What is the average Tractatus Quality?

I'm beginning to think that, instead of discussing assumptions, it might be more interesting to list them, with variables, so that GMs can tailor the availability of books in their games. Or not, they can already do that, of course.

I'm not sure. You may be conflating success and visibility with output.

IRL, do scientist that are good at writing clearly produce more than the others? Maybe, maybe not, I don't know. But it seems to me that those that write more scientific papers, are those that engage in interesting research and want to communicate it, period.

Hum... I have trouble conveying my idea... Being good at expressing clearly what you understand about a scientific subject doesn't mean you're more interested in conveying your ideas, nor that you have more interesting things to do. That's a matter of passion, ego, and what you're working on. As I see it, the same is true about magic, although, for tractati, we can scrap the last part (although... The more a magus writes, the less he increases his arts and abilities, so the less interesting things he has to write about)

Likewise, there are a TON of people who write out there, some intensively. Only a few of them are good enough at it to become "true" authors. I don't think the guys that write piles upon piles of fan fiction write any less than any author.

I'm not sure I buy that assumption, that 50% of the books were destroyed during the Schism War. Having 50% of the magi killed, or even 50% of the covenants destroyed, does not mean that 50% of all books were destroyed.

After all, the winning magi would have looted the covenants they destroyed, not simply burned their library. Sure, part of the pretext of the Schism War was human sacrifice, but that is not being equated with infernal taint of their books on Arts. And they were practicing Hermetic Magic, so their books were as valuable as any other in the Order.

I've just finished my new version, so I'll post it in a seperate message.

One very important thing to consider is the potential for PC's to write high quality books. If you make high quality texts too hard acquire and valuable then a PC who is a good writer can produce a rare and high value resource. If Magi are expected to travel and adventure to get the books they want then those in search of knowledge should come knocking at your Covenant. If PC's have to jump through hoops to study from good sources then a great PC author should rightly expect to have needy NPC's ready to jump through the author's hoops. I think one of the reasons relatively high quality tractatus seem so cheep and easily available in covenants is to limit this path to power.

Booby traps in libraries? Fights breaking out in said libraries? Entire Diedne covenants disappearing into regio, coupled with their nominal secrecy and unwillingness to share knowledge otherwise? Then you have the Quaesitores continue the witch hunt stamping out all record of the Diedne from the official records. You don't think books wouldn't be burned or destroyed as a part of that? I think you're only looking at the Diedne side of things, and even a small portion of that. Diedne were winning the war for quite a while, until a sudden reversal of fortunes. How many covenants/books did they capture/destroy? And what happened to the captured books when the covenants that remained at the very last just simply disappeared?

I stand by my 60% reduction at the midpoint as being reasonable, based on the canonical history of the Order. There would have been extensive time before and during the open Schism (open conflict lasted for 14 years) for covenants to put booby traps into their libraries. I mean, if a a covenant is invaded, do they really want the invaders walking away with loot? What's more, it's a bit more than your 300 books (20 per Art) of Q11 and greater in existence.

Path to power is fraught with a heck of a lot of work, and quite a bit of silver. Silver for the skilled craftsmen to manufacture the book, and the resonant materials. We'll assume that for the purposes of your example, the PC covenant is just buying expensive materials, and not adventuring for them. We'l assume that this character has a Com of 3, and Good Teacher, so the base quality is Com 3 + 3 + 3 (professionals)+1 for resonant materials +3 Good Teacher. for a total tractatus quality that he can produce of 13. So that begs the question, how much does he charge to have people com read his book? And how much does he charge to make a copy and sell his book (which at this point just costs silver, so it's a silver to vis conversion scheme).

A Com +3 + Good Teacher character is geared towards teaching and writing, no doubt about it. He may be good at other things, but there are signficant opportunity costs to creating such a character. Com +3 takes 6 of the 7 available characteristic points. So he has Int +1, and his LT suffers for it, but that's ok, because he writes. But then he's kind of one dimensional to play, as well. If he wants to do other things, he has to start making tough choices. Or maybe he's Com +1 and Good Teacher, as I proposed, and he writes sound tractatus at Q10-Q11, depending on things, and does other exciting things as time permits. I'm honestly not concerned about the PC player who is geared towards writing. Eventually it will stop, and the pay off is ultimately the troupe discretion.

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%)


  • 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.


  • 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.


  • 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]

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.

I still don't buy 60%, but it's really a YMMV issue.

IMHO, if someone is threatening your life, you'll be more concerned with eliminating the threat than trapping your safe so that they also die once they've killed you.

Yes, books would get destroyed, libraries burned and knowledge purged. But applying a 60% destruction rate throughout the Order simply does not take into account that many books would have surviving copies. They may not have as good a quality as the destroyed original, lacking the resonant materials, but you can always create a new copy for which resonant materials are added back (nothing in Covenants prevents that).

But then, that's why I concentrated my efforts on simulating how many tractatus would have been authored. I leave the actual availibility up to each troupe to decide on.

Very good discussion! A few random thoughts.

I agree with Arthur that 50% of covenants lost during the Schism war does not mean 50% of books lost, but also acknowledge Jonathan's counter-point that books would have been lost from the "winning" side's libraries during the conflict. Still, I think that while 60% is not unreasonable I would go with 40% or so.

I am wondering also about the tally of lesser attrition during the Order's history. The corruption of House Tytalus would, in my opinion, do a lot to wipe out any book written by anyone even suspected of diabolism, for fear of Corruption; this would be, how much, 5% of the texts? 2%?

Then there is the 10% of the collection written in Greek. Granted that - how much is written in other languages? I could totally see many Ex Misc magi writing mainly for their own tradition, in their vernacular or "holy" languages; and many cultists doing similarly. This, too, perhaps removes another 5% from the Latin greater collection?

Another thought - all those mysteries, cults, societies, confraternities, religions.... It is very often in the interest of these organizations to amass a library of tractatus (and/or a good few summae) on a given topic - like their Cult Lore, duh, but also probably a few Arts their magic focuses on. And writing it down makes a good initiation component, too, so it's even better for bother cultists and cult. I'm not sure what effect this will have on the simulation, though. It will increase the motivation of some magi to write books, which can significantly increase the totals in the Greater Collection. But most of these books will be "secret", not widely available. And also - just how wide-spread is this? How wide-spread are cults in the Order anyway is left intentionally undefined. In short - I think this is very much a loose-end, that can dramatically increase the number of available tractatus in a given Art to initiates of cult (or thieves stealing its secrets!) but probably won't affect the overall generally "available" books total much.

Another point to consider is that some Arts are probably much more commonly written about than others. Ignem gets lots of ink; aquam less so. This is again very much a YSMV situation, however.

Last but not least - I think there would be a lot of "vain" tractatus on very minor topics, such as spell mastery of the magus' (non-core, not widely used, perhaps lost) spells, his hobbies (painting, hunting, chess...), lessons he wants to impart to others but no one really cares about (moral philosophy, etiquette, crazy cosmological/theological theories...), memories (area lore?), and so on. While magi won't write about things as often as we do in the internet era, they are still wealthy, literate people with time on their hands and big egos to go with their vast power - they will write stuff, lots of stuff, that will be far less "commercial" than a tractatus-on-art.

I also take the corebook at its word that 0 is an average (or rather, for me, median) stat.

Slightly off topic here, but I assume the rules for character creation - +7 points to apply to stats, equal numbers of virtues and flaws, etc., are rules intended for player characters. I've never felt a desire to apply them to each and every NPC. I certainly don't think that NPCs should be designed around optimal "builds", such as teaming Good Teacher up with high Com.

Not convinced by that. As far as I can remember, all the (NPC) magi that are statted out in the various sourcebooks use those same rules. Since 4th edition, I believe the intent has been to design all NPCs using the same rules as PCs. Particularly when magi are involved.

I can buy that your average peasant would have lower stats or virtues. I have more difficulty seeing that in magi.

Again, YMMV, but I've tried to base my simulation upon RAW, and RAW doesn't say that NPCs get fewer points in characteristics.

Not sure why you think NPCs shouldn't be optimized. If it's good for the PC, why not the NPC? Or do you never optimize any of your NPCs to be good at something, especially when confronting PCs in a story? The +5 Com and Good Teacher combo is going to be pretty rare, and such a character might be interesting as an NPC. He sacrificed all of his vis wealth to improve his communication... Or he was naturally communicative, but spent 30 seasons teaching his apprentice instead of 15 or so, and managed to earn the Good Teacher Virtue in the process. So now he's an even better teacher...what to do. I know, write a book! Optimized NPCs are interesting things for PCs to interact with, be it adversarially or complementary. He's good at something, the characters can use him, or enlist him as an ally or other aid, or he's an antagonist who turns the rest of the Tribunal against them with his superior oratory skills, and the fact that he writes books like nobody's business.

I've just uploaded my spreadsheet on our saga wiki here, so people can download it and play with the various parameters and assumptions. Have fun!

I'm pretty sure you're right about published NPCs but I don't feel the need to make everyone in the universe of magi equal. Some people simply have higher characteristics than others. Averaging out to 0 works for me. Averaging +7 development points works equally well but leads to a somewhat higher power level, which to me is undesirable. Having everyone come out to exactly +7 is worse than either alternative. Ditto for virtues and flaws, there's no need for everyone to come out to the same point totals.

To be clear, I'm not disagreeing with your model. I dislike the outcome but I think you take into account properly the assumptions conveyed in the recent published material and work logically from there.

I don't have a problem with optimizing story NPCs. What I mean to say is that I don't see the population of the world as being built according to optimal game "packages".

Hi there. I've been following this discussion with interest, as I'm a dozen sessions into the campaign I'm running and my players - having encountered the limits of their own covenant's library - are starting to ask very specific questions about what books they might be able to trade for.

I started working up some numbers - along similar lines to what several people on the forum have been doing, trying to figure out how many books have been written and what stats their authors might have had - and to my mind, one of the main questions is how those books get passed around. I agree that some tractati have been written with a Quality of 3, but I also assume that no one ever bothered to put out any effort to acquire copies of them. On the other hand, a tractatus with a Quality of 13 is probably worth trading for. At the other end, a tractatus with a Quality of 16 might never have copies traded to other covenants because its rarity makes it so valuable.

Being a programmer, I started writing some code designed to model all this, just a week or so back. Essentially, it generates a few core stats for hundreds of magi, then tracks them throughout their careers (removing them as they die and generating new magi as time passes) and generates books written by them. It was going to then compute values for the books (based on not only their stats, but other economic factors - e.g., a Quality 16 tractatus on Intellego is more valuable if it's the only one than if there's another one out there of the same subject and Quality) and model trades between covenants, but I didn't get that far yet. The ultimate goal was to not only generate book lists for dozens of covenants across the entire Order, but it would even produce records of how each covenant acquired their copies (e.g., covenant A might have acquired their copy in 1165 from covenant B, which traded for it with covenant C (where it was written) back in 1021.)

If there's interest, I could try to finish that up this weekend. As others in this discussion have observed, there are a LOT of assumptions that are going to vary from campaign to campaign. How many books were lost in the Schism War? What are the chances that any given book will be lost or destroyed in a given year? How many magi with a Communication of 3 or more are out there? How often are books copied rapidly (at -1 Quality) instead of copied carefully? How much trade is there between covenants located in the same Tribunal, as opposed to physically distant Tribunals? And so forth. I have to model these factors anyway, so it wouldn't be too hard to set those up to allow anyone trying out the program to choose their own settings.

Anyway, if this sounds useful to anyone, say so and I'll see if I can put something online in a couple of days.

That part is wrong, score 6 is enough for 2 tractatus.

Maybe I missed it, but it seems another point has been missed which raises the averages. Characteristic-boosting spells are in the core book. If you have Good Teacher, it's worth your while to pay for these. It may take a bit of time to see returns, but you will definitely see them. It's also worthwhile for someone with good CrMe to learn those rituals since a nice profit can be earned. So while I may not agree that such a high percentage of those with initially high Communication scores should have Good Teacher, I would expect most magi with Good Teacher to write many of their books after having attained a very high Communication.

Second, Arthur, why this focus on 11+? What I would do is focus on 10-12 to respond to the OP. How many tractatus are in that 10-12 region. I think even if you two find a balance between you, if the focus is put on this, we'll see there are a huge number of "sound" tractatus as this number is nearly double what you're reporting for 11+. And that's without the boosting rituals.


I'm thinking the number of Tractatus for spell mastery might be too low. Mastery is very powerful, and for a lot of spells very useful, some spells less so. Rituals are desirable from removing botch dice... There are over 1,000 published spells according to this list by technique. I'll have to think about this a bit more.

Good catch. The exact text regarding the authoring of tractatus is:

It is debatable whether "rounding up" means "round all fractions up". If you round all fractions up, you need only a score of 1 in an Art to write your first tractatus in an Art, and a score of 6 to be able to write your second. If you do a standard "rounding up", you'd need a score of 3 for the first tractatus, and a score of 8 for your second. Personally I prefer if the tresholds are at 3, 8, 13, etc.

It does not change my spreadsheet much -- simply replace 5, 10, 15 and so on by 3, 8, 13 and so on.

It changes the tresholds for Abilities to 1, 3, 5 and so on instead of 2, 4, 6 and so on.

I'll update my spreadsheet with the corrected tresholds, and add the assumption that "rounding up" is not "rounding all fractions up".

Actually, I mentioned as one of my assumptions in step 1 that characteristics-boosting rituals are not used much. If they are used, then of course the average quality goes up since higher Com scores become more likely. I'd probably bump up the average Com by 1 point if I wanted to reflect common usage of such rituals.

A Quality of 11 is what Covenants uses as the Quality of a sound tractatus. You'll note that in my second version of the simulation, I did not group the tractatus by Quality, but gave numbers for all of them.

Using the spreadsheet, this is easy to adjust. Simply go in the "Author Capability" tab and change the first value of the "Mastery ratio" (the other rows are linked to it) for an overall adjustment. Or you can adjust each row seperately if you prefer, for example to reflect that magi with fewer spells may have more of them mastered.

That's the nice thing about using a spreadsheet for such a simulation -- you can adjust each of the parameters as many times as you like.