Crafting Recipes - Master List

[Deleted User - 4646370]

http://fr.forum.elvenar.com/index.php?threads/lartisanat-commentaires.16897/post-1010402
(My statistic is 3 posts above in this thread).
I didn't link in my first post because it was in a foreign language.

 

[Deleted User - 3932582]

Elvengems claims #105, 106, 107 replaced #13, 15, 17. So you can turn #13, 15, 17 to not active.

Thanks, that's a good catch. Found the official statement for those who are interested:

https://beta.forum.elvenar.com/index.php?threads/release-notes-version-1-88.13588/

Of course, nothing detailed like that was posted on live. Typical.

However, I crafted some of the winter-themed recipes in December (or maybe January). So I think as @Crow Last Elf they are seasonal.

Good, I think I'll treat these as such for now, and we'll see if we get them next winter (or if someone sees them before that).

Note : The statistic above was aimed at determining whether or not all recipes have the same probability, and it turned out they haven't (it has been then confirmed by French Community Manager on March 16.
I saw @MinMax Gamer said in another thread he thought all recipes have the same probability (what is actually wrong), so maybe we can try to estimate probabilities...

That's some interesting data in there. I wouldn't dismiss uniform hypothesis outright just yet. First of all, community managers, hmm, have been wrong before So I wouldn't take just those words as a gospel.

Now, your actual data is interesting, and indeed points in the direction of non-uniform. I'd like to see more data though. There are some (minor) issues there - you have included seasonal items, which we now believe wouldn't be showing up in there in March. I am not sure if you used the complete active recipe list (it's pretty close though). Not quite sure how exactly you treated unique recipes (chess set etc). Don't think these adjustments would have changed the conclusion though.

Now, if we assume that distribution is non-uniform, the next thing I'd test if we can reject uniformity of each of the Rarity classes in my list. Perhaps it is indeed indicative of something. One big argument against non-uniformity is the fact that they have added temporary Phoenix building recipes to bump up their frequencies. If they could adjust individual recipe probabilities at will, that would be a very strange way of doing that. Even if rarity is a factor, those recipes are at the max rarity, so to increase frequencies for those they could have just temporarily bump rarity down. This is not a fool-proof evidence of anything, but still.

So now when you have rarity info, you can split your collected data into 5 pools, and see if there are any patterns there. Regardless, I think that more data is likely needed to establish proper distribution here empirically.

 

[Pheryll]

http://fr.forum.elvenar.com/index.php?threads/lartisanat-commentaires.16897/post-1010402
(My statistic is 3 posts above in this thread).
I didn't link in my first post because it was in a foreign language.

Looking over your statistics, it does not seem that your most common items are based on the rarity of the item; for example the 100% coin rain and supply windfall are much more common in your statistics than the average for the lower tiers. I am not sure you have enough data to make a good statistical analysis either. As for the moderator comments, they do sometimes repeat the developer's words without fully understanding the context. Disabling some recipes and doubling up on others may be enough for the developers to say that not all recipes have equal probability.

 

[Deleted User - 3932582]

Alright, all unconfirmed cases are closed for now. We can move onto figuring out the probabilities

 

[Deleted User - 4646370]

I updated my statistic with a bit more data and regrouped recipes by rarity :

• Recipes of rarity 1 : 19 recipes, got 133 times (average : ×7)
  • Supply Windfall 10% ×0, 5% ×4 ; 1 Runeshard ×3
  • 5Relics : marble ×8, steel ×4, planks ×7, crystal ×9, scrolls ×7, silk ×7, elixir ×7, dust ×8, gems ×12
  • Spells : 2PoP × 8, 1EE ×13, 1MM ×11, 3IM ×9
  • 1KP ×5, 3KP ×5, Time boost 6×10m ×6
• Recipes of rarity 2 : 10 recipes, got 46 times (average : ×4.6)
  • Supply Windfall 20% ×3, 15% ×4 ; Portal Profit 5% ×2
  • 2 Runeshards ×1, 10 RR spells ×8
  • 6KP ×3, 2×3AWKP ×12, 3AWKP(rs) ×7 (where AWKP(rs) means AWKP with cost in Runeshards.)
  • Time boost 9×15m ×3 ; PetFood(sf) ×3
• Recipes of rarity 3 : 19 recipes, got 125 times (average : ×6.6)
  • Coin Rain 33% ×7, 25% ×8 ; Supply Windfall 33% ×13, 25% ×17 ; Portal Profit 10% ×4
  • 3 Runeshards ×5, 20 RR spells ×3
  • 10KP ×4, 2×5AWKP ×13, 7AWKP ×1, 10AWKP(rs) ×4
  • Time boost 5×30m ×2, 5×45m ×4
  • Pet Food by cost in relics : elixir ×13, dust ×4, gems ×8
  • Buildings : rainbow flower cage ×2, unicorns : silver ×7, crystal ×6
• Recipes of rarity 4 : 19 recipes, got 70 times (average : ×3.7)
  • Coin rain 50% ×7, Supply Windfall 50% ×3 ; Portal Profit 15% ×5
  • 30 RR spells ×3, 30RR(sf) ×5
  • 10AWKP ×3, 15AWKP ×6, 15AWKP(rs) ×2
  • Time boost 7×1h ×3, 4×2h ×2, 1×5h ×3
  • Military buildings : UUU ×1, MMM ×3, ELR ×6
  • Traveling Merchants : I×4, II×3, III×3
  • Other buildings : rainbow unicorn ×2, lava codex ×6
• Recipes of rarity 5 : 13 recipes, got 51 times (average : ×3.9)
  • Coin rain 100% ×12, supply windfall 100% ×9, portal profit 20% ×3
  • 15KP ×2, 20AWKP ×6
  • Time boost 8h ×3, 14h ×1, 20h ×2
  • Buildings : festival merchant ×2, mana sawmill ×4, orc nest ×3, orc strategist ×0, vallorian valor ×4

That's a total of 425 recipes, plus 18 special ones that I take out of the statistic since they are not always available.

 

[Pheryll]

That's a total of 425 recipes, plus 18 special ones that I take out of the statistic since they are not always available.

Assuming equal probability your observations are within 32% off the expected value. That is not all that far off, yet there are issues at trying to make the data fit a model with frequencies based on rarity including the low value for rarity 2 (when compared with rarity 1 & 3) and the high individual value for the 100% coin rain instant. If tier 5 is very rare then the coin rain statistic will be vastly improbable, much more so than the 32% variance of the rarity groups that we see here.

 

[Deleted User - 3932582]

That's a total of 425 recipes, plus 18 special ones that I take out of the statistic since they are not always available.

Thanks for the update. Hm, with this data, it can almost be from underlying uniform distribution. Almost...

I hope you'll continue you data gathering. Each of the datapoints by itself is not particularly unusual (even 17/425 for 1 out of 80 recipes is fairly plausible). But all of them together makes for a rather unlikely sample if underlying distributions are uniform. But just eyeballing frequencies doesn't reveal any obvious groupings to me. Some of the recipes I am almost certain have the same probabilities (e.g. I see no reason to believe why 3 different relic Pet Foods would have different probabilities) -and yet existing observations place them at quite different ends of the spectrum (from 3-4 up to 13).

I think we need more data

 

[Deleted User - 4646370]

Some of the recipes I am almost certain have the same probabilities (e.g. I see no reason to believe why 3 different relic Pet Foods would have different probabilities)

Fair point, but probabilities could depend on relic boosts. I didn't precise, but I'm mixing stats from a city with elixir bost with stats from a city with gems boost.
So my stat could indicate we're more likely to get pet food with cost in T3 boost and then with S3 boost, but we haven't enough data to affirm that now.
Unfortunately I didn't note from which city come the recipes I got.

 

[Enevhar Aldarion]

Fair point, but probabilities could depend on relic boosts. I didn't precise, but I'm mixing stats from a city with elixir bost with stats from a city with gems boost.
So my stat could indicate we're more likely to get pet food with cost in T3 boost and then with S3 boost, but we haven't enough data to affirm that now.
Unfortunately I didn't note from which city come the recipes I got.

My boost is gems, so my sentient boost is elixir/soap and I see more pet food requiring dust or elixir relics than I ever do for gems. And no, I do not think the three show up in even one-third amounts either. Sometimes it feels like 9 out of 10 times, the pet food does not require gems relics, so I do not think those three recipes are weighted for your normal boost relic to show up most often.

 

[Deleted User - 4646370]

Updated data :

• Recipes of rarity 1 : 19 recipes, got 162 times (average : ×8.5, standard deviation = 3.3)
  • Supply Windfall 10% ×3, 5% ×4 ; 1 Runeshard ×4
  • 5Relics : marble ×10, steel ×5, planks ×7, crystal ×12, scrolls ×7, silk ×10, elixir ×9, dust ×8, gems ×15
  • Spells : 2PoP × 11, 1EE ×15, 1MM ×11, 3IM ×10
  • 1KP ×7, 3KP ×6, Time boost 6×10m ×8
• Recipes of rarity 2 : 10 recipes, got 56 times (average : ×5.6, standard deviation = 2.7)
  • Supply Windfall 20% ×4, 15% ×5 ; Portal Profit 5% ×3
  • 2 Runeshards ×3, 10 RR spells ×8
  • 6KP ×4, 2×3AWKP ×12, 3AWKP(rs) ×8 (where AWKP(rs) means AWKP with cost in Runeshards.)
  • Time boost 9×15m ×4 ; PetFood(sf) ×5
• Recipes of rarity 3 : 19 recipes, got 138 times (average : ×7.3, standard deviation = 4.7)
  • Coin Rain 33% ×7, 25% ×10 ; Supply Windfall 33% ×14, 25% ×18 ; Portal Profit 10% ×5
  • 3 Runeshards ×5, 20 RR spells ×3
  • 10KP ×4, 2×5AWKP ×14, 7AWKP ×2, 10AWKP(rs) ×4
  • Time boost 5×30m ×3, 5×45m ×4
  • Pet Food by cost in relics : elixir ×15, dust ×5, gems ×8
  • Buildings : rainbow flower cage ×2, unicorns : silver ×7, crystal ×8
• Recipes of rarity 4 : 19 recipes, got 85 times (average : ×4.5, standard deviation = 1.8)
  • Coin rain 50% ×8, Supply Windfall 50% ×5 ; Portal Profit 15% ×6
  • 30 RR spells ×3, 30RR(sf) ×5
  • 10AWKP ×4, 15AWKP ×8, 15AWKP(rs) ×3
  • Time boost 7×1h ×3, 4×2h ×3, 1×5h ×3
  • Military buildings : UUU ×3, MMM ×3, ELR ×7
  • Traveling Merchants : I×5, II×4, III×3
  • Other buildings : rainbow unicorn ×2, lava codex ×7
• Recipes of rarity 5 : 13 recipes, got 63 times (average : ×4.8, standard deviation = 3.0)
  • Coin rain 100% ×12, supply windfall 100% ×10, portal profit 20% ×4
  • 15KP ×2, 20AWKP ×6
  • Time boost 8h ×4, 14h ×1, 20h ×3
  • Buildings : festival merchant ×2, mana sawmill ×6, orc nest ×5, orc strategist ×4, vallorian valor ×5

That's a total of 504 recipes, plus 28 special ones that I take out of the statistic since they are not always available.

 

[Deleted User - 3932582]

Updated data :

Hm, the data looks slightly more plausible than the last time, but still. I plotted histogram of frequencies:

This doesn't fit well with any of the obvious answers right away I think with more data we will either converge to the usual normal distribution, or we will see distinct peaks on the histogram (multimodal) indicating that we have several groups with different probabilities (and it doesn't look like these groups would be rarity-based). Something like this:



So keep them coming

 

[Deleted User - 4646370]

Updated data :

• Recipes of rarity 1 : 19 recipes, got 187 times (average : ×9.8)
  • Supply Windfall 10% ×5, 5% ×5 ; 1 Runeshard ×4
  • 5Relics : marble ×11, steel ×6, planks ×7, crystal ×12, scrolls ×7, silk ×11, elixir ×13, dust ×9, gems ×19
  • Spells : 2PoP × 12, 1EE ×17, 1MM ×13, 3IM ×11
  • 1KP ×9, 3KP ×6, Time boost 6×10m ×10
• Recipes of rarity 2 : 10 recipes, got 70 times (average : ×7)
  • Supply Windfall 20% ×7, 15% ×5 ; Portal Profit 5% ×3
  • 2 Runeshards ×6, 10 RR spells ×10
  • 6KP ×7, 2×3AWKP ×12, 3AWKP(rs) ×8 (where AWKP(rs) means AWKP with cost in Runeshards.)
  • Time boost 9×15m ×6 ; PetFood(sf) ×6
• Recipes of rarity 3 : 19 recipes, got 163 times (average : ×8.6)
  • Coin Rain 33% ×7, 25% ×12 ; Supply Windfall 33% ×15, 25% ×19 ; Portal Profit 10% ×6
  • 3 Runeshards ×7, 20 RR spells ×4
  • 10KP ×5, 2×5AWKP ×15, 7AWKP ×6, 10AWKP(rs) ×6
  • Time boost 5×30m ×4, 5×45m ×4
  • Pet Food by cost in relics : elixir ×18, dust ×6, gems ×10
  • Buildings : rainbow flower cage ×2, unicorns : silver ×7, crystal ×10
• Recipes of rarity 4 : 19 recipes, got 100 times (average : ×5.3)
  • Coin rain 50% ×8, Supply Windfall 50% ×7 ; Portal Profit 15% ×7
  • 30 RR spells ×3, 30RR(sf) ×6
  • 10AWKP ×5, 15AWKP ×9, 15AWKP(rs) ×3
  • Time boost 7×1h ×3, 4×2h ×4, 1×5h ×6
  • Military buildings : UUU ×4, MMM ×3, ELR ×7
  • Traveling Merchants : I×5, II×6, III×4
  • Other buildings : rainbow unicorn ×2, lava codex ×8
• Recipes of rarity 5 : 13 recipes, got 73 times (average : ×5.5)
  • Coin rain 100% ×16, supply windfall 100% ×10, portal profit 20% ×5
  • 15KP ×3, 20AWKP ×6
  • Time boost 8h ×5, 14h ×1, 20h ×3
  • Buildings : festival merchant ×3, mana sawmill ×7, orc nest ×5, orc strategist ×4, vallorian valor ×5

That's a total of 593 recipes (average : ×7.4), plus 41 special ones that I take out of the statistic since they are not always available.

Number of recipes gotten X times in function of X (in parentheses, expected normal distribution if recipes have the same probability):
0 ×0 (0.0)
1 ×1 (0.3)
2 ×2 (1.3)
3 ×8 (3.2)
4 ×8 (6.0)
5 ×10 (9.0)
6 ×13 (11.2)
7 ×11 (11.9)
8 ×3 (11.0)
9 ×3 (9.0)
10 ×5 (6.7)
11 ×3 (4.5)
12 ×4 (2.8)
13 ×2 (1.6)
14 ×0 (0.8)
15 ×2 (0.4)
16 ×1 (0.2)
17 ×1 (0.1)
18 ×1 (0.0)
19 ×2 (0.0)

 

[Deleted User - 3932582]

Updated data :

Hm, it is possible that some other recipes are also on some kind of rotation, similar to suspected winter ones. I noticed that the only culture/pop buildings on the list - rainbow cage and rainbow unicorn - have been encountered only 2 times each. And none in the recent updates. This picked my attention. I don't keep detailed logs of recipes, but I am crafting both of these any time I see. And I also haven't seen a single one of these two for weeks.

And it's not that they used to be particularly rare. Some not a long time ago I was crafting these almost daily, certainly a few a week. I have probably a couple of dozen placed and more in the inventory. But for the last few weeks - nothing.

If this kind of cycling of probabilities is more prevalent than we assumed, then it would be difficult to establish patterns by observing just a couple of cities...

 

[Enevhar Aldarion]

Hm, it is possible that some other recipes are also on some kind of rotation, similar to suspected winter ones. I noticed that the only culture/pop buildings on the list - rainbow cage and rainbow unicorn - have been encountered only 2 times each. And none in the recent updates. This picked my attention. I don't keep detailed logs of recipes, but I am crafting both of these any time I see. And I also haven't seen a single one of these two for weeks.

I saw both the unicorn and the flower cage yesterday. And I consistently see them both at least once every week.

 

[Deleted User - 3932582]

I saw both the unicorn and the flower cage yesterday. And I consistently see them both at least once every week.

I am not saying that this is confirmed, but it is still possible that they cycle probabilities for individual players. For something with a stable distribution seeing long periods with high frequency of appearing followed by long dry seasons should be a fairly unlikely scenario. And I have seen this kind of setup with several recipes more than once.

 

[Deleted User - 3932582]

I think with more data we will either converge to the usual normal distribution, or we will see distinct peaks on the histogram (multimodal) indicating that we have several groups with different probabilities (and it doesn't look like these groups would be rarity-based). Something like this:



So keep them coming

OK, so I went ahead and tried some groupings, even though we probably don't have enough data yet. So while the data fit for all-equal-probabilities hypothesis is indeed pretty bad, if we assume that recipes fall into just 2 different categories, then it looks much, much better.

As it stands, if we assume that there are 2 pools of recipes, and each pool has the same probability of being chosen, and every recipe in a particular pool has the same probability of being chosen, then it fits existing data pretty well. The pools don't have the same number of recipes - something like 24/56 split, meaning recipes in the smaller pool have higher frequency of popping up (slightly more than 2x more often).

This is all highly speculative so far, of course

 

[Pheryll]

OK, so I went ahead and tried some groupings, even though we probably don't have enough data yet. So while the data fit for all-equal-probabilities hypothesis is indeed pretty bad, if we assume that recipes fall into just 2 different categories, then it looks much, much better.

As it stands, if we assume that there are 2 pools of recipes, and each pool has the same probability of being chosen, and every recipe in a particular pool has the same probability of being chosen, then it fits existing data pretty well. The pools don't have the same number of recipes - something like 24/56 split, meaning recipes in the smaller pool have higher frequency of popping up (slightly more than 2x more often).

This is all highly speculative so far, of course

Keep in mind that the Random Number Generator that the Elvenar team uses may have issues with clumping similar values together. This would mean that a small sampling of consecutive iterations would yield a pronounced favoritism to random elements for a period of time. Over the long haul things would even out, but many different small samplings would each show great favoritism in differing elements.

 

[Deleted User - 4646370]

Updated data :

• Recipes of rarity 1 : 19 recipes, got 234 times (average : ×12.3)
  • Supply Windfall 10% ×5, 5% ×5 ; 1 Runeshard ×4
  • 5Relics : marble ×11, steel ×12, planks ×11, crystal ×18, scrolls ×10, silk ×12, elixir ×16, dust ×12, gems ×21
  • Spells : 2PoP ×15, 1EE ×20, 1MM ×17, 3IM ×14
  • 1KP ×12, 3KP ×8, Time boost 6×10m ×11
• Recipes of rarity 2 : 10 recipes, got 91 times (average : ×9.1)
  • Supply Windfall 20% ×9, 15% ×6 ; Portal Profit 5% ×4
  • 2 Runeshards ×8, 10 RR spells ×14
  • 6KP ×7, 2×3AWKP ×14, 3AWKP(rs) ×12 (where AWKP(rs) means AWKP with cost in Runeshards.)
  • Time boost 9×15m ×10 ; PetFood(sf) ×8
• Recipes of rarity 3 : 19 recipes, got 201 times (average : ×10.6)
  • Coin Rain 33% ×8, 25% ×13 ; Supply Windfall 33% ×19, 25% ×23 ; Portal Profit 10% ×6
  • 3 Runeshards ×10, 20 RR spells ×4
  • 10KP ×6, 2×5AWKP ×21, 7AWKP ×7, 10AWKP(rs) ×7
  • Time boost 5×30m ×5, 5×45m ×4
  • Pet Food by cost in relics : elixir ×23, dust ×7, gems ×15
  • Buildings : rainbow flower cage ×2, unicorns : silver ×8, crystal ×13
• Recipes of rarity 4 : 19 recipes, got 112 times (average : ×5.9)
  • Coin rain 50% ×10, Supply Windfall 50% ×10 ; Portal Profit 15% ×7
  • 30 RR spells ×3, 30RR(sf) ×6
  • 10AWKP ×5, 15AWKP ×9, 15AWKP(rs) ×4
  • Time boost 7×1h ×3, 4×2h ×4, 1×5h ×6
  • Military buildings : UUU ×4, MMM ×3, ELR ×7
  • Traveling Merchants : I×5, II×6, III×5
  • Other buildings : rainbow unicorn ×2, lava codex ×13
• Recipes of rarity 5 : 13 recipes, got 84 times (average : ×6.5)
  • Coin rain 100% ×20, supply windfall 100% ×13, portal profit 20% ×5
  • 15KP ×3, 20AWKP ×6
  • Time boost 8h ×7, 14h ×1, 20h ×4
  • Buildings : festival merchant ×3, mana sawmill ×7, orc nest ×5, orc strategist ×5, vallorian valor ×5

That's a total of 723 recipes (average : ×9), plus 52 special ones that I take out of the statistic since they are not always available.

Current distribution :
0 ×0
1 ×1
2 ×2
3 ×5
4 ×8
5 ×10
6 ×7
7 ×8
8 ×5
9 ×2
10 ×5
11 ×3
12 ×5
13 ×4
14 ×3
15 ×2
16 ×1
17 ×1
18 ×1
19 ×1
20 ×2
21 ×2
22 ×0
23 ×2

 

[Deleted User - 3932582]

That's a total of 723 recipes (average : ×9), plus 52 special ones that I take out of the statistic since they are not always available.

Thanks. 2-pool theory still looks OK:


But 3-pool is starting to look good, too:

 

[Pheryll]

But 3-pool is starting to look good, too:

The more pools, the more it will look like the one-pool model. Keep the data coming in, but I have a feeling that a larger sample size will make these numbers look more and more reasonable.