All good and well, seems like the above are calculations for the ultimate FA score from teams that can do spire all the way to the top and can all do 30 provinces for 6 rounds in tourney. Reality for the better average fellowship is far from that. What is the situation where say all can do 10 provinces in tourney for 5 rounds and the team just can get a silver medal in the spire? These teams will struggle with the hats, the marbles and the ghosts as the quantities where you get lots of these are after province 10. I have to agree with Gargon667, doing well in tourneys is a big factor.
While it is academically interesting, indeed, to gain an insight into the new-style FA from the rarefied perspective of the most highly determined and competitive players and Fellowships, the reality is that most of us are very, very far from being in a similar position to those few ultra-dedicated individuals and groups. As a more 'average' player who is fortunate to belong to an excellent 10-Chest Fellowship, it is still the 'usual suspects' - Arcane Residue and Bracelets, plus to a lesser extent Blacksmiths' Guild and Farmer's Delight Badges - which remain the most difficult items, and in the shortest supply
throughout the FA's duration, whether aiming for single-path completion or competitive full Map clearance and/or Pit Stages.
That said, it's true that Witch Hats (primarily) and also Elemental Marbles and Ghost Badges, too, seem to be proving a reasonably difficult type to earn, especially because it's very easy to simply forget to collect these while going through the Tournament and/or Spire (and the fault/'feature' whereby the 'Green Tick' showing Badge completion disappears as soon as another Badge is partially completed only exacerbates this problem).
Therefore, while the argument that Tournament/Spire completion ability may well be the
ultimate limiting factor for the most high-performing FA Fellowships, especially those which are willing to spend many Time Boosters, other Resources, and/or Diamonds on [especially] Arcane Residue production, for
most types of Fellowship the Arcane Residue Badge remains, overall, so difficult and expensive to produce that it is still the primary limiting factor, with Bracelets also still coming in as a close second for pretty much all [post-Guest Race] FS Members, not just myself (Ch. VIII).
For info, I am speaking with experience of completing [quite competitively, and to the Pit Stage] the new-style FA in two different but equally high-performing, dedicated 10-Chest Fellowships, with most Members completing enough Tourney and Spire Encounters to ensure that Hats, Marbles, and Ghosts, while certainly not the easiest of Badges, are plentiful enough to more than keep pace with Residue and Bracelet needs, with a fair percentage of players having at least a few of some or all of these left over after the FA ends - and with the potential for more to be earned, too, by those of us who are forgetful enough to fail to collect at least some of what we earn, as already mentioned above. I've yet to hear of
anyone forgetting to collect Residue or Bracelets... quite the opposite, since most of us, in my experience, spend much time actually
waiting for those two specific Badges to become collectable, one at a time, while all other Badges seem to build up in Inventory at moderate-to-speedy rates without any comparable effort.
In short: for non-élite Fellowships which do not finish the Spire and/or score very highly in Tournaments, Arcane Residue is the major limiting factor in the new-style FA, with Bracelets being the next (and very) significant limitation, with all other [non-Workshop] Badges, even the more difficult Tourney/Spire-related ones, being reduced to 'also-rans' which most players find [comparatively] easy to amass. This means that the FA has become, in essence, a contest as to which FS can produce the most Arcane Residue and/or Bracelets, although the comparative ease with which low-Chapter (I-V) Cities can produce Bracelets probably means that, for very young FSs, it will be Arcane Residue alone which is the primary limiting factor.
The new-style FA therefore appears to be noticeably unbalanced for the majority of 'average' Fellowships, and I agree with the many commentators who have already suggested the following solutions to this imbalance:
1. Reduce Arcane Residue requirements to 1 x VV [or, better, 1 x Crafted Item, to avoid the illusory but troublesome perception of 'wasting' VV] - and I would
also suggest reducing the number of these MA Resource-intensive Badges required overall, especially in Map 3 and in the Pit Stages, and;
2. Either
significantly [50%+] reduce the amount of T1 Goods required for Bracelets (and balance according to Manufactory level available, not just Chapter progress), or, ideally, alter the requirements to include ALL types of Goods (including Sentient Goods)
and reduce the amounts required.
In my opinion, and as mentioned above, Blacksmiths' Guild and Farmer's Delight Badges are
also far more difficult than most other Badges, and I would say that both of these (especially Farmer's Delight) need to have their requirements reduced if better FA balance is to be achieved, but while Arcane Residue and Bracelets are the overwhelmingly most significant limiting factor, these other two Badges are, at present, less of a priority.