So people asked me how the algo works. I'll detail it to make people aware of how this market came to be and to help future WMs:
The algo cost column is:
=arrayformula(if(mod(row(A2:A471),2)=1,"",IF(E2:E471="Quanta", 0, (CEILING(0.3*12*(log( ( (Q2:Q471-6)*(Q2:Q471-3)*(Q2:Q471)*(Q2:Q471+2) + 180)*(H2:H471)^3/(SQRT(G2:G471+8))/(log(Q2:Q471+6,2)) + 288, 2))*if(isnumber(find("Nymph",B2:B471)),1.3,1)/if(B2:B471="Nymph's Tears",1.3,1)))*2 -30 )))
which in less spreadsheet-cell-names means..
Pillars cost 0,
Nymphs cost 130% of what's to be described (Because nymphs are underused in war for a significant reason not linked to power level, they would be underrepresented otherwise)
The final result is rounded up
NOTE: Shards and Nymph no longer have no of decks used doubled because it was a silly blanket nerf to all of them without considering individual power levels.
This leaves us with the core:
0.3*12*log( D^3*P[T]/sqrt(U+8)/log(T+6,2) + 288 , 2)
And the final result after all modifications is multiplied by 2 and 30 is subtracted from it. This linear transformation fits it into the range from experimental market nicely (tho in the algo's case the larger values are a bit deflated).
U = Total usage of card
D = Number of decks using card (The main measurement behind the cost)
T = Number of teams which used this card at some point
P[T] = (T-6)(T-3)T(T+2) + 180, a polynomial to weight the effect of T
The main components of the stuff inside the log are:
1. D^(3/2), The main measure of popularity/usefulness of a card
2. P[T], Which was designed to give a low change when a card was used by 3-6 teams (i.e. a versatile, well-liked card), slightly higher when used by only one or two teams (narrow application) and very much higher for higher values (ubiquitous cards which are prolly thoughtlessly put into vault).
3. sqrt(D/(U+8)), scales down the cost for cards which have more copies put into deck slightly (by about 10 points from 1x to 6x), since one-off or low U/D cards are more likely to be in vault in less numbers, their cost should be a bit higher to compensate.
4. D/log(T+6,2), a rough measure of how many times specific teams would use a card. Mainly serves to dampen the extreme effect of almost every team using some card smartly.
Log is used because it scales these variables to price nicely. They are multiplied instead of added because if these are added within log, it is impossible to strike a balance where each variable affects the log with a good enough variation.
Some things to consider for future:
1. Introduce the amount of the card in initial vaults as a variable
2. Consider use in-element and off-element seperately
3. Change P[T] from a quartic polynomial since it makes for a very extreme change going from 10 to 11 to 12.
4. The linear transform/changed distribution might make nymphs cost too high with the 130% increase.
5. Simply round the values to nearest multiple of 5.
The min reason why I used the algorithm is not to provide a definite value to the prices. But to provide a baseline measurement which is unbiased (the main formula was set only based on test values and overall distribution, not individual cards) and thus would not carry my lackings in knowledge, while also giving us a good measure of reaction to prices and effects last war. These were tweaked quite a bit based on our thoughts and everyone's feedback on experimental market. One big change is that the higher values in the distribution have been decreased in price, which was received favorably. There is a chance that this might have made them too damp/low to be really effective - we'll see.
To end, a big thank you to Physsion and Serprex for making the amazing gdoc which let me easily develop these prices. Thanks extends out to all the people they built on top of as well. And a more thanks to the people who've sent vaults in so far! Your input is really invaluable. On that note, we are still happy to receive vaults, thoughts and feedback on these prices. There are a few questions listed above - please reply to them if you construct a vault, or you feel like returning feedback. here's to a great war!