As I said, I don't think you have to push it so extremely hard. You just need a long, slow-running saga (not an infrequent scenario in my experience) and a character who'll use that ability a lot. How much is a lot? Let's say 10 rolls per session, which means about 2 sessions out of 3 will yield the 5xp. We play about once per week, so if the PC is a "regular", over a year of gaming it will trigger about 35 times, for 165xp. Midway there it's 80-85xp, and 85xp is what Puissant is worth at 7+2 (easy rule: Puissant at Ability score X+2 is worth (10X +15)xp). So, yes, over a year of gameplay, the two are probably comparable. And, LfM has better synergy with Affinity, and it's also better for a character who'll get to pass on what he learned to others.
Affinity is still probably better than LfM in most (though not all) cases, but for slow, long-running sagas, LfM+Affinity can yield far more xps than Puissant+Affinity.
I did this analysis above. LfM loses out unless you run with little downtime in between and also choose not to put much experience into your favored Ability in the first place.
But now put all the experience from those adventures and time between adventures as you would normally into put into Puissant. If you're pushing this high, you probably started at 5+2. Now it depends how many sessions per adventure. If it's 2 and both characters put in 5 points per adventure, you're between 8+2 and 9+2. Let's call it 8.5+2. And how many points have been put into it between all those adventures?
No, it doesn't. It has worse synergy than does Puissant. Puissant's +2 remains +2 even when you get extra levels via the extra points from Affinity. But LfM +5 buys fewer bonus levels after counting the extra points from Affinity.
It's generally agreed that with Abilities Puissant is better than Affinity. Now you're saying generally Affinity > LfM > Puissant?
Didn't forget, which is why I emphasized 'during play.' And yes, I meant 'many' that is vastly greater than 10. And clearly also vastly greater than 18, since Gild Trained can provide that up front.
Like I said, degenerate case. I'm not recommending the virtue.
Hmm. Which virtues grant xps based upon sessions or hours spent in the real world other than LfM?
I posted some above, but not all. You could make an argument for Enigmatic Wisdom and things that adjust it. Those aren't wonderful, though. Corrupted Abilities, Corrupted Arts, and Corrupted Spells can manage much better returns and can apply much more broadly. Faerie Sympathy and other Virtues that grant Sympathy Traits can as well; sure, they only provide 1 point and sometimes lose 1, but they can apply to quite a few different Abilities with good choices for a character.
The reason I say you could make the argument is that they increase the odds of picking up experience from Twilight episodes, which happen during sessions. So overall they provide a net increase in experience picked up in the midst of sessions. But they don't do it directly, which is why I just said an argument could be made rather than lumping them in with Corrupted (stuff) and Faerie Sympathy.
While Puissant X is much better than Affinity with X by the simplest mathematical models where 1.5 XP never quite manages to catch up with the +2 bonus, this is probably somewhat misleading as by applying to all Study Totals Affinity is probably better in play than it looks, gaining ground as the abilities start taking longer and longer to advance - it also has the fringe benefit of allowing the character to exceed the Age Cap by a margin of two points which is quite nice too (especially if your SG agrees that the normal cap of '9' qualifies as an Age Cap.)
Huh??? What model gives that? That's not correct at all.
The reason Puissant is usually considered better is where they match. It's high enough for Abilities, that it's very rare that Affinity gets noticeably further than Puissant, while Puissant nearly always starts well ahead. It's reversed for Arts.
Benefit compared to what? Puissant allows you to effectively exceed it by 2 as well. If we're talking compared to LfM, that's in-play and the age caps cease to exist after character creation.
And what do you mean by "normal cap" v. "Age Cap"? There is only one cap there, and it's based on age.
By "A degenerate case", you mean "playing with my troupe's Alpha SG when he's got a story he really wants to tell". Some of our adventures take many weeks to go through, others we do in a session then sit around chatting about next season's lab work. His 4th ed saga had people with massive levels in abilities like Parma Magica, Finesse and Affinities so when people tried to translate them to 5th ed, they looked massively overpowered in terms of Parma and Finesse because of all that real-world number of sessions that clocked up.
So, in some troupes it will work really well. As always, the true value of most virtues and cost of most flaws is highly saga dependent. Book Learner isn't as awesome as usual if book trading is hard, in a low vis game waster of vis can be a crushing flaw, susceptibility to the infernal is a death sentence if your SG likes 3rd edition "Demons everywhere!" sourcebooks.
Little downtime = what I called a slow-running saga. I've seen a lot of sagas that end up advancing about 10 years of game time per year of real time. "Not much" is a bit subjective, I've almost never seen a "real" PC pour more than 1/2 his experience into a single ability, and few put more than 1/3 (which is consistent with the ability caps at character creation).
Ok, let's do it. Stories are supposed to net you 5-10xp, and in my games they typically last 1-4 sessions... let's say about 3xp per session? So, over 52 sessions, that's 156xp, for a dozen to a score stories, 1-2 stories per game year. Now, how much xp do you gain from downtime? I'd say such "adventurous" PC from my experience might gain about another 10xp/game year (magi get more, but they thin out their xps over many more things).
So, 256xp (again, note that's about 25xp/game year between story and downtime xp). As I mentioned above, the practical maximum I've seen a character devote to a single ability is between 1/2 and 1/3 of all total experience. So, let's say 100xp at the end of the period, and 50xp at the middle of it. A Puissant PC starting with 5+2 is at 6(20)+2 at the middle of the period, and just short of 8+2 at the end of it (technically, 7(35)+2).
Now let's look at a PC who Learns from mistakes and starts at 5, and gains not only those 100xp (50 midway) in that Ability, but also an additional 175xp (88 midway) from the 35 game sessions (about 2/3) of the total where the Virtue activated. Midway, he has a score of 8(33), so he's caught up with the Puissant character. At the end, he has a score of 11(20), so he's ahead (and he's even better at teaching).
I believe you are mistaken (in the long run, as usual). The "xp equivalent" of Puissant grows roughly like the square root of the total xp invested in an Ability; that's because it's roughly proportional to the score of the Ability (10x score + 15xp). So the "extra benefit" Puissant derives from the presence of an Affinity is proportional to the square root of the extra xps granted by the Affinity. On the other hand, the xps granted by Learn From Mistakes gain a 60% bonus from the Affinity, which is proportional to the xps granted by the Affinity.
But let's run the numbers above, with our two PCs, Pablo the Puissant and Leo the Learner, now having an Affinity, and starting at 7+2 vs. 7.
Midway, Pablo has gained 75xp, and at the end 150xp. Well, probably a tad more than that, because of the rounding ... let's say 80 and 160. So he is now at 8(40)+2 midway, and 10(25)+2 at the end. This means that the "extra effective xp" Puissant gains thanks to the Affinity synergy are about 20 midway, and 20 to 30 at the end of the period.
Leo has gained the same 80-160 xp, plus another 140-280xp from his learning experiences (each yielding 8xp instead of 5 thanks to the Affinity). Note that the total "extra effective xp" LfM has gained thanks to the Affinity synergy are about 53 midway, and 105 at the end of the period, definitely more than Puissant has. And in fact, Leo midway has a score of 11(30), already ahead of Pablo, and at the end 14(55), closer to 15 than Pablo is to 11+2.
No. I did not.
I said that LfM can be comparable to (or better than) Puissant in many realistic game scenarios.
I said that LfM can also beat Affinity, but only rarely.
I already looked at LfM vs. Puissant above.
Let's look at Affinity vs. Puissant. This is easy -- the higher the score, the better Affinity is, because its "effective xp" grow proportionally to the total xp in the Ability, whereas those provided by Puissant grow roughly proportionately to the square root of the total xp.
Now. 8+2 requires 180xp. 10 requires 275, which is 183xp with an Affinity at character creation, but probably a few less xp for a character built over time, thanks to the rounding up of Affinity. I'd say this is roughly the point where they are equal; Puissant wins below, Affinity wins above. You say it's generally agreed that Puissant is better than Affinity? Well, then, I must be the exception
I'd say they are more or less balanced, but in longish sagas -- those taking more than a year of play, Affinity is probably better (and, as we saw above, it has better synergy with anything granting additional xp). Note: not "ahead at the end", but "ahead for more than half the time". In the example above, they are about the same, with Puissant very slightly ahead in the absence of LfM, and slightly behind in the presence of it.
Now, the only point left is Affinity vs. LfM. I said Affinity is generally better, but LfM can win. This is easy. LfM provides an extra 5xp /session it kicks in. Affinity adds 50% of all xp, or a little more thanks to rounding; plus it applies to starting xp too. In the example above, Alice-who-has-an-Affinity, at the end of the 10 game years, has gained 47xp at character creation from it, plus another another 60 (30 midway) or so during the 10 game years from it. She also gained the ability to place 18 more starting xp into it at the beginning, which is an advantage. Leo the Learner-again-without-an-Affinity would have gained about 88xp midperiod, and 175xp at the end of it. So, in this case, LfM is roughly on par with the Affinity, perhaps a tad better.
I probably got a few numbers wrong, but I hope I clarified my point: In longish (1+ years of play) slow-running sagas (10 years of game time / real year or less) Learn from Mistakes beats Puissant, in the sense that it's better for more than half the time; and it can beat Affinity too. Also. Learn from Mistakes and Affinity work better in synergy than either does with Puissant, and each wins out over Puissant given sufficient time -- while Puissant is generally better early on.
Since we're doing this, we might as well also include Gild Trained, which provides 90xp up front and nothing afterward. I'm ignoring limits on Abilities due to age because it's possible to create a character who effectively ignores these and because it is possible to benefit from any of these virtues without reaching that limit.
When those 90xps are dumped into a single Ability, this is better than Puissant for that Ability until the character reaches Ability10, better than Affinity until the character has dumped 180xp into the Ability, and better than Learns from Mistakes until the player has triggered the virtue in 18 sessions.
In many sagas, GT, Baccalaureate and Good Parens are the best virtues of this kind.
You cannot go by this. When comparing LfM, you have to look at seasons not adventuring compared to seasons adventuring. Comparison to real time is irrelevant.
I was leaving it vague to not have to estimate and calculate a ton. My ballpark as I wrote that was definitely <1/4, probably less than <1/5. 1/3 is way, way over the point to weaken LfM.
You missed an enormous point I made above. A really, really huge point. You're now assuming the average opponent this person competes against has a score around 10. If that's true for everyone, then the NPCs are advancing at something like 125 experience per year, taking a quick guess at numbers of players and all. Leaving out this factor drastically inflates the value of LfM. I get similar results to you if I choose to ignore the probability of missing by 1.
No, they don't. LfM gives you bonus experience. These don't get multiplied by Affinity. Once the game starts, Affinity multiplies Qualities Study/Adancement Totals, not experience.
This is a whole different thing to break down. You're on the right track. You've expressed half the math well enough without calculating it with 5(x-2)(x-1)/2=5(x)(x+1)/3, but you left out an important other half: the floor function. For simplicity, we'll assume the advantage of a higher score (Affinity) for teaching/writing is balanced by the advantage of a lower score of learning (Puissant). Also, I'm going to ignore rounding here; the book does not say what you say about it here. With Arts we round up, while it is left undecided for Abilities. I like to round up, but many people don't, and I'm looking at the general advice I mentioned so I have to keep this more general.
To see the greater complexity, I'm going to break down experience point allocations and which Virtue gets you a higher score:
0-69 Puissant
70-74 tie
75-93 Puissant
94-104 tie
105-119 Puissant
120-139 tie
140-149 Puissant
150-179 tie
180- 183 Puissant
184-219 tie
220-224 Affinity
225-259 tie
260-274 Affinity
275-303 tie
304-329 Affinity
330-349 tie
350-389 Affinity
390-399 tie
400+ Affinity
What does this mean? Until you place 220 experience in an Ability (330 after Affinity), you're always at least equal or ahead with Puissant. Due to aging rolls kicking in and age limits, and the number of points available in general, the majority of characters won't put more than 120 points or so in an Ability at character creation. That leaves you 100 points of experience to gain while being ahead or tied with Puissant, meaning you may well succeed at some things you wouldn't have, resulting in more gains than you would otherwise have had with Affinity early on. Even at 220, Affinity is only better for 5 points, which you might even skip over, but may well be 1 adventure when you're behind. So until you've spent 260 experience, you've been ahead in numerous adventures by choosing Puissant and behind in maybe maybe one adventure by choosing Affinity. Do you spend enough adventures in the 260-274 region to balance out how much you were ahead earlier on, or do you have to reach 304 to manage that?
So, for average starting characters, Puissant is generally the better choice until you at least reach an investment of 260 points, possibly in total performance until you reach an investment of 304 points. There will be exceptions to this, such as starting a character at 75 years old. But, the reason for the general agreement is that most characters will be better off having chosen Puissant until they would have reached either 12 or 13 with Affinity.
Sorry, yes, you're right. I misstated it. It goes like this:
Quality -> Study/Advancement Total -> Experience
This is the one of the few cases where the writers handled the math really, really well.
Yes, they switch between "study total" and "advancement total." This can be seen by looking at earlier versions. They've gone back and corrected a whole bunch of "study total" to read "advancement total," but they missed a few.
