Ok, I've just finished my new simulation for the number of tractatus that would have been authored during the existence of the Order. I'll describe my assumptions at each step. This time I used an Excel spreadsheet, to reduce the chance of mistakes.

Note that this pool of tractatus represents what has been written. This would then be reduced by attrition (books lost or destroyed), understandability (language it is written in) and accessibility (can you get your hands on a copy).

Step 1: Author Quality

Author Quality is the term I use to describe the magus' Com score and the presence of the Good Teacher virtue. The distribution that I used was as follow: -3 (3%), -2 (10%), -1 (20%), 0 (20%), +1 (25%), +2 (15%), +3 (5%), +4 (1%), +5 (1%)

Overall, 5% of magi with non-negative Com score have the Good Teacher virtue.

This means the Author Quality is distributed as follow: -3 (3%), -2 (10%), -1 (20%), 0 (19%), +1 (23.8%), +2 (14.3%), +3 (5.8%), +4 (2.2%), +5 (1.7%), +6 (0.3%), +7 (0.1%), +8 (0.1%)

Assumptions:

- Assumption 1.1: As previously commented on, I do not believe that there would be very many magi with horrid Com scores (-4 or -5), simply because it is unlikely that those Gifted individual would be picked to become apprentices. For a magus to recognize that a potential apprentice is smart requires a certain degree of communication.
- Assumption 1.2: Only characters with non-negative Com score will have the Good Teacher virtue. Some of those with negative Com score may have the virtue, but are undistinguishable from characters with a slightly positive Com score.
- Assumption 1.3: Characteristics-boosting ritual are not used very often. If they are used, the average Com score would rise significantly.

Step 2: Author Capability

This is how much knowledge the author has to impart.

In the Hermetic Arts, I assumed that a typical magus would have 5 Arts in which he would be able to scribe 1 tractatus (thus a score from 1 to 9), and that the number of Arts in which he could write an additional tractatus was divided by 2 each time. This gave me a capability to write Arts tractatus as follow: 1 tractatus (5 Arts), 2 tractatus (2.5 Arts), 3 tractatus (1.25 Arts), 4 tractatus (0.625), 5 tractatus (0.3125), 6 tractatus (0.15625), 7 tractatus (0.078), 8 tractatus (0.039). This leaves, on average, 5 Arts with scores of 0, in which the magus is unable to write anything. I multiplied the value by the number of tractatus per Art to obtain the total number of tractatus that the magus can author: 19.6

I did the same for Abilities, using the appropriate tresholds (2, 4, 6, 8, 10, 12, 14 and 16) but starting with 4 scores at 2 and dividing by 2 for each treshold. This gave me a capability to write Abilities tractatus as follow: 1 tractatus (4 Abilities), 2 tractatus (2 Abilities), 3 tractatus (1 Ability), 4 tractatus (0.5), 5 tractatus (0.25), 6 tractatus (0.125), 7 tractatus (0.0625), 8 tractatus (0.03125). Again I multiplied the value by the number of tractatus per Ability to obtain the total number of tractatus that the magus can author on Abilities: 15.6

For Spell Masteries, I started with probabilities that your typical magus would know a certain number spells: 5 spells (1%), 10 spells (10%), 15 spells (15%), 20 spells (20%), 25 spells (25%), 30 spells (15%), 35 spells (10%), 40 spells (4%). I then applied a ratio of 5% to determine how many of those spells would be mastered. This gave me a potential of 9 mastered spells per magus.

Assumptions:

- Assumption 2.1: Average knowledge of a magus 50 years past Gauntlet.

Step 3: Number of Magi

How many magi has there been throughout the existence of the Order? That's a whole subject all by itself, so I've tried to keep it relatively simple. I won't go into the details, but I was surprised by the number I got, which was higher than I expected: 8204.

Assumptions:

- Assumption 3.1: Current size of the Order is about 1000 magi. (I got 1192 in the end of my calculations.)
- Assumption 3.2: Availability of Gifted children has been diminishing in recent years. (I reduced the number of apprentices a magus trains in a 50-year period to 1.25)
- Assumption 3.3: Magi on average live about 100 years (this is lowered by early fatalities). The attrition rate of old magi is 1% per year, while it is 0.5% for new magi. In addition to that, the Schism War killed off 50% of the Order.
- Assumption 3.4: 50% of the magi were killed during the 50-year period of the Schism War.

Step 4: Books Authored

Here, I used three factors to determine how many books each magus would author during his life. First was his Author Quality. It was used to establish the other two factors, which are the Willingness rate and the Proclivity rate.

Willingness determines his interested that magus is in authoring books. I used the following formula: 25% + (3% x Author Quality).

Proclivity determines how much of his potential he actually writes. I used the following formula: 10% + (2% x Author Quality).

For his Author Quality, I multiplied the author capacity (step 2) with the number of potential authors (step 3), his willingness and his proclivity to obtain the number of tractatus authored in each type of tractatus.

This gave me the following table:

[table][tr][th]Author Quality[/th][td]-3[/td][td]-2[/td][td]-1[/td][td]0[/td][td]+1[/td][td]+2[/td][td]+3[/td][td]+4[/td][td]+5[/td][td]+6[/td][td]+7[/td][td]+8[/td][/tr]

[tr][th]Willingness[/th][td]10%[/td][td]15%[/td][td]20%[/td][td]25%[/td][td]30%[/td][td]35%[/td][td]40%[/td][td]45%[/td][td]50%[/td][td]55%[/td][td]60%[/td][td]65%[/td][/tr]

[tr][th]Proclivity[/th][td]4%[/td][td]6%[/td][td]8%[/td][td]10%[/td][td]12%[/td][td]14%[/td][td]16%[/td][td]18%[/td][td]20%[/td][td]22%[/td][td]24%[/td][td]26%[/td][/tr][/table]

Step 4: Quality Improvements

I established another matrix to determine how likely it was that the various improvements would be applied to a given tractatus. These are skilled mundane specialists (scribe/illuminator/binder), purchased resonantmaterial, story resonant materials, and clarification.

Although I tweaked them a bit based on the Author Quality, it wasn't by much. I assumed it would be unlikely that a poor book would ever be clarified, but on the other hand I figured a low-Com magus was more likely to obtain story resonant materials. I also figured that a good author was less likely to be without any form of mundane support, since efforts would probably be taken to capitalize on his superior work.

Essentially, though, most books would have +2 to +5 applied to them (about 20% chances of each value). With 0 and +6 getting only values between 0% and 5%, while +1 got 7% to 15%.

Step 6: Putting it all together

Finally, I assumed that only 5% of the tractatus would be Commentaries, granting a further +1 bonus to Quality.

This gave me the following table:

[table][tr][th]Tractatus Quality[/th][th]Arts[/th][th]Abilities[/th][th]Spell Mastery[/th][/tr]

[tr][td]0[/td] [td]1[/td] [td]1[/td] [td]0[/td][/tr]

[tr][td]1[/td] [td]22[/td] [td]17[/td] [td]10[/td][/tr]

[tr][td]2[/td] [td]50[/td] [td]40[/td] [td]23[/td][/tr]

[tr][td]3[/td] [td]144[/td] [td]115[/td] [td]66[/td][/tr]

[tr][td]4[/td] [td]305[/td] [td]244[/td] [td]140[/td][/tr]

[tr][td]5[/td] [td]539[/td] [td]431[/td] [td]247[/td][/tr]

[tr][td]6[/td] [td]744[/td] [td]596[/td] [td]342[/td][/tr]

[tr][td]7[/td] [td]872[/td] [td]698[/td] [td]400[/td][/tr]

[tr][td]8[/td] [td]842[/td] [td]673[/td] [td]386[/td][/tr]

[tr][td]9[/td] [td]695[/td] [td]556[/td] [td]319[/td][/tr]

[tr][td]10[/td] [td]448[/td] [td]359[/td] [td]206[/td][/tr]

[tr][td]11[/td] [td]247[/td] [td]197[/td] [td]113[/td][/tr]

[tr][td]12[/td] [td]132[/td] [td]106[/td] [td]61[/td][/tr]

[tr][td]13[/td] [td]63[/td] [td]50[/td] [td]29[/td][/tr]

[tr][td]14[/td] [td]16[/td] [td]13[/td] [td]7[/td][/tr]

[tr][td]15[/td] [td]6[/td] [td]5[/td] [td]3[/td][/tr]

[tr][td]16[/td] [td]2[/td] [td]2[/td] [td]1[/td][/tr]

[tr][td]17[/td] [td]0[/td] [td]0[/td] [td]0[/td][/tr][/table]

Final Notes

I want to stress again that this is the number of tractatus that would have been authored, not what would be available at this time of the Order, nor what would be available to a typical covenant.

All my calculations are in an Excel spreadsheet. So if people are interested in the spreadsheet, I'll arrange to have it available somewhere.