is active and select to view the video in "Full Screen Mode" for best experience...***