The True Value of an Affinity?

Games Discussion Ars Magica
1

Starting a new topic since this was pulling another one off topic quickly...

Just how much bonus does an Affinity provide on average? While some say 50%, this requires ignoring the rule about rounding. Some claim using the rounding is gaming the system. To those critics, I have two points. First, that is how the rules work and I only want to base this on the actual rules. Second, even if you heavily game the system with and Affinity, the Affinity will still not nearly provide the benefit of Virtues like Book Learner. Book Learner essentially gives you half an Affinity for any Ability/Art when you learn from a book, which is where a large portion of a magus's experience comes from. Let's say the magus earns 1/3 of his experience from books. Then, roughly, the magus gets an extra 1/4 (+3 is roughly a quarter of a typical Quality) of 1/3 of his experience - an extra 1/12 of his experience - in every Art and many Abilities. So Book Learner provides 1/6 of the Affinity where you would have placed the Affinity, plus 1/6 an Affinity in every other Art and many other Abilities. Overall, even accounting for a large portion of experience being placed in the Art/Ability with the Affinity, Book Learner is much more valuable than an Affinity. Thus even heavily gaming Affinity keeps its value under that of some other Minor Virtues and so shouldn't be unacceptable.

All this being said, let's see what this rounding really does.

The first question is how many sources are odd? There are several sources where the Quality is effectively random. We have books, teaching/training, realia, Vis study. Meanwhile exposure, adventure, and practice can be split up as desired and so an odd source Quality can be guaranteed. Due to the separation of practice and Vis study the value shifts a little between Abilities and Arts. For now I'm going to assume we're dealing with Arts, recognizing and Affinity with an Ability will be even better. I'm also going to ignore the potential use of correspondence to make random odd Qualities become non-random.

The second question is what fraction of the magus's seasons are spent gaining experience in any one of these ways? This is highly saga dependent. However, I think we can make some reasonable estimates. I've played in many sagas with many different players and SG's, and they've all been reasonably similar in this regard. Teaching/training, Vis study, and realia tend to be used far less often than books. Since those are all random, too, we can lump them in with books for consideration here. Meanwhile, I would estimate a magus spends about 1 season per year adventuring. Based upon service to covenants and their own need to develop spells and items, there seems to be a balance between seasons in the lab and seasons spent studying. So as a rough estimate a year consists of 1 season of adventure, 1.5 seasons of lab work, and 1.5 seasons of study. Variations here will of course skew the numbers, but this should provide a good starting point.

The third question is how much experience is earned in a typical Art in a season? For the adventure you're limited to 5, so you're best off choosing 1, 3, or 5. On average that is 3 experience placed in the Art for 5 experience after the Affinity. For the lab work you're best off choosing 1 or 3 (correspondence can push the season of exposure from 2 to 3). On average that is 2 experience placed in the Art for 3.5 experience after the Affinity. For books I believe 10 to 11 is typical of Qualities, especially since you probably won't spend much time with a low-level summa for an Art in which you have an Affinity. On average that is 10.5 experience placed in the Art for 16 experience after the Affinity.

Now let's put that all together. (1x5+1.5x3.5+1.5x16)/(1x3+1.5x2+1.5x10.5)=34.25/21.75=1.575. So the Affinity gives +57.5% on average to an Art.

Just to take a quick look at the Ability and practice side of things, many Abilities that are practiced are usually either trained, taught, or practiced. If you have an Affinity, trainers/teachers become scarce much more quickly, so practice becomes a larger part. Also, grogs and the like rarely do correspondence, so I'll drop that from exposure. I'll assume ratios of 1 adventure : 1.5 exposure : 1 practice : 0.5 training. Practice usually doesn't provide Qualities above 4, though there are a bunch of instances of 5 or more. I'll leave 4 as the cap for now, though. You're best off choosing 1 or 3. So on average that is 2 experience placed in the Ability for 3.5 experience after the Affinity.

Now let's put that all together. (1x5+1.5x2+1x3.5+0.5x16)/(1x3+1.5x1+1x2+0.5x10.5)=19.5/11.75=1.660. So the Affinity gives +66.0% on average to such an Ability.

So it seems like an overall average somewhere around +60% is pretty accurate. Sure, you could see this drop as low as +50% or as high as +100%, but those are extreme cases. Also, do note that I did not include apprenticeship/creation since this can skew things heavily in either direction depending on which character creation method you use and depending on how much is placed in the given Art/Ability during apprenticeship/creation.

Chris

2

{BTW, Affinity loses terribly to Puissant Ability except for Craft/Profession/MT (30+ seasons of Exposures) or those worth pushing above 10 (MT again).}

Now, the problem I have with this overly complex method is that it hides the fact that you gain +50% + 2 xp per year at most. Sure if you spend 4 seasons in the lab and only account for the 1 xp per season you put in that Art you get +100% whereas you actually went from 8 to 12 xp overall. Sure, an average of 20xp per year in that Art/Ability might return 60%. But no matter what, you will never gain more than 2 xp per year above the 50%.

I can see why troupe would rather offer more for adventures and higher quality books than deal with the meager rounding bonus.

3

Yes, but given an amount of time using books and an amount of time in the lab, it's more efficient to put lab points towards your Affinity's Art and spend more time reading on a different Art than vice versa. Also, if you want to get higher and you are spending time in the lab, you might as well use the points, right?

We have an extreme case in one of our sagas. Affinity w/ Magic Theory, Affinity w/ Perdo, and Affinity w/ Vim I think. He is a Bonisagus doing research in PeVi. So he spends a season experimenting in the lab and corresponding with other Bonisagi. After a year he has Magic Theory +8, Perdo +8, and Vim +8. Sure, a total of 24 experience doesn't sound so hot. But when you realize he just invented four different 5th to 6th magnitude PeVi spells and now has those in his arsenal, getting 24 experience on top of it is pretty good.

Chris

4

While I agree that Puissant Ability is usually at least as good as Affinity w/ Ability, just how does Affinity w/ Ability lose terribly?

Chris

5

I've becomes lost in the math. You can only get XP from one source a season. Exposure XP while working in the lab on a project is 2XP. The most you can get is +12XP. Am I missing something.

Also just to point this out, skilled parens give +60xp. An affinity doesn't catch up with that until around level 19. If you plan to push an art over 20 an affinity makes sense. Magister in Artibus or Doctor can also be good, although only 80XP from those virtues correspond to something that you were clearly going to buy anyway.

6

Let's ignore the technicality that it's actually one type (exposure, practice, etc.) as opposed to one source. This gets us past reading 90 different summas each for one day earning 90 experience in a season. (Yes, this is valid in canon but it will also get you throttled by the SG and all the rest of the players. I would say that ties with the other most abusive thing I've come up with.)

Given that, yes, it is true that only one source gives you experience. However, in many cases the experience can be split. For this extreme case you have 1x1.5=1.5->2 (by rounding) experience in each of the three areas. That's 6 experience per season, for 24 experience per year.

Chris

7

You are assuming that books are freely available. If instead books have to be earned, then the seasons spent acquiring them (one way or another) slow down Book Learner and give more importance to other sources of learning. The most extreme case being character generation past-Gauntlet, which in theory has no provision for learning from books: Affinity works, Book Learner does not.

But perhaps the most important point about Affinity is that it stays useful when your Arts or Abilities go beyond the available summae (unless you have access to an endless supply of tractati). The true specialist knows that at some point, he will have to develop his Arts by himself, past what his forebears have written...

And finally: the true munchkin does not choose between Affinity and Book Learner, he takes both with Seconday Insight and Study Bonus on top !

8

Ugh Secondary Insight?
Take Flawless Magic instead, and any efforts at mastery will be richly rewarded.

9

A rock falls on your head and you die. Please roll up a new character.

10

I don't agree with that. You should spend time in the lab doing what you need, no more. Even with correspondences, it takes 3-4 seasons of Exposure {(2+1)1.5 = 5} to equate 1 season of reading. {35 = 15 = Q9+1, 4*5 = 20 = Q12+1} If you read until you cap your summae, you'll get there 3-4 times faster. So, do you need your nifty lab work now or can you wait until you are capped?

It comes to this: you do lab work because you need it now, or because you have no better way to advance your Art.

Nice and exceptional. That comes to {4*(2+1)*1.5 + 2 + 2 + 2 = 24}, or 50% + 2 xp per year per Affinity.

He could also have read 2 Q11+1 tractatus (of Pe/Vi/MT) and invented 2 PeVi spells for 48 xp. A perfect example of what I mean.

11

Seconday Insight is Major. Take Apt Student, Free Study and Book Leaner and keep your Major Hermetic for something useful. Sure you cannot move the xp to another Art, nothing that a few seasons of lab work won't cure. And not only do you get more on average, but 2 of those work for Abilities!

And Affinity with Art is still better than any of those 3. By the time you hit 20 you saved 70+ xp, or 23 seasons of Book Learner.

12

I think you misread. I didn't say do lab work specifically to improve. I didn't say do things you don't need in the lab. I didn't come close to saying those. I said given some amount of time in the lab, spending those points on the Affinity's Art is more efficient than spending them entirely on the non-Affinity Arts. Take a look at this case:

Given the same 40 seasons, which was was more efficient?

Yes, but that would be if he wanted to do that. What he wants to do is develop his spells. I'm not saying your method is wrong in general, but it doesn't produce what he needs: as many experiments as possible for insight. I'm just pointing out how much gain he can get while pursuing his other goals and that in this case his Affinity +% climbs quickly because it's an extreme case.

Chris

13

I'm pretty sure I said this was highly variable or dependent upon the saga, didn't I? I said I based it upon many I'd been in, and even the few where we were relatively starved for books, we still managed one or two a year.

Also, if you want general gains such as you get from Book Learner, you should assume there are many books relatively freely available to a magus. Purchasing lots of books on Artes Liberales, Philosophiae, etc. should be trivial for magi. As such, being able to use Book Learner regularly should be relatively trivial. Maybe this is in areas you don't care about. Fine, but it doesn't diminish the value of Book Learner in general.

Yes, though the same is generally true of studying Arts from Vis or from teachers: they cost. Books are generally a cheaper way to go.

Yes. That system is essentially completely incompatible with the advancement rules. It's a system that gives you 0 experience for 3 seasons of lab work and 1 season reading a Q11 tractatus. What happened to the 6 experience from exposure and 11 experience from the book? Of course, as I pointed out with apprenticeship, this is under the assumption that you use the quick method as opposed to the difficult method.

Chris

14

You might say it's an hyperbole, but... How many seasons of odd Quality does Affinity needs to match Puissant?

  • 50 xp = score 4 : Puissant 6 = 105 xp; Affinity = 75 xp; 60 seasons = impossible
  • 75 xp = score 5 : Puissant 7 = 140 xp; Affinity ~ 112 xp; 56 seasons ~ 46 * 1 xp + 10 * 3 xp
  • 105 xp = score 6 : Puissant 8 = 180 xp; Affinity ~ 157 xp; 46 seasons ~ 16 * 1 xp + 30 * 3 xp
  • 140 xp = score 7 : Puissant 9 = 225 xp; Affinity ~ 210 xp; 30 seasons ~ 25 * 3 xp + 5 * 13 xp
  • 180 xp = score 8 : Puissant 10 = 275 xp; Affinity ~ 270 xp; 10 seasons = easy

Hitting score 10 will take more than 10 seasons, you can use many odd Quality Source to get there. You can tell me 15-23 xp is nothing, being 1 score behind is nothing. But except for lab work, where will you spend 30+ seasons of Exposure?

As I believe this goes woosh above most list members (why should you care about number crunching anyway), lets make a story for MT9

I have Affinity with MT, you have Puissant MT. We studied for a little more than a year, you mastered MT faster than I did.

  • Puissant score for 5 seasons of 13 xp = 3, 4, 5, 6, 6
  • Affinity score for 5 seasons of 20 xp = 2, 3, 4, 5, 5
    Then it was time for some lab work: we spent years in the lab using our full 3 xp of Exposure + Correspondence. My MT stayed weaker than yours, but as the years crept by I started to catch up and finally after more than 6 years I managed to stay abreast.

Puissant had 5 seasons of Quality 13, then 25 seasons of Quality 3, for 140 xp or score 7+2.
Affinity had the same, but Q13 gave 20 xp and Q3 gave 5 xp each, for 225 xp or score 9.

Hopefully this bird will be slow enough to follow. :wink:

15

Then we agree on that. I am sure we could find an example that nets more than the 9 xp you got, but it doesn't matter.

Of course, if progressing in his Arts are secondary to experimenting... he can spend years fooling around with PeVi and not care about having 20 variations on the same spell. :wink:

16

No, that isn't correct. For this to be correct you are saying the Affinity allowed you to get there in no time.

Rather, it takes time to apply the Affinity. Roughly speaking, it would take about 12 seasons at Q10.5 to get those +70xp with books. So that would be a savings of about 11 seasons over Book Learner's 23 seasons. (It would actually save you a few more seasons with some assumed starting points that got multiplied, assuming you use the straight-forward character creation method.) The question then is have you spent more than those 11 (or maybe 13 or so) saved seasons extra in reading things outside of your Affinity. If you have, you've lost out by taking the Affinity even with your favoritism toward that one Art. How much experience have you put into Artes Liberales, Philosophiae, Magic Theory, Finesse, Penetration, Parma Magica, [Realm] Lores, the other 14 Arts, etc. from reading by the time you've brought that one Art to 20?

Yes, if you really want to excel in a single Art and get there quickly, Affinity is the way to go. However, this is only true with a true focus in the one Art/Ability. As I said in the beginning, the power of Book Learner comes from breadth.

Chris

17

Ah, this is a classic interpretation of breaking even with Affinity and Puissant. It misses a crucial point, though. At low levels it looks at when Puissant moves ahead but not at when Affinity catches up. For a large portion of the time in the middle levels you get exactly the same score with either one. At other times you are better off having taken Puissant, but during those times it makes no difference. So while Affinity loses out to Puissant, I still don't see it losing terribly. Here are the scores based on points put in without any rounding:

50-69 = Puissant 6 or Affinity 5
70-74 = Puissant 6 or Affinity 6
75-92 = Puissant 7 or Affinity 6
93-104 = Puissant 7 or Affinity 7
105-119 = Puissant 8 or Affinity 7
120-139 = Puissant 8 or Affinity 8
140-149 = Puissant 9 or Affinity 8
150-179 = Puissant 9 or Affinity 9
180-182 = Puissant 10 or Affinity 9
183-219 = Puissant 10 or Affinity 10
220-225 = Puissant 10 or Affinity 11

First, note the fraction of the time from 120 experience to 219 experience that Puissant is actually ahead. That's a spread of 100 points. Puissant is ahead by 1 point on 15 of them, or 15% of the time; 85% of the time they're even The same is true the other way around for a while above 220 experience. I wouldn't rate either one of them as winning or losing "terribly" except for experience below 69 or way above 220. Sure, one or the other is losing, but there must be a difference between losing and losing terribly.

Then we need to remember seasonal rounding was not included. Note that you get an extra 0.5 xp from Affinity for any odd source, so somewhere between 0.25 (random) and 0.5 (controlled) per season. Let's go with an average of 0.35 or so, slightly favoring random. How many seasons do you need to get to 180 experience? If it is 15 or more seasons, which is fairly likely, the Affinity surpasses Puissant a little below an input of 150 xp, not at 183 xp. How much below 150 xp? How many seasons does it take to get that 150 xp? If you start with 50, then it will still probably take around 10 seasons, so then you're looking at Affinity moving ahead around 148 xp. This also drops the amount of time between 120 and 219 xp that Puissant is 1 point ahead to just under 10% of the time. If it's something like Magic Theory that will be may be getting lots of 1-point exposure, then Affinity moves ahead a little below 120 xp instead, but that's fairly rare.

So once you've invested about 120 xp, Puissant is no better than Affinity about 90% of the time for most Abilities. Similarly, Affinity isn't that much ahead of Puissant for quite a way after 220 xp. There's a huge range where, while one might be a little better than the other, they're fairly even.

Chris

18

I know all about this. Sure, in this contrived example with years of 3xp Exposure, Affinity is 1 point behind Puissant 6 of the 25 lab seasons.

It will always take 30 seasons of odd Quality to catch up no matter what you do, why take the weaker Virtue?

Seasonal rounding was included. Lets do score 9 again:

  • 140 xp for Puissant = score 7+2
  • (140*1.5 = 210 xp) for Affinity = score 8 {15 xp short of 9}

You need 30 seasons of odd Quality to match Puissant 9.

19

No, this is precisely correct. Don't read things I didn't say.

You spend around 12 seasons reading your Art book, you will reach score 20 and get 70 free xp. In those 12 seasons of reading the same book, I only got 36 free xp. We spend the next 11 seasons reading other books, after 23 seasons of reading we both get 69-70 free xp.

Clear now?

Now, we will read more books since we want an apprentice down the line. And we would never have considered Affinity if we didn't plan on going higher than 20 in our Art. We should extend the line further to see which side of it we fall on.

20

Yet you make the same mistake below?

No, it wasn't. Read my analysis. I explicitly excluded it until that point. Only then did I start including it, and I specifically said I was doing so (which you quoted).

No. Let's be honest. Puissant 9 does not indicate exactly 140 xp. Rather it indicates 140-179 xp. This was my whole point which you said you understood. You need 30 seasons of odd Quality to match 2.5% of the time at Puissant 9. So your 30 seasons of odd Quality is what is actually required to start matching shortly into Puissant 8. You don't need those 30 seasons to match Puissant 9 97.5% of the time at Puissant 9. You don't need any (0, none) odd seasons to match Puissant 9 75% of the time at Puissant 9.

So we look at the only place after that Puissant is ahead: 180-182 xp. We look at the worst-case scenario: 180 xp. Affinity makes that equivalent to 270 of the needed 275 xp. So we need 5 more xp. That's 10 seasons of 0.5 xp bonuses from odd Qualities. Therefore 10 seasons of odd Qualities makes the catch-up point prior to 180, and that is extremely likely given. Since even without the rounding Affinity is even with Puissant down to 150, the point falls below 150. How far below 150 depends on the number of odd seasons. If we estimate exactly 10 odd seasons by the 180 point, which is probably an underestimate, it's likely there have been at least 6 odd seasons by close to 150. That brings the point where Affinity catches Puissant to 148 xp. After that Puissant will never be better than Affinity, though it will commonly be equal.

I haven't said take the weaker Virtue. You said

I disagreed with "terribly," not the losing out. I have shown pretty well that even when Puissant is ahead there is rarely a gap between them from an input of just under 120 xp onward. I also disagreed with "above 10" for losing out. I have shown pretty well that Affinity does not lose out once you've put in just under 150 xp, so it should be "above 9."

If the problem with the classical interpretation still isn't clear, let's look at an example that doesn't even use exposure. Let's say you start by placing 50 points into your Ability, which hits nice marks for both Puissant and Affinity. Let's say you get half your experience from Practice/Adventure, place 3 points into it each time, and the other half of your experience from books, half of Quality 10 and half of Quality 11. I'll do it this way: Q3, Q10, Q3, Q11, repeat. (I chose this before seeing any results below, just trying to balance out the rounding issues.)

50 = Puissant 6 or Affinity 5 (75)
53 = Puissant 6 or Affinity 5 (80)
63 = Puissant 6 or Affinity 5 (95)
66 = Puissant 6 or Affinity 5 (100)
77 = Puissant 7 or Affinity 6 (117)
80 = Puissant 7 or Affinity 6 (122)
90 = Puissant 7 or Affinity 6 (137)
93 = Puissant 7 or Affinity 7 (142)
104 = Puissant 7 or Affinity 7 (159)
107 = Puissant 8 or Affinity 7 (164)
117 = Puissant 8 or Affinity 7 (179)
120 = Puissant 8 or Affinity 8 (184)
131 = Puissant 8 or Affinity 8 (201)
134 = Puissant 8 or Affinity 8 (206)
144 = Puissant 9 or Affinity 8 (221)
147 = Puissant 9 or Affinity 9 (226) <--- catch-up point
158 = Puissant 9 or Affinity 9 (243)
161 = Puissant 9 or Affinity 9 (248)
171 = Puissant 9 or Affinity 9 (263)
174 = Puissant 9 or Affinity 9 (268)
185 = Puissant 10 or Affinity 10 (285)

So once this sample character has reached an input of 147 xp Puissant is never better than Affinity. They'll be even for quite a while, but Puissant will never be better past that point. Meanwhile, let's examine how much Puissant helped in the adventures up until that point. Puissant gave +1 during 6 of the 8 seasons and nothing the other 2 seasons. Even if 100% of these were adventure and none were practice, that means Puissant was advantageous for 6 adventures only in the character's entire career. In a short saga that will be more beneficial than in a long saga since all of those 6 seasons are basically up front.

Interestingly, if you happen to read a book just short of reaching an investment of 140 xp, then you still hit a catch-up point close to an investment of 120 xp. But that is a fringe case.

This brings me back to my original disagreements. Puissant provided +1 for a total of 6 adventures over the character's career, not even every early adventure. I'd hardly call that "terribly" far ahead. Meanwhile the catch-up point was back well within Puissant 7+2, not after 8+2 was first reached. And note that this happened after only 15 total seasons, 11 of them being of odd Quality. So we see it does not "always take 30 seasons of odd Quality to catch up no matter what you do."

So, while I agree that Puissant is generally better for most Abilities, it is only marginally better, the margin growing for shorter sagas with younger characters.

Chris