Equation for the mana cost of a card - 2.0 (with abilities)

in #splinterlands2 years ago

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

Equation for the 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 and abilities of the cards. By doing a regression on this data, we find the following (approximate) formula

(The coefficients have been rounded to gain a nice equation. The exact coefficients, to two decimal points can be found below)

Much of the equation is the same as when we didn't include abilities, but the intercept (the first constant) is different from earlier. The terms in the equation are as follows:

• 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
• S is the speed value minus one

The new addition is the last term, which is a sum over all abilities, the "Ability" variable is either 1 or 0 (depending on if the card has the ability or not), and each ability has a coefficient C which is specified in the table below.

The interpretation of the coefficients are (as for the stats) how much mana you pay for the ability. The coefficient for Affliction is 0.37, which means that, on average, a card with affliction has 0.37 mana worth of stats less than a card without it (this is roughly the same as 1 armor or 2 speed).

Coefficients

 Intercept -0.43 Level -2.53 Attack 0.69 Ranged 1.02 Magic 1.41 Health 0.49 Armor 0.39 Speed 0.15 Affliction 0.37 Amplify 0.36 Backfire 0.21 Blast 1.02 Blind 0.54 Bloodlust 0.3 Camouflage 0.53 Cleanse 0.54 Close Range 0.58 Cripple -0.14 Deathblow 1.11 Demoralize 0.78 Dispel 0.58 Divine Shield 0.32 Dodge 0.19 Double Strike 2.45 Enrage 0.27 Flying 0.37 Forcefield 0.95 Giant Killer 0.18 Halving 0.57 Headwinds 0.36 Heal 0.14 Immunity 0.24 Inspire 0.52 Knock Out 0.25 Last Stand 0.39 Life Leech 0.89 Magic Reflect -0.17 Opportunity 0.63 Oppress 0.23 Phase 0.25 Piercing 0.66 Poison 0.38 Protect 1.15 Reach 0.94 Recharge 0.59 Redemption 0.45 Repair 0.94 Resurrect 1.65 Retaliate 0.31 Return Fire 0.48 Rust 0.28 Scattershot 0.59 Scavenger 1.11 Shatter 0.48 Shield 0.69 Silence 0.43 Slow 0.36 Snare 0.46 Sneak 0.67 Snipe 0.03 Strengthen 0.76 Stun 0.42 Swiftness 0.25 Tank Heal 0.77 Taunt 0.1 Thorns 0.65 Trample 0.64 Triage -0.05 True Strike 0.39 Void 0.51 Void Armor 0.6 Weaken 0.36

Some summaries

The top 10 most EXPENSIVE abilities are:
Double Strike, Resurrect, Protect, Deathblow, Scavenger, Blast, Forcefield, Reach, Repair, Life Leech

The top 10 CHEAPEST abilities are:
Magic Reflect, Cripple, Triage, Snipe, Taunt, Heal, Giant Killer, Dodge, Backfire, Oppress

What do we think of this? In a sense, cheap abilities should weaker than expensive abilities. In my opinion, this is not really reflected in the coefficients here. For example, Deathblow is definitely less useful than many of the cheapest abilities. But if there is a mismatch between the cost and the effectiveness of an ability, we can use that to identify strong and weak cards.

Below, we present the top ten and bottom ten cards in terms of mana effectiveness for each league. Within each league, we only consider the highest level cards.

Closing remarks

In this post we have presented an equation for explaining the mana cost of each card. The equation tells us how much mana each stat and ability in Splinterlands is worth (on average). We looked at which cards that are mana-efficient and which are inefficient at max level in all leagues above Novice.

The ultimate mana-efficient card is (still) the Cruel Sethropod:

At the highest level of competition, the most mana-effective cards tend to be magic attackers. Perhaps the developers are a bit generous in giving that final magic damage at max level. In Gold, there is a good mix of all types of cards with high mana-effectiveness, while in silver and below, the most efficient cards tend to be very low mana cost legendaries or epics.

The mana inefficient cards tend to be high-mana cards, which are intented for play at the mana ranged where mana efficiency is not an issue. At 99 mana, it is not possible exhaust your mana supply, so efficiency is irrelevant. However, at the lower mana ranges, mana efficiency can be very important. However, actual gameplay strength and mana cost are not necessarily the same. It is usually more important to build synergies in your team than to stack up on stats and abilities.

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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Incredibly useful guide. Keep it up. !1UP

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This is some high quality information and quite the mathematical work that went into it.

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