So first, sparring - I don't see any conclusive evidence that Observer boosts EXP gained from sparring. Definitely it goes up while sparring, but it doesn't seem to have an effect on learn rates. The distribution of EXP gains in weapon skill from one day of sparring had an average of ~73 with a standard deviation of 40 (i.e. it was a wide distribution).
Leadership didn't do anything for EXP gain rates.
Organiser didn't have any noticable effect on how fast the organisations were finished but maybe there'd be a difference at Legendary vs Novice. Neither did it affect how many lessons were given per day. Something I did notice at the very end was that a 3-man squad was simultaneously sparring in a 1v2 match, something I've never seen before (and I look at quite a few sparring logs). Possibly this is what Organiser does - more testing is needed though I'm not sure if I'll get to it quite so fast.
So, as has been mentioned before: Lessons give +10 in Teacher/Student/Concentration and +5 in the Taught Skill for the teacher. How much students gain is what's changed by all 4 of the above skills - no matter how good the teacher is at teaching and how good the student is at learning, if the teacher doesn't know anything about the subject matter then the student can only learn ~15 EXP per lesson. This did not change even in the 3-man squad where the teacher was giving lessons to 2 students at once.
Teacher 5, Student 5, Concentration 5, Teacher's Sword 5:
Average gain per lesson: 56
Standard Deviation: 11
Teacher 5, Student 5, Teacher's Sword 5:
Average gain per lesson: 36
Standard Deviation: 4
Teacher 5, Concentration 5, Teacher's Sword 5:
Average gain per lesson: 32.5
Standard Deviation: 5.5
Student 5, Teacher's Sword 5:
Average gain per lesson: 29
Standard Deviation: 12
Teacher 4, Teacher's Sword 2:
Average gain per lesson: 25
Standard Deviation: 5.5
Teacher's Fighter 5:
Average gain per lesson: 22
Standard Deviation: 4
So, each of the 4 skills mentioned above have some weight in how much EXP is gained per lesson. But I felt something wasn't quite right, S3b and S3c had fairly consistently different gain rates in Sword demonstrations. Then
this page came into my memory. S3b had great analytical ability but S3c had great focus. Maybe that explains why S3c has better gains overall from demonstrations.
This is a tiny handful of data. Science (and thus, !!SCIENCE!!) wants cross-checking and further statistics (more data points) to consolidate these existing conclusions. Someone could probably try fiddling around in Runesmith or the raws to make sure all the attributes are equalised to make this a fair test.
Next I will investigate how live training (against animals) gives out EXP.
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Charge + Stab
+6 Wrestling
+13 Sword
+20 Fight
Charge + Punch + Strike + Sword + Punch + Sword
+3 Wrestling
+22 Strike
+21 Sword
+62 Fight
Charge + Slash
+3 Wrestling
+17 Sword
+44 Fight
Punch
+11 Strike
+11 Fight
Slash
+11 Sword
+11 Fight
Slash
+14 Sword
+14 Fight
Sword Pommel
+11 Sword
+11 Fight
Slash
+17 Sword
+17 Fight
Charge + Stab
+3 Wrestling
+13 Sword
+28 Fight
Stab
+11 Sword
+11 Fight
Thus a steady stream of live combat training for an embark teacher/manager in the early years of a fort might be the most beneficial for good organised training later on. I'm going to make a fort to test this out.