Slinterlands Study: valuing cards by the cost of mana - frequent abilities

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(Edited)

Greetings, Battlemages!

Well, well, while my study is well advanced, I'm far behind for redacting and formatting!
We defined in my last post a formula to determinate the mana cost of cards based on their stats. This following is long overdue!

We will use the same abbreviations as before:
Me = Melee damage
Ma = Magic damage
Ra = Range damage
S = Speed
A = Armor
H = health

ERRATUM: Ranged damages

Haha! What a poor start!
If you remember, I compared Angelic Mandarin, Sould Strangler and Scavo Firebolt to determine the cost of Ranged damage to 0.5
By doing so, it is like saying "these 3 units are the standard and will be used to judge the other units". The problem with Ranged units is that, well, they are all over the place. There are good units, bad units, and pretty bad units! They certainly have the most variability of all types of monsters.

So I increased the sample size for it to be more representative. See the results when we compare different cards:
Soul-Strangler-Angeluc Mandarin-Scavo Firebolt give Ra=0.5
Supply Runner-Kulu Swimhunter: Ra=1.5
Lava Spider-Hunter Jarx: Ra=1.5
Portal Spinner-Coastal Nympl: Ra=1
Lava Launcher-Queen of Crows: Ra=3.5 (Queen of Clowns actually! She's so bad!)
Goblin Tower-Primologist: Ra=1
Runeslinger-Iloth Dhampir: Ra=1.75

So on average, the cost of Ranged damage is 1.1, so we will just use Ra=1
I like it better. Melee and Range are physical damages and are valued the same.

So the corrected formula is:

Mana cost = Me + Ra + 2Ma + 0.5(S+A+H) - Rarity + Neutral/reward penalty + Ability

where
Rarity = 2 (Common) 2.5 (Rare) 3 (Epic) 3.5 (Legendary)
Neutral penalty = 1.2
Reward penalty = 0.5

Before we get deeper into the formula (and the abilities), we can first discuss a few conclusions derived from the formula.

Discussion

So, what do you think? Speed, Armor and Health are valued the same. Does it seem right to you?
Armor is useless against Magic attack, so it is worth less than 1 Health.
But 1 point of armor can save you 2-3-4 points of Health, so it is worth more than 1 Health!
And 2 points of armor, it's likely to be as useful as only one point, right?
What I mean is that in all cases, the real value of cards is situational. We can look at the mana cost of cards relatively to their stats, but we should not forget that the value of these stats will be realized (or not) according to the battle situation. A bit like: Ever-Hungry Skull has good stats for sure, but a single magic attack makes it worth nothing.

Because of the mana allowance given to cards according to their rarity, you would usually want to play rarer cards as they would usually be more powerful (yeah! thank you Captain Obvious!). That is true if you manage to saturate your lineup.
Another consequence is that it would be usually better to play smaller but more numerous monsters to take advantage of this mana allowance. Playing four 3-mana monsters would put more stats on the board than playing three 4-mana monsters. Not a guarantee to win though.

Frequent Melee Abilities

The abilities represented frequently will be easy to determinate, as we will have a sample size big enough to be representative.

To determine that, we will need a few calculations, and some abbreviations also...
Raw = the raw stats given by the formula
Rarity = the rarity allowance or bonus
Abi = the ability cost
Neu/Rew = the Neutral/Reward malus if any
Expected = the mana cost calculated with the formula (=what we expect the card to cost mana-wise)
Diff = the difference between the real and calculated mana cost
Raw/mana = the raw stats per point of mana

Let's start with the most basic units at level 1, the ones without any ability. They can just attack when in first position, nothing more. Hence we consider a cost of 0 for this non-ability.

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The average deviation from the formula is only -0.12 if we exclude the Biceraptops (who really sucks). We also notice that the ratio raw stats/mana decreases with the mana cost of the cards, so as we just said: if you cannot saturate your whole lineup, you get a bigger bang for your mana by playing smaller units.

Shield

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Back to our units comparisons, let's have a look at the Cruel Sethropod versus the Crypt Beetle. For the same mana cost and rarity, the Sethropod has 2 Armor and 2 Health more than the Beetle. Let's consider it the cost of the Shield ability, we would have Shield=2

Now is the moment of truth. You may be thinking "ok, this guy just throws formulas and stuff fom a few observations, but how real is it really?" Let's check it on the other units:

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Average deviation of 0.08, quite consistent, isn't it?
I find it quite fascinating, that along the range of monsters, from 3 to 8 mana, they check almost perfectly a quite simple formula
Chaos Knight is a bit better than expected for its cost, just 0.5 point. It means it has a free point of Speed, Armor, Health or whatever compared to the equivalents.

Reach

Let's compare now Bramble Pixie and Mycelic Infantry.

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The Mycelic Infantry has 3 Armor more and 1 Health less than the Pixie = 1
As it is a Rare unit, he has a bonus of 0.5 mana allowance compared to the Pixie and it costs 1 mana, so the difference in raw stats should be 1.5
But in reality, the difference is only 1 point, which means that Shield costs 0.5 point more than Reach, and so Reach=1.5

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The average deviation is here -0.05, nice consistency!
You certainly noticed that Tide Biter is good, and indeed he is anormally good! Arachnee Thug is also better than average.
One deception for me was Junker, he doesn't fare well compared to the competition, either on raw stats or on stats per point of mana. That's mostly due to the Neutral malus

Sneak

Crypt Beetle and Stitch Leech
The Leech has a full point of raw stats (4 versus 3) compared to the Beetle. So Sneak costs 1 mana less than Shield, so Sneak=1

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Average deviation -0.11
I was surprised that Tenyi Striker is a bit below average. Probably the boost from Tarsa makes him look way better than he is!
Other units are pretty equivalent, but the Leech really stands out with the cheapest 2 Melee damage for only 3 mana.

Opportunity

Now we compare Deeplurker and Dumacke Exile

Same reasoning again, the Exile has 1 point more of raw stats than Deeplurker, so Opportunity should cost 1 more mana than Sneak, so Opportunity=2

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Average deviation -0.03
After seeing that cost, I realized Opportunity was actually expensive, and certainly better applied to high-ish mana monsters. Let's think about it that way: you pay 2 mana in order to have an additionnal attack, but if your monster does 1 damage/turn, you pay 2 mana for 1 melee damage, and that's not the best efficiency.

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Thorn

Let's look now at Venari Knifer and Dumacke Exile
You know the drill, blabla, raw stats, blabla, cheaper than Sneak, blabla and so Thorn=0.5

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Perfect match. I'm surprised Thorn is so cheap. In my opinion it's a very useful ability for a tank, and as it's cheap, you get more stats for your mana! Win-win!

Fly

Ok, last one, we compare Vampire Bat and Cruel Sethropod and find that Fly=0.5

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**Hungry Skull **is an anomaly, certainly by design considering its vulnerability to Magic attacks.

Frequent Magic Abilities

We already know that magic attacks costs twice mana-wise than physical attacks. But it's not the only cost. The ability to attack from any position also comes at a cost, even without ability per se!
It's a bit empiric, but if with calculate the mana cost of the cards using the formula, the average deviation is -0.63, which is significative enough to be taken into account. In order to minimize the deviation, a 0.5 penalty should be applied. I make the hypothesis that it is the cost of the ability to throw magic attacks.

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Average deviation is then -0.13 for basic magic monsters, and if we exclude Untamed cards, it's almost perfect at 0.05

Recharge

The unloved ability! Funny that the worst ability is also the most represented! From Insiduous Warlock and Djinn Apprentice, we get that Recharge=2
That's expensive for an ability that is not actually desirable...

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Yeah, and it also checks with Uriel, despite his physical attacks.
By the way, we can also apply the same principle between different types of attacks. We saw with Melee that Shield=2 and Sneak=1. We add the 0.5 for the magical type of attacks, and...

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Perfect checks!

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Stun

That's an easy one, Djinn Apprentice and Technowizologist make it so obvious that Stun=1

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And here Water Caller looks so bad! Same raw stats than Revealer, for 1 mana more!

Frequent Ranged Abilities

Same as for Magic, we have to consider the cost of Ranged Damage as a "non-ability". After all, these units get to attack every turn, whereever they are (except the first position of course), without paying the cost of Reach, or Sneak, or Opportunity.

Matching the stats with the base formula, we get an average deviation of -1.09, which means that Ranged units have stats inferior to what it is expected by 1 mana. This is the cost of being able to use a ranged attack.

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We see that Naga Assassin is extremely good! Despite being a Rare Reward card, she has the stats equivalent to those of the Epic Igor Darkspear! On the contrary, Angelic Mandarin is particularly bad, but who cares when you can replace him with a Kulu Swimhunter?

Scattershot

Another ability that is usually not loved. We have a perfect comparison available between Acid Shooter and Igor Darkspear.

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Scattershot costs 1 point of Health, that is Scattershot = 0.5
Hopefully this ability is not really expensive, but you also know how unreliable it is. So well, it's a bet. The malus of 0.5 is not much, but the Scattershot may be an handicap by itself!

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Close range

Range attack is convenient, it's additional attacks per turn, until your ranged unit reaches the first position and wait for death doing nothing. That's where Close Range gets useful!
As there isn't too much choice, we will need to extrapolate a bit between Molten Ash Golem and Kulu Swimhunter. The Swimbunter has raw stats of 5 for 4 mana. If it had 6 mana, its raw stats would be 7, and if it was a Rare, it would be 7.5 (following me?). As the Golem has raw stats of 6, then Close Range = 1.5

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Snipe

We compare the Molten Ash Golem and Hunter Jarx here. Same mana, and Jarx has 1 more point of raw stats than the Golem. As he's an Epic card, it means the difference between Snipe and Close Range is 0.5 so Snipe = 1

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I never noticed Lava Spider was actually this good! Probably because Health is not what I look for in a ranged unit.

Next steps

So, what do you think? Pretty accurate for now, right?

I still have a lot of work to do still. Or to write it down actually!
Working to expand to less common abilities. The samples sizes is smaller, so it's harder to get reliable figures. But heck, I just solved the Double Strike mystery so I'm on a good way!
Working on how upgrading cards influence the stats, and finding the best ones at Bronze, Silver, Gold levels (we stayed at level 1 cards for now)
And of course, adding the new Soulbound cards! And the Gladius ones, now that we can play them in ranked!
Aaaaah! So much work!

I hope I have been clear enough, which is not a given as I've been in that juice for some time and I may have missed some explanations. Do not hesitate to ask, it's a lot to digest!

See you on the Battlefield!

(tagging @arc7icwolf @gregory-f @mirroredspork @adcreatordesign @cursephantom who waited long enough for this second part!)

If my nerdiness makes you want to join this awesome game: join us!



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27 comments
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Math gets upvotes from me 😁

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Woa! Thank you, you made me a big honor!
"yeah dude, true story: I got upvoted by bulldog!"
!LOLZ

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Wow, you are doing an incredible and awesome work! I hope these posts of yours can get the visibility they deserve (I just reblogged it to give you some help... at least a bit!).

@libertycrypto27 I think you could like going through this post, as it's full of stats and data and it's something unique that I haven't found anywhere else :) also, his work can be extremely valuabe in finding good and undervalued cards to buy from the market!

Now I'm even more curious about the next episodes @engilhramn!

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thanks for the tag!
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!PIZZA

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Thank you mate! Highly appreciated! Honestly, I wonder how simple it is and yet everything fits together. I'm mostly done on Novice level cards. Bronze I need to collect a lot of data still, but it will be the same. Then Gold level will be more complicated, with the gain of abilities and such. I can't just sum the mana cost of everything: look how expensive Recharge is!
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Recharge looks more and more like a negative ability... it's like giving an advantage to your opponent for free (free for him ahahah) !LOL

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Outstanding research and explanation. Looking forward to more of these in-depth breakdowns! Thanks for the work you poured into this.

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Thank you mate! I will try to accelerate the redaction, the analysis is mostly done, but time is so precious!

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(Edited)

PIZZA! PIZZA! PIZZA!

PIZZA Holders sent $PIZZA tips in this post's comments:
@engilhramn(3/15) tipped @gregory-f (x1)
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Learn more at https://hive.pizza.

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Interesting work and stats!
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!discovery 20
@tipu curate

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Thank you! Happy to share! More stats are coming, I will tag you if you don't mind once it's ready!
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It was a long wait, but well worth it.

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Yeah, been kind of busy... The study is far more advanced, but I lack time to properly redact it. I will try to accelerate!
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