Crafting Recipes - Master List

[Pheryll]

One more thing to keep in mind, is that crafting a recipe past the time that the recipes refresh has an effect of lowering the probability for that recipe as it cannot appear among the remaining options while it is being crafted.

 

[Deleted User - 3932582]

The more pools, the more it will look like the one-pool model.

Umm, no, mixture of normals does not look like a normal distribution, except in degenerate cases. If you go to 80 pools (e.g. each pool has only one recipe) and have enough data to justify that, then you will see a multimodal distribution (multiple density peaks), with each peak corresponding to a different recipe probability. The only way it will look like a one-pool (regular normal model with one peak) is if all the underlying recipe probabilities are indeed the same. Which so far does not look particularly convincing.

 

[Deleted User - 3932582]

One more thing to keep in mind, is that crafting a recipe past the time that the recipes refresh has an effect of lowering the probability for that recipe as it cannot appear among the remaining options while it is being crafted.

It's true, but it is unlikely to have appreciable impact on the high-level results. There are too many recipes and too many samples already. Even if we expect bias in crafting selection (i.e. @PaNonymeB always crafts certain recipes and not the others), it may impact somewhat deemed probabilities of these recipes, but it won't change the fact that results so far do not support single probability for all recipes. The biggest and obvious problems here are significant skew (you'd expect almost symmetrical results by now), and the fact that expected mode/mean in this case - about 9 for the latest data - literally has a trough in histogram right at that area. So the exact opposite of what you'd expect there.

 

[Pheryll]

The biggest and obvious problems here are significant skew (you'd expect almost symmetrical results by now), and the fact that expected mode/mean in this case - about 9 for the latest data - literally has a trough in histogram right at that area. So the exact opposite of what you'd expect there.

I am not convinced that we should be getting symmetrical results at this point. Subtract the 425 recipe result from the 723 recipe result and examine the 298 recipe addition to the 425 original. The 298 is also heavily skewed, but many of its focuses and dearths do not line up with the 425 skews. This suggests the issue is with the clumping of the RNG more than it is with averages. If a few hundred recipes keep on producing differing skewed results, then doubling the number should not reliably add in symmetry.

 

[DeletedUser22644]

just want pet food and dont care about the numbers....

 

[Deleted User - 3932582]

Subtract the 425 recipe result from the 723 recipe result and examine the 298 recipe addition to the 425 original. The 298 is also heavily skewed, but many of its focuses and dearths do not line up with the 425 skews.

Sure they do. The histograms that were plotted so far are not normalized for the number of observations, so the X axis numbers will drift upwards with more observations. You're looking at splits of 425 and 298, and total of 723 - of course they will produce different absolute sum numbers. After you normalize for the number of observations all 3 would look similar, and all have a trough at 0.0125 area (=1/80) where you'd expect the peak.

 

[Pheryll]

You're looking at splits of 425 and 298, and total of 723 - of course they will produce different absolute sum numbers.

I am not looking at absolute sum, I am looking at which elements of the recipe result are favored and which are not. The 425 displays differing elements that have favoritism compared to the later 298.

 

[Deleted User - 3932582]

I am not looking at absolute sum, I am looking at which elements of the recipe result are favored and which are not. The 425 displays differing elements that have favoritism compared to the later 298.

To make that judgement, there is not nearly enough supporting evidence in these two samples.

Spoiler: Danger! Math ahead!

You're effectively comparing pair-wise 80 separate binomial distributions using only 425 and 298 samples. If for each recipe you test the individual hypothesis that in both cases they have been sampled from the same distribution, you will see that you cannot reject that hypothesis pretty much for every singe recipe, for any reasonable confidence level. Meaning the differences between recipe preferences between 425 and 298 samples is very much compatible with a hypothesis of recipe distributions not changing between 425 and 298 samples. All you're seeing is a sampling error.

 

[Pheryll]

To make that judgement, there is not nearly enough supporting evidence in these two samples.

Lack of data has been my point from the beginning. Sample sizes in the hundreds may well be useless for establishing any trend or inherent probability. Taking a sample that is skewed and doubling the data does not mean that the combination will come closer to the actual probabilities. Any expectation that the curve should become symmetric with this small amount of data is not going to hold water. If one wants to suggest that there are multiple data pools with differing probabilities, one should be able to give some indication which recipes belong in those pools. When recipes that are thought more probable or more improbable are deemed the opposite in a later data collection, that puts even the assumption of multiple data pools on shaky grounds. And speculating a third and possibly more data pools from a small amount of data becomes useless extrapolation as the complexity of what is being suggested is not something that can be discovered in such a small amount of data.

 

[Deleted User - 3932582]

When recipes that are thought more probable or more improbable are deemed the opposite in a later data collection, that puts even the assumption of multiple data pools on shaky grounds. And speculating a third and possibly more data pools from a small amount of data becomes useless extrapolation as the complexity of what is being suggested is not something that can be discovered in such a small amount of data.

OK, this is getting way out of scope for this forum, but this is incorrect. You may want to read up on cluster analysis and Gaussian mixture of normals. As much as I would like to take credit for that, these are established statistical techniques and not something that I invented. Clustering is used all other the place for classification in unsupervised contexts. And yes, there is recipe classification into pools, and it is also probabilistic. The probabilistic differences in classification between these two sample sizes are not statistically significant. So while we cannot answer with certainly which recipe belongs to each pool (for most recipes), we can observe that model with 2 or 3 pools (clusters) is a significantly better fit with existing data than 1 pool model. This uses standard information criteria such as AIC and BIC, which both penalize extra variables/pools to minimize overfitting. There is plenty of data to make that determination.

With more data we are likely to see more separation between different pools/clusters and potential emergence of new pools (up to 80 total if all individual probabilities are different) which are statistically indistinguishable yet. But with existing data we can already move away from hypothesis of a single cluster. If all recipes would be effectively samples from the same distributions then yeah, we definitely have enough data here (hundreds of samples from the same distribution) to expect pretty good symmetry. Which we do not observe.

 

[Pheryll]

There is plenty of data to make that determination.

If the data of 425 recipes is assumed to be 425 independent random numbers, then yes, but the RNG is the very issue that I am disputing. Consider after a million rolls of two dice (added together), someone decided to rearrange the order. Every thousand rolls 2s and 12s were swapped so that 90% of the 2s occurred at the first half of the thousand and 10% of the 2s at the later half, and thus the 12s would gravitate toward the 10% and 90% probabilities. The tampering here would not change the general probability of rolling a 2 or a 12, nor would the standard deviation be impacted. However, any sampling of consecutive rolls could easily be swayed unless it was large enough to overcome the tampering. RNGs often are tested for how they perform with samplings of consecutive elements, however, the RNG that Elvenar uses may indeed have flaws that include the clumping of similar values. This discussion was brought up in the last winter event and at several other times in the past. If clumping does indeed occur, this would multiply the amount of data that would need to be collected before a consistent probability trend can be established.

I understand that challenge the RNG does upend much of the data analysis models that are used. If we make a large number of reasonable sized samplings, and the majority of those samplings are significantly skewed with differing probabilities, then that does call into question how large of a sampling size is actually needed to overcome the issue of the data being skewed. Regardless of how large the sample sizes may be, if they are complicated by clumping they can demonstrate far less than what they would if they were truly independent.

 

[Deleted User - 4646370]

Updated data :

• Recipes of rarity 1 : 19 recipes, got 276 times
  • Supply Windfall 10% ×8, 5% ×6 ; 1 Runeshard ×5
  • 5Relics : marble ×14, steel ×14, planks ×12, crystal ×18, scrolls ×13, silk ×13, elixir ×20, dust ×13, gems ×24
  • Spells : 2PoP ×18, 1EE ×22, 1MM ×21, 3IM ×18
  • 1KP ×14, 3KP ×9, Time boost 6×10m ×14
• Recipes of rarity 2 : 10 recipes, got 111 times
  • Supply Windfall 20% ×10, 15% ×7 ; Portal Profit 5% ×4
  • 2 Runeshards ×9, 10 RR spells ×16
  • 6KP ×7, 2×3AWKP ×17, 3AWKP(rs) ×18 (where AWKP(rs) means AWKP with cost in Runeshards.)
  • Time boost 9×15m ×12 ; PetFood(sf) ×11
• Recipes of rarity 3 : 19 recipes, got 235 times
  • Coin Rain 33% ×10, 25% ×17 ; Supply Windfall 33% ×22, 25% ×26 ; Portal Profit 10% ×6
  • 3 Runeshards ×10, 20 RR spells ×7
  • 10KP ×7, 2×5AWKP ×22, 7AWKP ×8, 10AWKP(rs) ×7
  • Time boost 5×30m ×6, 5×45m ×6
  • Pet Food by cost in relics : elixir ×25, dust ×8, gems ×18
  • Buildings : rainbow flower cage ×2, unicorns : silver ×11, crystal ×17
• Recipes of rarity 4 : 19 recipes, got 143 times (average : ×5.9)
  • Coin rain 50% ×13, Supply Windfall 50% ×15 ; Portal Profit 15% ×8
  • 30 RR spells ×5, 30RR(sf) ×8
  • 10AWKP ×6, 15AWKP ×10, 15AWKP(rs) ×8
  • Time boost 7×1h ×3, 4×2h ×4, 1×5h ×9
  • Military buildings : UUU ×6, MMM ×3, ELR ×9
  • Traveling Merchants : I×5, II×6, III×6
  • Other buildings : rainbow unicorn ×3, lava codex ×16
• Recipes of rarity 5 : 13 recipes, got 103 times (average : ×6.5)
  • Coin rain 100% ×25, supply windfall 100% ×16, portal profit 20% ×5
  • 15KP ×5, 20AWKP ×7
  • Time boost 8h ×7, 14h ×2, 20h ×7
  • Buildings : festival merchant ×4, mana sawmill ×7, orc nest ×6, orc strategist ×5, vallorian valor ×7

That's a total of 868 recipes (average : ×10.8), plus 71 special ones that I take out of the statistic since they are not always available.

Current distribution :
0 ×0
1 ×0
2 ×2
3 ×3
4 ×3
5 ×6
6 ×9
7 ×10
8 ×6
9 ×4
10 ×4
11 ×2
12 ×2
13 ×4
14 ×4
15 ×1
16 ×3
17 ×3
18 ×5
19 ×0
20 ×1
21 ×1
22 ×3
23 ×0
24 ×1
25 ×2
26 ×1

 

[Deleted User - 3932582]

Updated data :

Thanks. I started to collect this data as well, but it will take a while before mine adds up to something meaningful.

 

[Deleted User - 4646370]

Updated data - one thousand recipes !

• Recipes of rarity 1 : 19 recipes, got 313 times
  • Supply Windfall 10% ×8, 5% ×6 ; 1 Runeshard ×6
  • 5Relics : marble ×16, steel ×18, planks ×12, crystal ×22, scrolls ×14, silk ×16, elixir ×23, dust ×14, gems ×27
  • Spells : 2PoP ×21, 1EE ×26, 1MM ×22, 3IM ×18
  • 1KP ×18, 3KP ×11, Time boost 6×10m ×15
• Recipes of rarity 2 : 10 recipes, got 135 times
  • Supply Windfall 20% ×10, 15% ×8 ; Portal Profit 5% ×6
  • 2 Runeshards ×11, 10 RR spells ×21
  • 6KP ×8, 2×3AWKP ×21, 3AWKP(rs) ×21 (where AWKP(rs) means AWKP with cost in Runeshards.)
  • Time boost 9×15m ×17 ; PetFood(sf) ×12
• Recipes of rarity 3 : 19 recipes, got 265 times
  • Coin Rain 33% ×12, 25% ×19 ; Supply Windfall 33% ×24, 25% ×27 ; Portal Profit 10% ×6
  • 3 Runeshards ×11, 20 RR spells ×7
  • 10KP ×9, 2×5AWKP ×24, 7AWKP ×11, 10AWKP(rs) ×7
  • Time boost 5×30m ×9, 5×45m ×6
  • Pet Food by cost in relics : elixir ×27, dust ×9, gems ×23
  • Buildings : rainbow flower cage ×2, unicorns : silver ×13, crystal ×19
• Recipes of rarity 4 : 19 recipes, got 158 times
  • Coin rain 50% ×13, Supply Windfall 50% ×17 ; Portal Profit 15% ×8
  • 30 RR spells ×5, 30RR(sf) ×8
  • 10AWKP ×6, 15AWKP ×10, 15AWKP(rs) ×10
  • Time boost 7×1h ×3, 4×2h ×6, 1×5h ×10
  • Military buildings : UUU ×7, MMM ×3, ELR ×9
  • Traveling Merchants : I×7, II×6, III×8
  • Other buildings : rainbow unicorn ×3, lava codex ×19
• Recipes of rarity 5 : 13 recipes, got 113 times
  • Coin rain 100% ×30, supply windfall 100% ×19, portal profit 20% ×5
  • 15KP ×5, 20AWKP ×7
  • Time boost 8h ×7, 14h ×3, 20h ×7
  • Buildings : festival merchant ×4, mana sawmill ×7, orc nest ×6, orc strategist ×5, vallorian valor ×8

That's a total of 984 recipes (average : ×12.3), plus 81 special ones that I take out of the statistic since they are not always available.

Current distribution :
0 ×0
1 ×0
2 ×1
3 ×4
4 ×1
5 ×4
6 ×9
7 ×8
8 ×7
9 ×4
10 ×4
11 ×4
12 ×3
13 ×2
14 ×2
15 ×1
16 ×2
17 ×2
18 ×3
19 ×4
20 ×0
21 ×4
22 ×2
23 ×2
24 ×2
25 ×0
26 ×1
27 ×3
30 ×1

 

[Deleted User - 3932582]

I have added my own observations, binned and normalized to probabilities. The 2-pool hypothesis is still looking pretty good:

If this is indeed accurate, at about 3000 datapoints we should see complete separation of these two pools (e.g. basically no overlap)

 

[Deleted User - 4646370]

Since probability seems not to be linked with rarity, I came back to a sorting by type :

• Coin rain % : 100 ×35, 50 ×21, 33 ×15, 25 ×22
• Supply Windfall % : 100 ×20, 50 ×21, 33 ×27, 25 ×29, 20 ×11, 15 ×12, 10 ×10, 5 ×6
• Portal Profit % : 20 ×5, 15 ×10, 10 ×8, 5 ×8
• Ancient Knowledge : 20 ×7, 15 ×13, 10 ×6, 7 ×11, 5 ×27, 3 ×23
• Ancient Knowledge costing Runeshards : 3 ×25, 10 ×8, 15 ×12
• Knowledge Points : 15 ×5, 10 ×12, 6 ×9, 3 ×14, 1 ×24
• Runeshards : 3 ×11, 2 ×12, 1 ×8
• Relics : marble ×20, steel ×21, planks ×18, crystal ×26, scrolls ×16, silk ×17, elixir ×28, dust ×19, gems ×30
• Spells : PoP ×23, EE ×30, MM ×26, IM ×24
• Pet food costing relics : elixir ×30, dust ×12, gems ×26, spell fragments ×14
• Royal Restorations : 10 ×24, 20 ×8, 30 ×8, 30(costing spell fragments) ×9
• Time boosts : 10m ×22, 15m ×19, 30m ×11, 45m ×9, 1h ×4, 2h ×9, 5h ×11, 8h ×9, 14h ×5, 20h ×7
• Culture/population buildings : rainbow flower cage ×3, lava codex ×24, unicorns : rainbow ×6, silver ×18, crystal ×20
• Military buildings : ELR ×12, MMM ×6, UUU ×7
• Traveling Merchants : I ×9, II ×7, III ×8
• Other buildings : festival merchant ×5, mana sawmill ×9, orc nest ×7, orc strategist ×10, vallorian valor ×10
• Special recipes (evolving buildings, chess set, artifacts) : 100
• Total : 1283 (average for non-special recipes : 14.8)

 

[Alpha Lyrae]

While the information in this thread is interesting and the results useful, I must admit that I follow along mostly to behold the epic geekery!

[Note: That's a compliment, promise.]

 

[Deleted User - 3932582]

Since probability seems not to be linked with rarity, I came back to a sorting by type :

• Coin rain % : 100 ×35, 50 ×21, 33 ×15, 25 ×22
• Supply Windfall % : 100 ×20, 50 ×21, 33 ×27, 25 ×29, 20 ×11, 15 ×12, 10 ×10, 5 ×6
• Portal Profit % : 20 ×5, 15 ×10, 10 ×8, 5 ×8
• Ancient Knowledge : 20 ×7, 15 ×13, 10 ×6, 7 ×11, 5 ×27, 3 ×23
• Ancient Knowledge costing Runeshards : 3 ×25, 10 ×8, 15 ×12
• Knowledge Points : 15 ×5, 10 ×12, 6 ×9, 3 ×14, 1 ×24
• Runeshards : 3 ×11, 2 ×12, 1 ×8
• Relics : marble ×20, steel ×21, planks ×18, crystal ×26, scrolls ×16, silk ×17, elixir ×28, dust ×19, gems ×30
• Spells : PoP ×23, EE ×30, MM ×26, IM ×24
• Pet food costing relics : elixir ×30, dust ×12, gems ×26, spell fragments ×14
• Royal Restorations : 10 ×24, 20 ×8, 30 ×8, 30(costing spell fragments) ×9
• Time boosts : 10m ×22, 15m ×19, 30m ×11, 45m ×9, 1h ×4, 2h ×9, 5h ×11, 8h ×9, 14h ×5, 20h ×7
• Culture/population buildings : rainbow flower cage ×3, lava codex ×24, unicorns : rainbow ×6, silver ×18, crystal ×20
• Military buildings : ELR ×12, MMM ×6, UUU ×7
• Traveling Merchants : I ×9, II ×7, III ×8
• Other buildings : festival merchant ×5, mana sawmill ×9, orc nest ×7, orc strategist ×10, vallorian valor ×10
• Special recipes (evolving buildings, chess set, artifacts) : 100
• Total : 1283 (average for non-special recipes : 14.8)

Updated with my own data, so total is slightly more than 1,500 non-special recipes:

We continue to see better separation between the 2 pools (meaning overlap is getting smaller) - just as I hoped. Without retyping all the recipes, you can use @PaNonymeB post to bucket individual recipes. Basically, recipes that occurred <14 times are likely to belong to low-frequency pool (with about 0.8% chance of showing up), and recipes that occurred >14 times are likely to belong to high frequency pool (with about 2% chance of showing up). The ones in the 10-15 range are not entirely certain, but for everything else in different pools it would be extremely unlikely NOT to be different.

While recipes in each pool may actually have different probabilities themselves (so more pools), so far the data doesn't show it.

 

[Deleted User - 4646370]

Updated data :

• Coin rain % : 100 ×37, 50 ×24, 33 ×17, 25 ×25
• Supply Windfall % : 100 ×23, 50 ×24, 33 ×31, 25 ×32, 20 ×11, 15 ×13, 10 ×10, 5 ×7
• Portal Profit % : 20 ×5, 15 ×11, 10 ×9, 5 ×10
• Ancient Knowledge : 20 ×7, 15 ×14, 10 ×9, 7 ×13, 5 ×32, 3 ×26
• Ancient Knowledge costing Runeshards : 3 ×26, 10 ×9, 15 ×14
• Knowledge Points : 15 ×7, 10 ×13, 6 ×10, 3 ×17, 1 ×26
• Runeshards : 3 ×14, 2 ×14, 1 ×10
• Relics : marble ×25, steel ×23, planks ×21, crystal ×27, scrolls ×18, silk ×17, elixir ×33, dust ×21, gems ×32
• Spells : PoP ×24, EE ×33, MM ×29, IM ×29
• Pet food costing relics : elixir ×34, dust ×16, gems ×29, spell fragments ×15
• Royal Restorations : 10 ×25, 20 ×9, 30 ×9, 30(costing spell fragments) ×10
• Time boosts : 10m ×24, 15m ×21, 30m ×13, 45m ×9, 1h ×4, 2h ×11, 5h ×12, 8h ×9, 14h ×6, 20h ×9
• Culture/population buildings : rainbow flower cage ×4, lava codex ×30, unicorns : rainbow ×6, silver ×20, crystal ×21
• Military buildings : ELR ×13, MMM ×7, UUU ×8
• Traveling Merchants : I ×10, II ×8, III ×9
• Other buildings : festival merchant ×5, mana sawmill ×9, orc nest ×10, orc strategist ×13, vallorian valor ×10
• Special recipes (evolving buildings, chess set, artifacts) : 109
• Total : 1439 (average for non-special recipes : 16.6)

 

[Deleted User - 4646370]

Updated data :

• Coin rain % : 100 ×37, 50 ×26, 33 ×19, 25 ×26
• Supply Windfall % : 100 ×24, 50 ×25, 33 ×33, 25 ×33, 20 ×11, 15 ×15, 10 ×10, 5 ×7
• Portal Profit % : 20 ×5, 15 ×12, 10 ×10, 5 ×12
• Ancient Knowledge : 20 ×9, 15 ×15, 10 ×11, 7 ×13, 5 ×34, 3 ×26
• Ancient Knowledge costing Runeshards : 3 ×27, 10 ×10, 15 ×14
• Knowledge Points : 15 ×9, 10 ×14, 6 ×11, 3 ×18, 1 ×27
• Runeshards : 3 ×15, 2 ×15, 1 ×10
• Relics : marble ×28, steel ×25, planks ×22, crystal ×27, scrolls ×21, silk ×18, elixir ×38, dust ×22, gems ×32
• Spells : PoP ×25, EE ×33, MM ×31, IM ×31
• Pet food costing relics : elixir ×37, dust ×18, gems ×30, spell fragments ×15
• Royal Restorations : 10 ×27, 20 ×9, 30 ×9, 30(costing spell fragments) ×12
• Time boosts : 10m ×25, 15m ×21, 30m ×13, 45m ×10, 1h ×5, 2h ×12, 5h ×12, 8h ×9, 14h ×6, 20h ×9
• Culture/population buildings : rainbow flower cage ×5, lava codex ×30, unicorns : rainbow ×6, silver ×22, crystal ×22
• Military buildings : ELR ×14, MMM ×8, UUU ×9
• Traveling Merchants : I ×13, II ×8, III ×11
• Other buildings : festival merchant ×5, mana sawmill ×10, orc nest ×11, orc strategist ×14, vallorian valor ×10
• Special recipes (evolving buildings, chess set, artifacts) : 113
• Total : 1526 (average for non-special recipes : 17.7)