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How to evaluate vanilla creatures https://elementscommunity.org/forum/index.php?topic=48650.msg1062027#msg1062027
« on: April 20, 2013, 10:04:14 pm »
Bonsoir, in this post I would like to discuss how to evaluate the power level of vanilla creatures. I am hoping to both help PvP players who are trying to build a deck using creatures for a PvP Event as well as Card Designers who would like to balance their cards. I am going to differentiate between 5 aspects which are important.

1. Attack per Cost.

Rule No. 1: The higher the Attack/Cost ratio, the better.

This one is fairly obvious, and the one that most beginners will understand intuitively. Attack and Quanta Cost are the most important numbers on a creatures, and you naturally want to get the most bang for your buck. So: Cockatrice with 4/3 = 1.33 is better than Blue Crawler with 3/3 = 1.00 is better than Guardian Angel with 1/3 = 0.33.

So far so good, but this can't be all there is. For some creatures this rule does not seem to pertain. For example let's take the Ash Eater. It has a pretty convincing Damage to Cost ratio of 2/1 = 2.00. However it does not see any play in competitive Fire Rushes. An even more extreme example would be the Photon: With an Attack of 1 and a cost of 0, it's Damage to Cost ratio is actually infinite, however, similarly to Ash Eater it is not played in any competitive rush deck (other than those where its main purpose is to get sacrificed to Immolation). So we might need a few more rules to fit those creatures into the big picture.

2. Size.

Rule No. 2: The bigger a creature, the better.

Here by size I indeed mean a creature's size independant from its Attack/Cost ratio. If two creatures have the same Attack/Cost ratio, this rule says that the bigger one of them is better.

This one is a little less intuitive so let's try to understand this rule. One way to look at it is that big creatures allow you to put the same amount of potential damage into less cards. So if your deck contains a fixed amount of damage, taking few big creatures instead of many small ones will free up deck space for other cards, for example pillars. This means that the deck with bigger creatures will produce quanta faster than the deck with small creatures. Now, supposing that the small creature and the big creature have the same Damage per Cost ratio, this means that the deck with the big creatures will get their damage faster.

To demonstrate how this works, let us look at an Elements game with slightly modified rules: You have to build the fastest 3-card deck (with no mark) possible using only Purple Dragon, Abomination and Entropy Pillars. (Obviously there is no deckout rule). What deck do you build? According to Rule 1, Abomination and Purple Dragon are equally good. So which one is better? Let's find out:  1 Abomination, 2 Pillars kill on turn 23, 2 Abominations, 1 Pillar kills on turn 18, 1 Purple Dragon, 2 Pillars... turn 15!

So, the one-Abomination deck has the problem of simply not having enough damage in it compared to the life total it has to chew away, resulting in a fast start - it is the fastest deck to get a creature on the field - but nothing to follow up. This is comparable to the problem Photon or Ash Eater have in "real" Elements - you can obviously get them out fast, but you will need to get a significant fraction of the opponent's HP in damage on the field at some point, or it will simply take you forever to kill him.
The two-Abomination deck and the one-Dragon deck solve this problem by packing more damage. What makes the Dragon deck come out ahead is the fact that is has two pillars as opposed to one in the Abomination deck. Because its damage is concentrated in one card, it can play an additional pillar which means that at the time where the Abomination deck plays a five-damage card, it plays a ten-damage card.

Basically, a Dragon is two Abominations with the same prize quanta wise, but you invest one card less.
Alright! Now that we have understood this, let us move on to the next rule.

3. Size.

Rule No. 3: The smaller a creature, the better.

... so this is the opposite of rule 2, which is bad. However, the two rules don't always apply for the same kinds of creatures. What are the reasons for preferring a small creature?

While discussing Rule No. 2 we talked mainly about how much damage we can get into play after a certain amount of time, with that time being set sufficiently distant in the future. Now, getting a high amount of damage on the field certainly seems like a legitimate approach to trying to win a game. However, you must not forget to consider one thing: At some point, your opponent will die. This means that sometimes, while you were waiting to play your big creature, you maybe could have just played some cheap creatures and the opponent would be dead already.

As a hypothetical example: How good would this creature be?



Its atk/cost ratio is quite spectacular, better than any unupgraded creature that costs more than one, and it obviously wins any comparison regarding rule two. So does that mean it is the best? We will later determine that it is actually about on par with a dragon which is rather disappointing for that atk/cost efficiency. The problem is that while when in play, this creature ends the game immediately, you have to wait several turns in which you do nothing, except to accumulate quanta, to play it. This means we can also look at it this way: You want to optimally make full usage of your quanta every turn. Quanta that you do not spend at the end of every turn are did not do any work, so when you finally spend them, you need them to do more.

This explains why this rule has a stronger significance in duo decks than in monos. In a duo deck, your quanta production for one specific element is much slower than in a mono, meaning that you are more likely to be sitting on your quanta at end of turn waiting to be able to play your creature. This also explains why duo rushes are so much slower than mono rushes as they push you towards the weaker, smaller creatures.

Another lesson we can derive from this is: Mix the creatures in your deck up! If there are two creatures in the same element that have different cost but are roughly equally good, then the smart thing is to play a mix of both. The reason is that this reduces the chances of having to pass the turn with a big amount of quanta left, since if you have lots of quanta, you can play your big creature and otherwise just play another small one. In the early game when you tend to have less quanta you will more often play the small one while in the later game when your pillar stack has grown you will play your big creatures more often.

Now, the big question on your mind is probably: How do these rules mash up against each other? At what point will size trump atk/cost ratio? How big does a creature have to be before it is too big? Really how much better is a deck with a creature mix? At this point if you're a really good mathematician you could probably calculate all of that or you can take the easy way and just run some simulations which I did. For the results please see my second post in the thread as they are rather long and I would like to discuss two more rules (or pseudo-rules) first.

4. Hit Points.

Rule No. 4: Hit Points are not intrinsically valuable. Their worth depends on the metagame.

The HP of a creature do not help you kill the opponent. They make your deck neither faster nor slower. Showing their worth is entirely the job of your opponent. If your opponent is not running any cards that interact with your creature's hit points then you might as well just run all 1-HP creatures. That being said, this is a rather rare occurence in nowaday Elements PvP. Since interactive control cards are an integral part of todays metagame I would like to show some methods to categorize the various creature control cards and how to counter them.

To illustrate this I am going to analyze the forms of CC you might face in the War Event.
So the first thing I am going to do is make a little scale where every card gets a number on based on how prevalent the card is expected to be in the metagame:

5: War dominating card, heavily played by any team.
4: Heavily played in element, often splashed by other teams.
3: In-element staple.
2: In-element roleplayer.
1: Fringe playable.
0: Not played.

Alright, now to the real question: How do we counter CC? Before we go into the specifics, there is one rule that is applicable for almost any type of CC: Play more creatures and less pillars. If the opponent has CC, this means that the game will go longer and thus you will have more time to wait for quanta and play your creatures. If you took a deck that was purely optimized for speed then the opponent would simply kill your first couple creatures which destroys you quanta balance by postponing the point at which the game ends. For this reason you will rarely find a PvP deck that is looking for speed only; most of them will be a little overquanta'd.

Now to the various types of CC. The first category will be:

Damage-based, single-target CC:

CardRatingDamage
Lightning 4 5
Fire Bolt 4 Increments of 3
Shockwave 3 4
Owl's Eye 3 Increments of 3
Rage Potion 3 5
Ice Bolt 3 Increments of 2
Drain Life 3 Increments of 2
Red Nymph 2 Increments of 5
Grey Nymph 2 triangular numbers x 2
Toadfish 2* triangular numbers
Liquid Shadow 1 Increments of 1
Black Nymph 1 triangular numbers
Acceleration 1 Increments of 1
Aflatoxin 0 Increments of 2
Parasite 0 triangular numbers
*when they can use the ability

The obvious counter to those cards is to play creatures whose HP are above their damage. This forces the opponent to spend two cards killing it, thereby depleting his resources. More subtly, a softer counter to this kind of CC is to play smaller creatures. This reduces both the quanta advantage gained by destroying your creature as well as the percentage of your overall in-deck damage taken away by killing one creature.
Overall though the order in which creatures improve when you expect to run against this kind of CC:
Small creature, HP above damage > Big creature, HP above damage > Small creature, HP below damage > Big creature, HP below damage.

Damage-based, mass-CC:

CardRatingDamage
Rain of Fire 2 3
Thunderstorm 2 2
Blue Nymph 2 Increments of 1
Unstable Gas 2 1
Dry Spell 1 1
Plague 1 Increments of 1

Against these cards you obviously also want your creatures to be above the damage threshold, but additionally you have to consider that these cards almost eliminate the advantage small creatures have against CC by simply hitting all of them at once. The only advantage small creatures still have is that you can more finely adjust how much damage you commit to the board.

5. Metagame

Rule No. 5: The metagame can sometimes drastically change the evaluation of a creature.

This should not come as too big of a surprise. In the following paragraphs I would like to continue to outline how creatures interact with the metagame by continuing the with my War example.

Soft, single-target CC:

CardRating
Reverse Time* 4
Eternity* 3
Basilisk Blood 3
Arctic Squid 3
Freeze 2
Auburn Nymph 2
Antimatter 2
Purple Nymph 2
* Reverse Time and Eternity are a little special because they are an exception to the rule that you should take less quanta against decks with CC.

Soft CC does not care about the HP of the target creature. This means that playing small creatures is the major counter to them. Having extra HP is wasted quanta, simply play many creatures at once so that they cannot control them all. Also these cards often only work for a limited amount of time which helps you even more.

Next up are Shields. I'm going to first discuss the the damage prevention shields and then the rest of the bunch.

Damage reduction Shields:

CardRating
Titanium Shield 3
Skull Shield 2
Solar Shield 2
Ice Shield 2
Emerald Shield 1
Shield 0

The damage prevention shields all have in common that you would rather have big creatures against them since that way they prevent a lower percentage of your total damage. To the rest of the Shields:

Specialized Shields:

CardRating
Dimensional Shield 5
Bone Wall 4
Fog Shield 4
Wings 3
Dusk Mantle 3
Sundial 3
Dissipation Shield 2
Fire Shield 2
Gravity Shield 1
Procrastination 1
Spine Carapace 1

Spine Carapace and Fire Shield are basically mass-CC cards. Against Procrastination, big creatures are slightly preferrable as they need a lower number of attacks to kill the opponent, meaning their procentual prevented damage will be lower. Against Gravity Shield you obviously need creatures with 5 or less HP, against Wings airborne creatures. Sundial does not care about what type of creatures you have, but it only provides 1 turn of protection, and the opponent is hindered at doing damage as well. So a good way to counter it with creatures is to simply be as fast as possible, forcing him to try and start chaning early, meaning that you don't want to underquanta your deck too much. Dissipation Shield and Bone Wall both have in common that you mainly just need a lot of creatures, against Bone Wall preferrably small ones, against Dissipation Shield smaller creatures with (atk modulo 3) = 1 are preferred, but more importantly you need your creatures to be good against the CC that they are combined with. Against Dusk Mantle and Fog Shield it doesn't matter what you play except that smaller creatures with reduce the variance of the RNG. Finally, with Dimensional Shield there is no strategy involved at all as it is simply a hard counter against creatures (guess why it is a 5). You will need to find another way around it.

The last way of how your opponent can stop your creatures that I want to cover is healing. Healing is the most universal defense mechanism as it also works against damage that cannot be blocked or destroyed otherwise, such as Poison. The downside to this that the defense they provide against more specialiced sources of damage (such as creatures) is rather behind the curve. This means that you should do pretty well if you just have enough damage and underquanta your deck a little to account for the longer game times.

Healing Cards:

CardRating
Sanctuary 4
Miracle 3
Stone Skin 2
Heal 1
Empathic Bond 1

So those were the main ways of how your opponent can try to counter your creatures. As you may have noticed we get a wild mix of metagame effects, some pointing in completely oppsite directions, but for the metagame we analysed, the main trends are:

- Smaller creature rise in value a little.
- You generally want less quanta in your deck than you would need for optimal ttw.

Of course, the possibilities how your opponent can deal with your creatures are not the only ways the metagame influences the strenghth of creatures. For example Purple Dragon and Emerald Dragon are an innocuous-looking pair of creatures at first, with the Emerald Dragon seeming slightly superior due to his extra Hit Point. However if you look at some statistics you would find that Emerald is putting up some thoroughly mediocre results, while Purple Dragon is a total menace, one of the most winning creatures in War of all time. The reason for this of course is that Purple Dragon enjoys the in-element company of Discord, one of the strongest cards in the game that it combines very well with. So metagame is not only what your opponent can throw at you, but also what you can combine your cards with.

The inconvenient thing about the metagame is that it can also sometimes be dynamic. For our War analysis, we determined that Lightning was one of the predominant CC cards. Now if you managed to create a deck that Lightning is very ineffective against and that is also strong in the metagame in general, then the overall presence of Lightning in the metagame might decrease. This in turn can reinvigorate decks that were previously not competitive against Lightning but that are good against your new deck, which weakens your new deck. The equilibrium will be somewhere in the middle of those possibilities. This is particularly relevant in metagames with smaller cardpools. Here the strenghth of a card can drastically differ from what you are used to from the base game when important cards are taken away.

Ok those were my tips for players and designers on what to consider when evaluating vanilla creatures. Some of those can be applied to non vanilla creatures as well, especially those that have abilities that simply affect their atk or how easily they die. For others it is going to be more complicated. :)
"My big fear is that one day I may become so vain that I will quote myself in my own signature."  ---  10 men

Offline 10 menTopic starter

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Re: How to evaluate vanilla creatures https://elementscommunity.org/forum/index.php?topic=48650.msg1062028#msg1062028
« Reply #1 on: April 20, 2013, 10:05:03 pm »
Appendix: Some simulations on the ttw for different creatures.

As promised, here are some stats on how fast different creatures are in a vacuum. What I did here was to take a deck with thirty cards, of which some were pillars and all the others one certain creature that I wanted to test (usually ignoring the 6 card limit). I then ran one million test games for that deck on the play and on the draw and let it calculate the average ttw of those games. I then varied the number of pillars of the deck until I found the optimal ttw. The result of that pillar distribution is copied below.

Some further annotations: The sample size of games simulated was 1 million on the play and another million on the draw. Between two test runs, the first two decimals always remained stable. The third decimal usually fluctuated by one or two points. Another interesting observation was that near the optimum ttw from one pillar - creature distribution to the next, the average ttw fluctuates in the second decimal. A couple times it was pretty obvious that the optimal pillar-creature distribution was somewhere in the middle between two pillar amounts, meaning that the ttw could have been optimized by one or two hundredth of a turn by going up to 31 cards. The takeaway here however is that before being able to decide that you need to be able to pin down your average ttw to the second post comma digit... and from trying around a bit, this takes about 200k games. :))

With that out of the way, let's take a look at how the unupgraded creatures of Elements fared in the test:

Spoiler for Hidden:
Code: [Select]
Purple Dragon:
ttw for a creature with 10 cost and 10 attack in a 30 card deck with 20 pillars is 7.320453 turns on the play.
ttw for a creature with 10 cost and 10 attack in a 30 card deck with 20 pillars is 6.976924 turns on the draw.

Abomination:
ttw for a creature with 5 cost and 5 attack in a 30 card deck with 16 pillars is 7.718459 turns on the play.
ttw for a creature with 5 cost and 5 attack in a 30 card deck with 16 pillars is 7.379997 turns on the draw.

Fallen Elf:
ttw for a creature with 4 cost and 3 attack in a 30 card deck with 14 pillars is 9.304309 turns on the play.
ttw for a creature with 4 cost and 3 attack in a 30 card deck with 14 pillars is 8.881729 turns on the draw.

Flesh Spider:
ttw for a creature with 3 cost and 3 attack in a 30 card deck with 12 pillars is 8.590306 turns on the play.
ttw for a creature with 3 cost and 3 attack in a 30 card deck with 12 pillars is 8.256718 turns on the draw.

Skeleton:
ttw for a creature with 1 cost and 1 attack in a 30 card deck with 5 pillars is 12.203156 turns on the play.
ttw for a creature with 1 cost and 1 attack in a 30 card deck with 5 pillars is 11.670502 turns on the draw.

Mummy:
ttw for a creature with 4 cost and 5 attack in a 30 card deck with 15 pillars is 7.2937 turns on the play.
ttw for a creature with 4 cost and 5 attack in a 30 card deck with 15 pillars is 7.003629 turns on the draw.

Colossal Dragon:
ttw for a creature with 10 cost and 7 attack in a 30 card deck with 20 pillars is 8.577173 turns on the play.
ttw for a creature with 10 cost and 7 attack in a 30 card deck with 20 pillars is 8.193681 turns on the draw.

Sapphire Charger:
ttw for a creature with 5 cost and 4 attack in a 30 card deck with 16 pillars is 8.601171 turns on the play.
ttw for a creature with 5 cost and 4 attack in a 30 card deck with 16 pillars is 8.248238 turns on the draw.

Armagio:
ttw for a creature with 5 cost and 1 attack in a 30 card deck with 12 pillars is 16.152911 turns on the play.
ttw for a creature with 5 cost and 1 attack in a 30 card deck with 12 pillars is 15.60695 turns on the draw.

Antlion:
ttw for a creature with 2 cost and 2 attack in a 30 card deck with 9 pillars is 9.484811 turns on the play.
ttw for a creature with 2 cost and 2 attack in a 30 card deck with 9 pillars is 9.096609 turns on the draw.

Shrieker:
ttw for a creature with 8 cost and 8 attack in a 30 card deck with 19 pillars is 7.605749 turns on the play.
ttw for a creature with 8 cost and 8 attack in a 30 card deck with 19 pillars is 7.249803 turns on the draw.

Hematite Golem:
ttw for a creature with 4 cost and 4 attack in a 30 card deck with 14 pillars is 8.121903 turns on the play.
ttw for a creature with 4 cost and 4 attack in a 30 card deck with 14 pillars is 7.68828 turns on the draw.

Horned Frog:
ttw for a creature with 2 cost and 3 attack in a 30 card deck with 11 pillars is 7.882434 turns on the play.
ttw for a creature with 2 cost and 3 attack in a 30 card deck with 11 pillars is 7.472705 turns on the draw.

Cockatrice:
ttw for a creature with 3 cost and 4 attack in a 30 card deck with 13 pillars is 7.425771 turns on the play.
ttw for a creature with 3 cost and 4 attack in a 30 card deck with 13 pillars is 7.157909 turns on the draw.

Photon:
ttw for a creature with 0 cost and 1 attack in a 30 card deck with 0 pillars is 10.0 turns on the play.
ttw for a creature with 0 cost and 1 attack in a 30 card deck with 0 pillars is 9.0 turns on the draw.

Light Dragon:
ttw for a creature with 12 cost and 10 attack in a 30 card deck with 21 pillars is 7.772995 turns on the play.
ttw for a creature with 12 cost and 10 attack in a 30 card deck with 21 pillars is 7.392485 turns on the draw.

Guardian Angel:
ttw for a creature with 3 cost and 1 attack in a 30 card deck with 9 pillars is 14.550117 turns on the play.
ttw for a creature with 3 cost and 1 attack in a 30 card deck with 9 pillars is 14.044154 turns on the draw.

Azure Dragon:
ttw for a creature with 10 cost and 9 attack in a 30 card deck with 20 pillars is 7.8977 turns on the play.
ttw for a creature with 10 cost and 9 attack in a 30 card deck with 20 pillars is 7.507079 turns on the draw.

Ash Eater:
ttw for a creature with 1 cost and 2 attack in a 30 card deck with 6 pillars is 8.353613 turns on the play.
ttw for a creature with 1 cost and 2 attack in a 30 card deck with 6 pillars is 8.062089 turns on the draw.

Crimson Dragon:
ttw for a creature with 10 cost and 12 attack in a 30 card deck with 20 pillars is 7.077717 turns on the play.
ttw for a creature with 10 cost and 12 attack in a 30 card deck with 20 pillars is 6.689371 turns on the draw.

Seraph:
ttw for a creature with 9 cost and 10 attack in a 30 card deck with 19 pillars is 7.060312 turns on the play.
ttw for a creature with 9 cost and 10 attack in a 30 card deck with 19 pillars is 6.678878 turns on the draw.

Phoenix:
ttw for a creature with 7 cost and 7 attack in a 30 card deck with 18 pillars is 7.549629 turns on the play.
ttw for a creature with 7 cost and 7 attack in a 30 card deck with 18 pillars is 7.129611 turns on the draw.

Toadfish:
ttw for a creature with 5 cost and 6 attack in a 30 card deck with 17 pillars is 7.296341 turns on the play.
ttw for a creature with 5 cost and 6 attack in a 30 card deck with 17 pillars is 6.919189 turns on the draw.

Minor Vampire:
ttw for a creature with 3 cost and 2 attack in a 30 card deck with 9 pillars is 10.593839 turns on the play.
ttw for a creature with 3 cost and 2 attack in a 30 card deck with 9 pillars is 10.204243 turns on the draw.

Ghost of the Past:
ttw for a creature with 6 cost and 7 attack in a 30 card deck with 17 pillars is 7.116294 turns on the play.
ttw for a creature with 6 cost and 7 attack in a 30 card deck with 17 pillars is 6.764446 turns on the draw.

Anubis:
ttw for a creature with 8 cost and 5 attack in a 30 card deck with 18 pillars is 8.982828 turns on the play.
ttw for a creature with 8 cost and 5 attack in a 30 card deck with 18 pillars is 8.554788 turns on the draw.

Scarab:
ttw for a creature with 2 cost and 2 attack in a 30 card deck with 9 pillars is 9.485379 turns on the play.
ttw for a creature with 2 cost and 2 attack in a 30 card deck with 9 pillars is 9.097427 turns on the draw.

Phase Dragon:
ttw for a creature with 13 cost and 8 attack in a 30 card deck with 21 pillars is 8.824362 turns on the play.
ttw for a creature with 13 cost and 8 attack in a 30 card deck with 21 pillars is 8.428561 turns on the draw.

Immortal:
ttw for a creature with 6 cost and 4 attack in a 30 card deck with 17 pillars is 9.065354 turns on the play.
ttw for a creature with 6 cost and 4 attack in a 30 card deck with 17 pillars is 8.657919 turns on the draw.

Turquoise Nymph:
ttw for a creature with 8 cost and 7 attack in a 30 card deck with 18 pillars is 7.950266 turns on the play.
ttw for a creature with 8 cost and 7 attack in a 30 card deck with 18 pillars is 7.531602 turns on the draw.

Ok, that was a lot of data, so I think it is time for some rankings! First of all: The flop 3 unupgraded creatures:

RankCreaturettw
^-^ Skeleton 11,94
:( Guardian Angel 14,30
Armedilgo 15,88
(no comment) ;)

For the Top 6 unupgraded creatures:

RankCreaturettw
1 Seraph 6,87
2 Crimson Dragon 6,88
3 Ghost of the Past 6,94
4 Toadfish 7,11
5 Purple Dragon 7,15
6 Mummy 7,15

And the winner is... Seraph! Who would have guessed that ranking? Seraph leading and Purple Dragon as fast as Mummy? Seraph is obviously in a pretty sweet spot for this kind of ranking with his 10 attack nicely allowing him to land on exactly 100 damage. It is also one of the most prone to CC creatures in the game. Still, it might be somewhat underrated in the current metagame looking at how convincingly it leaves behind all these other PvP staples.

Now, that ranking is nice and all, but it cannot really be considered complete without the king of stupid beaters. I am of course talking about Graboid, which unfortunately is a little more complicated to simulate as it uses two types of quanta and you also might want to use Pendulums with it. However I did that too and also used the same script for a bunch of similar creatures with off-element abilities. Here is the data:

Spoiler for Hidden:
Code: [Select]
Forest Spirit:
ttw for Forest Spirit in a 30 card deck with 4 pillars and 13 pendulums is 7.543534 turns on the play.
ttw for Forest Spirit in a 30 card deck with 4 pillars and 13 pendulums is 7.251536 turns on the draw.

Graboid:
ttw for Graboid in a 30 card deck with 16 pillars and 0 pendulums is 6.574551 turns on the play.
ttw for Graboid in a 30 card deck with 16 pillars and 0 pendulums is 6.249374 turns on the draw.

Lycanthrope:
ttw for Lycanthrope in a 30 card deck with 5 pillars and 11 pendulums is 7.435191 turns on the play.
ttw for Lycanthrope in a 30 card deck with 5 pillars and 11 pendulums is 7.127477 turns on the draw.

Lava Golem:
ttw for Lava Golem in a 30 card deck with 17 pillars and 1 pendulums is 7.078634 turns on the play.
ttw for Lava Golem in a 30 card deck with 17 pillars and 1 pendulums is 6.727834 turns on the draw.

Chrysaora:
ttw for Chrysaora in a 30 card deck with 0 pillars and 16 pendulums is 9.511544 turns on the play.
ttw for Chrysaora in a 30 card deck with 0 pillars and 16 pendulums is 9.264361 turns on the draw.

Pegasus:
ttw for Pegasus in a 30 card deck with 10 pillars and 8 pendulums is 8.355831 turns on the play.
ttw for Pegasus in a 30 card deck with 10 pillars and 8 pendulums is 7.92257 turns on the draw.

In a completely unexpected turn of events, Graboid blows the whole competition out of the water. Considering that his actual strenghth lies in the combination with Nova, one of the most powerful cards in the game, it certainly seems that the other creatures have some catching up to do. Notably, Lava Golem also puts up some very respectable results.

Next up are the upgraded creatures (with upgraded Pillars). Here is the data:

Spoiler for Hidden:
Code: [Select]
Micro Abomination:
ttw for a creature with 1 cost and 2 attack in a 30 card deck with 7 pillars is 8.031331 turns on the play.
ttw for a creature with 1 cost and 2 attack in a 30 card deck with 7 pillars is 7.545119 turns on the draw.

Amethyst Dragon:
ttw for a creature with 11 cost and 12 attack in a 30 card deck with 20 pillars is 6.530984 turns on the play.
ttw for a creature with 11 cost and 12 attack in a 30 card deck with 20 pillars is 6.217776 turns on the draw.

Fallen Druid:
ttw for a creature with 5 cost and 3 attack in a 30 card deck with 14 pillars is 9.226453 turns on the play.
ttw for a creature with 5 cost and 3 attack in a 30 card deck with 14 pillars is 8.788845 turns on the draw.

Flesh Recluse:
ttw for a creature with 3 cost and 6 attack in a 30 card deck with 14 pillars is 5.54261 turns on the play.
ttw for a creature with 3 cost and 6 attack in a 30 card deck with 14 pillars is 5.244602 turns on the draw.

Elite Mummy:
ttw for a creature with 3 cost and 5 attack in a 30 card deck with 13 pillars is 6.159894 turns on the play.
ttw for a creature with 3 cost and 5 attack in a 30 card deck with 13 pillars is 5.726322 turns on the draw.

Ivory Dragon:
ttw for a creature with 10 cost and 11 attack in a 30 card deck with 20 pillars is 6.498202 turns on the play.
ttw for a creature with 10 cost and 11 attack in a 30 card deck with 20 pillars is 6.199744 turns on the draw.

Elite Charger
ttw for a creature with 5 cost and 7 attack in a 30 card deck with 16 pillars is 6.119037 turns on the play.
ttw for a creature with 5 cost and 7 attack in a 30 card deck with 16 pillars is 5.789429 turns on the draw.

Elite Armagio
ttw for a creature with 5 cost and 2 attack in a 30 card deck with 13 pillars is 11.139765 turns on the play.
ttw for a creature with 5 cost and 2 attack in a 30 card deck with 13 pillars is 10.653211 turns on the draw.

Massive Dragon
ttw for a creature with 11 cost and 8 attack in a 30 card deck with 20 pillars is 7.632767 turns on the play.
ttw for a creature with 11 cost and 8 attack in a 30 card deck with 20 pillars is 7.286117 turns on the draw.

Elite Antlion
ttw for a creature with 2 cost and 4 attack in a 30 card deck with 11 pillars is 6.233367 turns on the play.
ttw for a creature with 2 cost and 4 attack in a 30 card deck with 11 pillars is 5.863274 turns on the draw.

Steel Golem
ttw for a creature with 4 cost and 6 attack in a 30 card deck with 15 pillars is 6.127793 turns on the play.
ttw for a creature with 4 cost and 6 attack in a 30 card deck with 15 pillars is 5.701063 turns on the draw.

Elite Shrieker
ttw for a creature with 8 cost and 10 attack in a 30 card deck with 19 pillars is 5.970585 turns on the play.
ttw for a creature with 8 cost and 10 attack in a 30 card deck with 19 pillars is 5.582438 turns on the draw.

Giant Frog
ttw for a creature with 2 cost and 5 attack in a 30 card deck with 12 pillars is 5.402313 turns on the play.
ttw for a creature with 2 cost and 5 attack in a 30 card deck with 12 pillars is 5.177107 turns on the draw.

Elite Cockatrice
ttw for a creature with 3 cost and 5 attack in a 30 card deck with 13 pillars is 6.159782 turns on the play.
ttw for a creature with 3 cost and 5 attack in a 30 card deck with 13 pillars is 5.727425 turns on the draw.

Leaf Dragon
ttw for a creature with 1 cost and 1 attack in a 30 card deck with 5 pillars is 11.830554 turns on the play.
ttw for a creature with 1 cost and 1 attack in a 30 card deck with 5 pillars is 11.347726 turns on the draw.

Archangel
ttw for a creature with 6 cost and 7 attack in a 30 card deck with 17 pillars is 6.449803 turns on the play.
ttw for a creature with 6 cost and 7 attack in a 30 card deck with 17 pillars is 6.117128 turns on the draw.

Light Dragon
ttw for a creature with 13 cost and 12 attack in a 30 card deck with 20 pillars is 7.004929 turns on the play.
ttw for a creature with 13 cost and 12 attack in a 30 card deck with 20 pillars is 6.626092 turns on the draw.

Damselfly:
ttw for a creature with 0 cost and 2 attack in a 30 card deck with 0 pillars is 6.0 turns on the play.
ttw for a creature with 0 cost and 2 attack in a 30 card deck with 0 pillars is 5.0 turns on the draw.

Sky Dragon
ttw for a creature with 12 cost and 13 attack in a 30 card deck with 21 pillars is 6.407265 turns on the play.
ttw for a creature with 12 cost and 13 attack in a 30 card deck with 21 pillars is 6.142479 turns on the draw.

Elite Firefly
ttw for a creature with 3 cost and 4 attack in a 30 card deck with 13 pillars is 6.826906 turns on the play.
ttw for a creature with 3 cost and 4 attack in a 30 card deck with 13 pillars is 6.399985 turns on the draw.

Ruby Dragon
ttw for a creature with 12 cost and 15 attack in a 30 card deck with 21 pillars is 5.974296 turns on the play.
ttw for a creature with 12 cost and 15 attack in a 30 card deck with 21 pillars is 5.525071 turns on the draw.

Seraph (upgraded)
ttw for a creature with 9 cost and 12 attack in a 30 card deck with 20 pillars is 6.047591 turns on the play.
ttw for a creature with 9 cost and 12 attack in a 30 card deck with 20 pillars is 5.634041 turns on the draw.

Vampire
ttw for a creature with 5 cost and 4 attack in a 30 card deck with 15 pillars is 7.950265 turns on the play.
ttw for a creature with 5 cost and 4 attack in a 30 card deck with 15 pillars is 7.53476 turns on the draw.

Bloodsucker
ttw for a creature with 2 cost and 3 attack in a 30 card deck with 10 pillars is 7.319719 turns on the play.
ttw for a creature with 2 cost and 3 attack in a 30 card deck with 10 pillars is 6.94142 turns on the draw.

Elite Anubis:
ttw for a creature with 8 cost and 5 attack in a 30 card deck with 18 pillars is 8.244834 turns on the play.
ttw for a creature with 8 cost and 5 attack in a 30 card deck with 18 pillars is 7.807148 turns on the draw.

Ghost of the Past:
ttw for a creature with 7 cost and 9 attack in a 30 card deck with 18 pillars is 6.346538 turns on the play.
ttw for a creature with 7 cost and 9 attack in a 30 card deck with 18 pillars is 6.030959 turns on the draw.

(upgraded) Psion:
ttw for a creature with 4 cost and 5 attack in a 30 card deck with 15 pillars is 6.626789 turns on the play.
ttw for a creature with 4 cost and 5 attack in a 30 card deck with 15 pillars is 6.279136 turns on the draw.

Phase Recluse:
ttw for a creature with 4 cost and 7 attack in a 30 card deck with 15 pillars is 5.680882 turns on the play.
ttw for a creature with 4 cost and 7 attack in a 30 card deck with 15 pillars is 5.331224 turns on the draw.

Aether Nymph:
ttw for a creature with 8 cost and 8 attack in a 30 card deck with 18 pillars is 6.846621 turns on the play.
ttw for a creature with 8 cost and 8 attack in a 30 card deck with 18 pillars is 6.483466 turns on the draw.

Elite Phase Dragon:
ttw for a creature with 14 cost and 10 attack in a 30 card deck with 21 pillars is 7.530252 turns on the play.
ttw for a creature with 14 cost and 10 attack in a 30 card deck with 21 pillars is 7.087369 turns on the draw.

The unupgraded ranking is dominated pretty convincingly by heavy hitters. The upgraded Top 5 gives a different outlook with the smaller creatures getting a much more decisive buff from their upgrade:

RankCreaturettw
1 Giant Frog 5,29
2 Flesh Recluse 5,39
3 Damselfly 5,50
4 Phase Recluse 5,51
5 Ruby Dragon 5,75

And the ability creatures in their upgraded version:

Spoiler for Hidden:
Code: [Select]
Elite Graboid:
ttw for Elite Graboid in a 30 card deck with 15 pillars and 1 pendulums is 5.3560622 turns on the play.
ttw for Elite Graboid in a 30 card deck with 15 pillars and 1 pendulums is 5.1644678 turns on the draw.

Forest Spectre:
ttw for Forest Spectre in a 30 card deck with 2 pillars and 15 pendulums is 6.548753 turns on the play.
ttw for Forest Spectre in a 30 card deck with 2 pillars and 15 pendulums is 6.242775 turns on the draw.

Werewolf:
ttw for Werewolf in a 30 card deck with 8 pillars and 6 pendulums is 6.31142 turns on the play.
ttw for Werewolf in a 30 card deck with 8 pillars and 6 pendulums is 6.032228 turns on the draw.

Lava Destroyer:
ttw for Lava Destroyer in a 30 card deck with 18 pillars and 0 pendulums is 5.764585 turns on the play.
ttw for Lava Destroyer in a 30 card deck with 18 pillars and 0 pendulums is 5.383428 turns on the draw.

Physalia:
ttw for Physalia in a 30 card deck with 0 pillars and 12 pendulums is 6.800399 turns on the play.
ttw for Physalia in a 30 card deck with 0 pillars and 12 pendulums is 6.302576 turns on the draw.

Elite Pegasus:
ttw for Elite Pegasus in a 30 card deck with 7 pillars and 11 pendulums is 6.387504 turns on the play.
ttw for Elite Pegasus in a 30 card deck with 7 pillars and 11 pendulums is 5.974232 turns on the draw.

So Graboid is still King of the hill, but by a much narrower margin than in the unupgraded field.

Those were the stats for the existing creatures in Elements, but out of curiosity I also simulated some games for some hypothetical creatures such as the one I mentioned under point 3. I started with my 100 atk creature and then moved down in attack so that the creature would need exactly one more hit than before to kill the opponent. For each of those attack numbers I varied the cost so that the ttw would lie roughly around that of the best existing creatures.

Spoiler for Hidden:
Code: [Select]
Dei Mudda:
ttw for a creature with 50 cost and 100 attack in a 30 card deck with 25 pillars is 7.324322 turns on the play.
ttw for a creature with 50 cost and 100 attack in a 30 card deck with 25 pillars is 6.840954 turns on the draw.

50/38:
ttw for a creature with 38 cost and 50 attack in a 30 card deck with 25 pillars is 7.302965 turns on the play.
ttw for a creature with 38 cost and 50 attack in a 30 card deck with 25 pillars is 6.824145 turns on the draw.

34/27:
ttw for a creature with 27 cost and 34 attack in a 30 card deck with 24 pillars is 7.226003 turns on the play.
ttw for a creature with 27 cost and 34 attack in a 30 card deck with 24 pillars is 6.814337 turns on the draw.

25/23:
ttw for a creature with 23 cost and 25 attack in a 30 card deck with 24 pillars is 7.301123 turns on the play.
ttw for a creature with 23 cost and 25 attack in a 30 card deck with 24 pillars is 6.880131 turns on the draw.

20/18:
ttw for a creature with 18 cost and 20 attack in a 30 card deck with 22 pillars is 7.213819 turns on the play.
ttw for a creature with 18 cost and 20 attack in a 30 card deck with 22 pillars is 6.960209 turns on the draw.

17/16:
ttw for a creature with 16 cost and 17 attack in a 30 card deck with 22 pillars is 7.217016 turns on the play.
ttw for a creature with 16 cost and 17 attack in a 30 card deck with 22 pillars is 6.881173 turns on the draw.

15/14:
ttw for a creature with 14 cost and 15 attack in a 30 card deck with 22 pillars is 7.259572 turns on the play.
ttw for a creature with 14 cost and 15 attack in a 30 card deck with 22 pillars is 6.844749 turns on the draw.

13/12:
ttw for a creature with 12 cost and 13 attack in a 30 card deck with 21 pillars is 7.249529 turns on the play.
ttw for a creature with 12 cost and 13 attack in a 30 card deck with 21 pillars is 6.901468 turns on the draw.

As you can see, the first three creatures still need a pretty heavy discount to be competitive, their atk/cost ratios all being significantly above one. However after that, at 25 attack the ratio is pretty normal already at atk/cost = 25/23 = 1,09. So that is where, for mono decks, the "business size" seems to start, despite no creatures existing in the game in that range at this point.

Finally I put my claim that decks with creature mixes are better than uniform decks to the test. I took two creatures that scored very similarly in the previous ttw test, Bone Dragon and Mummy, and tested some decks that contained both of those creature. And lo' and behold, the new deck was indeed faster than either of the single creature decks. Many different configurations beat them out in speed and the best of them was:

Spoiler for Hidden:
Code: [Select]
Mummy + Bone Dragon:
ttw for a deck with 30 cards, 4 Bone Dragon and 10 Mummy, is 7.21702 turns on the play.
ttw for a deck with 30 cards, 4 Bone Dragon and 10 Mummy, is 6.935755 turns on the draw.

Feel free to ask any questions you may have on my post. :)
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Offline eaglgenes101

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Re: How to evaluate vanilla creatures https://elementscommunity.org/forum/index.php?topic=48650.msg1062029#msg1062029
« Reply #2 on: April 20, 2013, 10:13:13 pm »
Also: It costs time to wait for cards to be drawn and quanta to be accumulated from pillars. Might help in solving the small creature for 0 cost discreptancy and help determine where rule 2 and 3 should be used.
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Re: How to evaluate vanilla creatures https://elementscommunity.org/forum/index.php?topic=48650.msg1062044#msg1062044
« Reply #3 on: April 20, 2013, 10:33:07 pm »
Nice long post is nice and long :) Kudos to you for compiling all those data.

Back in the day in one of my articles, I tried to introduce a littlie something called "threat level" for creatures, which could be described by the following parameters:

Threat level= (damage/cost ratio)+ (damage/opponent HP ratio)- (cost)- (the opponent's incentive to deal with the creature)+ (resilience to CC.) +(handy ablilties)

- dmg/cost ratio: I think this is obvious, the bigger the better.
- damage/opponent's HP ratio: This basically covers the 2. aspect in your analysis
- cost: this refers to the 3. point of your analysis. The earier you can play a creature, the better.
- incentive to deal with the creature: This is a subjective factor. The incentive is low if the creature is not the most dangerous on the board, or if it costs too much to deal with (aka has a high resilience: You won't use your single Lightning on an Abyss Crawler.) This factor is interesting because it scales up with all the other factors except resilience. (It scales down with resilience)
- resilience: Scales with HP and immortality. Sadly, immortality also raises the cost factor.
- abilities: While your article is about vanillas, some abilities raise the threat level by a lot.

Of course, some of those cannot be quantified, but the equation basically says "the more dangerous the creature is for the opponent, the more likely that s/he will want to deal with it, so if the creature is also hard to deal with, then it is a great creature"

Based on the equation, I think the best hitters are something like Steel Golem (cheap and hits hard, yet very hard to deal with) and the like. Seraph may be fantastic, but its "incentive" factor is high while its resilience is low (at first... then it goes to high), so all in all IMO the "threat level" is mediocre at best.
« Last Edit: April 20, 2013, 10:41:10 pm by Acsabi44 »
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Offline Marsu

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Re: How to evaluate vanilla creatures https://elementscommunity.org/forum/index.php?topic=48650.msg1062047#msg1062047
« Reply #4 on: April 20, 2013, 10:49:24 pm »
Absolutely great post. I rarely +rep guides as I find most of them to be - good, but not more, but I will do now.

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Re: How to evaluate vanilla creatures https://elementscommunity.org/forum/index.php?topic=48650.msg1062048#msg1062048
« Reply #5 on: April 20, 2013, 10:57:22 pm »
Those were fantastic posts. The information regarding creatures is certainly useful, and not just to players less familiar with the game. I also commend you for statistically proving the benefit of the quanta sink by testing that a Mummy + Dragon deck is better than a pure Mummy deck.
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Re: How to evaluate vanilla creatures https://elementscommunity.org/forum/index.php?topic=48650.msg1062055#msg1062055
« Reply #6 on: April 20, 2013, 11:17:23 pm »
This was a wonderful read, another game theory article like Acsabi's ones. A pair of ttw tests surprised me a bit though.
A single +rep isn't enough for this article and the tests.
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Re: How to evaluate vanilla creatures https://elementscommunity.org/forum/index.php?topic=48650.msg1062284#msg1062284
« Reply #7 on: April 21, 2013, 03:30:30 pm »
I've been enjoying your insights into game theory, 10 men. Plus you write really well. Keep it up.

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Re: How to evaluate vanilla creatures https://elementscommunity.org/forum/index.php?topic=48650.msg1062315#msg1062315
« Reply #8 on: April 21, 2013, 06:17:19 pm »
An inspiring article, 10 men. It deserves to be in the wiki.
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Re: How to evaluate vanilla creatures https://elementscommunity.org/forum/index.php?topic=48650.msg1062318#msg1062318
« Reply #9 on: April 21, 2013, 06:41:52 pm »
An inspiring article, 10 men. It deserves to be in the wiki.
You should take a look at Acsabi's ones too.
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Re: How to evaluate vanilla creatures https://elementscommunity.org/forum/index.php?topic=48650.msg1062335#msg1062335
« Reply #10 on: April 21, 2013, 07:21:23 pm »
Apparently, Graboid > Frog in terms of speed. huh, I would've guessed that giant frog worked better.
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Re: How to evaluate vanilla creatures https://elementscommunity.org/forum/index.php?topic=48650.msg1062372#msg1062372
« Reply #11 on: April 21, 2013, 08:23:10 pm »
One of the best guides I have read for a long time.
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