# Equation for the mana cost of a card

(Edited)

In this post, we present a simple equation for explaining the mana cost of each individual card, based on the stats for this card. This equation is useful for telling us how the Splinterlands developers value each stat, and how you might want to evaluate them compared to each other. We will also use this equation to identify the top ten cards in each league based on how much stats you get for your mana with the card.

We do not account for abilities in this post. Abilities do obviously have a mana cost, and we will cover that in an upcoming post.

We start by looking at the raw data:

The chart above shows a simple summary of how much stats are available for a given mana for the four different card rarities. The number on the y axis is the sum of stats on the card, and along the x axis are the mana costs of the cards. This is a combination of all card levels, which is why there is such a wide spread along the y-axis in each plot.

It is interesting that there are some common cards that have a higher total number of stats than any of the rare and epic cards. At the very top of the stats list is in fact the Goblin Mech (lvl 10), which has a total stats sum of 26. This is only rivaled by a two legendary cards, and beaten by three:

# Linear equation for mana cost

Taking the data from all cards and all levels, we can fit a linear formula for mana-cost as a function of the stats of the cards. We could include abilities in this formula, but we will leave that for the next post to keep the amount of information in each post at a tolerable level. Doing this, we find the following formula:

Here, L is the normalized card level ((level -1)/(maxlevel - 1)), A is the attack value, R is the ranged value, M is the magic value, H is the health value minus 1, Armor is the armor value, and S is the speed value minus one. Level was adjusted this way in order to have a formula that covers all card rarities. For Health and Speed we take the stats minus one, because no card can have either zero speed or zero health.

The coefficients have been rounded for simplicity. The exact values, to two decimal points are 1.15, -2.56, 0.72, 1.01, 1.42, 0.5, 0.41, and 0.14. The attentive reader will notice that the rounding of the armor value is inaccurate. The coefficient could instead be taken as 4/10, which would be more precise, but harder to use for an on-the-fly evaluation of a card's stat efficiency.

What can we learn from this? There are a lot of interesting details here.

• 1 attack, 1 ranged or 1 magic are worth 2/3, 1 and 4/3 mana, respectively. This means that magic attack costs double of melee attack stats. This makes sense, since magic can be used from any position, and doesn't miss unless the defending card has Phase. However, in melee favored rulesets (Super Sneak, Equal Opportunity, Melee Mayhem), you can find much higher damage teams if you go for melee cards.
• When cards are leveled from level 1 to max, they gain, on average, 2.5 mana worth of stats.
• Speed is a very cheap stat. Every card rarity gains more more stat value per level than one speed is worth. Therefore, the levels where cards gain one speed are inefficient. Of course, you have to level cards past these levels, but you might want to work towards other level breakpoints.
• Health is worth a bit more than armor, but not much.

We can now use this equation to look at which cards that have the highest deviation from it. These are the cards where you get the most value for your mana, in terms of raw stats. In essense, these are cards that are great in the Back To Basics ruleset, unless you're playing at high mana.

# Top 10 stat-per-mana cards in Bronze League

The fiends and the chicken have not been included. They are infinitely mana efficient.

In Bronze league, Water, Death and Dragon have the most mana efficient cards.

# Top 10 stat-per-mana cards in Silver League

In silver league, Earth has an advantage when it comes to stats, with five of the top ten cards.

# Top 10 stat-per-mana cards in Diamond/Champion League

In this post we have looked at which cards that give you the best value for your mana. The ultimate mana-efficient card is the Cruel Sethropod:

It does have good company in several other low-mana cards. Interestingly, there does not appear to be much power creep in terms of stats per mana, as there is a good mix of cards from all editions within the top ten list.

Let us know if this guide has helped you, and if you have any other comments or suggestions please let us know

Please also check out our other content:

Rule set strategies
We are also creating guides for specific rules. You can find them here:
Strategycorner with Mammuter #5: How to WIN in Reverse Speed
Strategycorner with Mammuter #4: How to WIN in Melee Mayhem
Strategycorner with Mammuter #3: Noxious Fumes

If you would like to see more of this content, please let me know, like and share the post. Also, if you have not yet started playing Splinterlands, you can join and support me and the same time with the following link

Join Splinterlands

Another way to support us is through card delegations or donations. If you want to do that, we are @kalkulus and @mammuter.

Best of luck in Splinterlands!
Kalkulus

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Great writeup! It's been a while, happy to see some more of your content. I can't wait to see what this looks like once abilities are factored in 😁

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The idea is pretty good. I love this kind of article exactly. Rebloged!

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Love it! I usually build my own bias toward a card based on common sense / gut feeling so to see that bias backed up or refuted by data like this is a nice contrast.

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Great post, definitely something to learn from. Thanks for sharing your analysis.

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