# Study: valuing cards by the cost of mana

(Edited)

Greetings, Battlemages!

My love of excel tables strikes again! Have you ever wondered which cards are good or bad for their mana cost? That's what I'm trying to figure out! We will go comparing card by card, and try to find an universal formula which integrates stats and abilities.

We will only look at the building of the formula in this post. It will be long enough I think and I will bore everyone to sleep before I could start applying the formula on cards.

## Scope and hypothesis

I will focus on Chaos Legion and Rift Watchers cards. I looked a bit at Untamed cards, but they don't deviate much, so let's focus on the latest edition for now.

Concerning the hypothesis:

• the mana cost of cards can be predicted from its stats and ability (obviously the most important hypothesis or else I could close the study here!)
• rarer cards should have an increased mana allowance (that is: rarer cards should have better stats for the same mana cost), like a bonus
• neutral cards should have a penalty (the flexibility should have a cost)
• reward cards should have a penalty (or else, why would you buy cards if the best ones are given to you?)
• we expect Rift Watchers cards to have better stats (or same, why would you buy newer cards if the older ones are better?) but it is to be verified

For the sake of formulas:
S = Speed
A = Armor
H = Health
Me = Melee damage
Ma = Magic damage
Ra = Ranged damage
Mana is expressed as plain numbers

## Valuing stats

First thing first: we need to value the stats before being able to go further. In order to do that, we will start with basic cards, at level 1, Novice level.

For the comparisons to be meaningful, we would need cards of the same characteristics: same rarity, same ability, same edition ideally, rewards and neutral cards isolated.

Let's look first at Crypt Beetle and Antoid Platoon: same rarity, same ability.

The Antoid Platoon costs 1 mana more for 1 Armor and 1 Health more. We could then say that A+H=1

Same logic and we compare Sunkai Harvester and Shadow Snitch:

We could deduct that 1 Armor and 1 Speed are equivalent to 2 Health, so S+A=2H

Let's look at some Sneak units: Stitch Leech, Sha-Vi and Dumacke exile.

For 1 mana, the Exile gets 1 Speed and 1 Armor over Sha-Vi. So S+A=1
From Sha-Vi and Stich Leech, we get: 2S+2H=2 (2 Speed and 2 Health for a cost of 2 mana)
We can still compare Stitch Leech and the Exile: 3S+A+2H=3

From Venari Scout and Whelp Herder: S=H

3 variables for 6 equations, we have plenty enough and can verify if everything fits together.

And as S+A=1, then S=1-A, so A=0.5

So actually, S=A=H=0.5
We verify the other equations: A+H=1 true, S+A=2H true, 3S+A+2H=3 also true!
Everything fits together, nice!

### Valuing Melee attack

That one should be easy, we look at Shadow Snitch and Radiated Brute. Same everything except that the Brute has 1 more Melee Damage and costs 1 mana more. So we would have Me=1

Would it be that easy?
From Flying Squid and Bramble Pixie, we get that 1 Melee damage is equivalent to 2 Speed. Speed is valued 0.5 mana, so it checks Me=1
So let's go with that, it is easy enough.

## Valuing Ranged attack

We will look at Angelic Mandarin, Sould Strangler and Scavo Firebolt, as they are of the same rarity.

Soul Strangler has 1 more attack at the cost of 1 Health. So we would have Ra=H=0.5
Same for the Scavo Firebolt, 1 more attack and 1 more Health for 1 mana more. So Ra+H=1 and again Ra=0.5

### Valuing Magic attack

The difficulty here is to find similar cards, of the same ability/rarity... There's not too much choice.

But we have Dax Paragon and Nerissa Tridawn. Quite some mana difference: 7, for 2 more Magic damage and 6 Health. That gives us 2Ma+6H=7, that is Ma=2

## Valuing neutrality

Neutral cards should have a penalty, it makes sense as the cost of flexibility.

So let's take Flying Squid, Bramble Pixie and Junker. All the same rarity and mana cost.

If we calculate the "raw stats" valued with Me=1 and S=A=H=0.5 we have
Flying Squid => 21+0.5(3+8)=7.5
Bramble Pixie => 21+0.5(1+8)=7.5
Junker => 21+0.5(1+7)=6

So somehow there would be a penalty of 1.5 point somewhere.

If we compare the raw stats of other Neutral cards, we see a penalty of:
Vampire Bat - Gargoya Lion : 0.75
Gargoya Lion - Pelacor Mercenary : 1
Magi of Chaos - Nerissa Tridawn : 1.33
Kulu Swimhunter - Supply Runner : 1.5

So on average, the malus for Neutral cards is 1.2
That means that, on average, playing a Neutral card puts on the board as many stats as a non-neutral one costing 1.2 mana less.

## Valuing rarity

That's an interesting topic, how much more stats do rarer cards have?

Let's look at Venari Knifer and Cursed Windeku: they have 1 rarity level of difference. And their difference in raw stats is just 0.5 : 1 Speed for 2 Health

So Rare cards would have a bonus of 0.5 over common cards.

Tide Bitter and Twilight Basilik - both reward cards, so if penalty there is, it should be nullified. The difference between the raw stats is again 0.5

Grund - Carnage Titan: same 0.5 difference between Epic and Legendary

But indeed it's not always true. Scavo Firebolt and Kulu Swimhunter have exactly the same stats, while being of a different rarity. It could be that Scavo Firebolt is a "bad" Rare while Kulu Swimhunter is a "good" Common.
The same actually goes for Chaos Knight and Mycelic Infantry.

We can say that these exceptions to the rule reveal which cards are "better" or "worse" compared to their equivalents. It should not be surprising: the idea is to find which cards deviate from the rule. If all cards were strictly equivalent, it wouldn't be fun, right?

So let's keep this 0.5 allowance gap between each rarity.
And if we look at the simplest cards, let's say Cruel Sethropod, its stats are valued for 5 mana, yet the card costs 3, that means the mana allowance for Common cards is 2.
So it should be 2 - 2.5 - 3 - 3.5 respectively for Common - Rare - Epic - Legendary

## Valuing reward cards penalty

It's just an intuition, but possibly reward cards could be "not as good" as they should be.

Again, we will value similar cards, for example Mycelic Infantry and Harklaw.

Mycelic Infantry has raw stats of 8.5, while Harklaw has 9, with a mana allowance superior of 1 mana (Rare->Legendary). That means Harklaw has 0.5 less point of stats than it is expected.

This 0.5 penalty is also consistent comparing Cursed Windeku vs Djinn Chwala, and also Revealer vs Technowizologist

Even easier, I should have started there. Venari Bonesmith and Life Saper. The Bonesmith costs 1 mana more, for which it gets 1 Health more, valued 0.5, so it also gets a penalty of 0.5 mana for being a reward card.

## Wrap-up

So we have it!

The global formula would be:

###### Mana cost = Me + 2Ma + 0.5Ra + 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

That's where you ask: "wait, you didn't talk about Ability and yet you put it in your formula!"
Indeed, and there's a lot of different abilities, so we will talk about it in the next post. We will set up the Ability cost, as well as looking (finally) at the cards to find the best ones of their category!
As you can see, it's unlikely that we would find Neutral or Reward cards among the best ones!

See you on the battlefield!

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@gregory-f - tagged as promised!
It's just the "first chapter", I will go further

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Fascinating! And to think my sons said that Algebra had no real world uses. I can't wait to read the next post on Ability cost.

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Well, algebra is like the rule of the world, you can apply it to literally anything! Throw in some excel for the calculations, and you're golden!
!PIZZA

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Awesome! I'll be waiting for part 2 :)

!PGM
!LOL

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Part 2 in progress! Maybe not this week, but for next week I should have finished it!
!LOLZ
!PGM

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This is awesome data. Looking forward to the next post highlighting more of the math behind the cards!

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Hi, @engilhramn
This is a very interesting comparison to excel formulas.
Clever ideas!
Barb 😊
!BBH
!CTP
!HBIT

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That's a good thing that I couldn't even think of... I'm not playing Splinterlands anymore but I see a good formula of yours is interesting. Keep it up~

!PIZZA

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