THE LAW OF DIMINISHING RETURN IN CARDS

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Have you ever thought of the value you would gain when leveling up a card? Take for example Scavo Chemist, a normal type card. Upgrading it from Level 2 to Level 3 will grant the card +1 health. And then you have Tusk The Wide, an epic type card. Upgrading it from Level 1 to level 2 give the same +1 health. Now does it looks fair? You will think you gained less from Tusk The Wide, when you find that this card cost 6 mana while the other only cost 2 mana.

Now consider bringing Scavo Chemist, Igor Darkspear, and Celestial Harpy together; each having 2 mana cost, and combined as one making up 6 mana. Levelling up each of them to Level 2 will grant you two +1 health and a +1 speed. That's a lot of gain if compared with +1 health coming from a single Tusk The Wide. Then the question again will be : Shouldn't we gained more health on levelling up Tusk The Wide? At least for two main reason. One since the card cost you higher mana; and second since the card initially had 12 health.

FIRST REASON

To understand the first reason, we must understand the concept of "Law Of Diminishing Return". Based on Investopedia, the law stated that :

Advantages gained from slight improvement on the input side of the production equation will only advance marginally per unit and may level off or even decrease after a specific point

The real life example would be a business which hire additional servant to service customer in the restaurant. A single servant can serve up to 5 tables / hour; double the servant and the restaurant can serve up to 10 tables / hour. But triple the servant, the restaurant could only serve up to 12 table / hour. Why it didn't give the output of 15 table / hour instead? Then again the law said:

However, adjusting production inputs advantageously will usually result in diminishing marginal productivity because each advantageous adjustment can only offer so much of a benefit.

Now consider that the mana value is the number of employees and servant; and then the status (health, armor, speed, and damage) is the total output. You will see the application for this concept, where Tusk The Wide doesn't have 9 speed, 3 damage, and 12 health which would equal to three Igor Darkspear combined. Then again when you double Tusk The Wide mana, making up a total 12 mana, there's no way you would get an alternative single 12 mana card having double the status of Tusk The Wide (although since Tusk The Wide damage is quite low, there might be a card with more than 2 damage value).

So yes there's clearly a diminishing return happened. But what's the benefit of knowing it?

Now think about this : If you have 6 mana left, and you know you gained more benefit from deploying three 2 mana card, then why would you bother to use a single 6 mana card instead? Okay we might save the 6 mana card for the higher mana where we have limited row available. But if the idea of mana is to represent the equal WHOLE value of a card, then it should be understood that card with different mana are not comparable solely by the status value and abilities.

There's a LEVERAGE happened when status value are combined into chunck under a single card. There's a LEVERAGE happened when abilities are utilized by card with greater status value. This LEVERAGE which drive me to write my further post about cards comparison by constraining on its mana value.

But what is the real instance of this LEVERAGE already said? Here are some of the point:

1. Resistance to debuff effect.
   Higher status means less impact from any debuff effect. A card with 2 damage will go down to 1 damage under Demoralize effect; which become useless when facing card with Shield ability. But a card with 4 damage will undergo less impact. But the contrary will happen with buff effect, where it will have less impact to card with higher status.

2. Single card is a mothership rather than an armada
   A mothership can withstand a lot of incoming attack; and as long as the mothership hold on, it can shoot its full artillery. But a fleet of ship forming an armada are susceptible from being crippled when the ship are shot down one by one.

3. Effective abilities
   Some abilities, like for example Heal, gain the best leverage from large chunk of health. Enrage are another example of abilities leverage, where it multiply attack and speed by 1.5x.

SECOND REASON

Next we continue to understand the second reason. There's another concept called "Marginal Utility". Based on Investopedia, the law stated that:

Marginal utility is the added satisfaction that a consumer gets from having one more unit of a good or service. Economists use the idea of marginal utility to gauge how satisfaction levels affect consumer decisions. Economists have also identified a concept known as the law of diminishing marginal utility. It describes how the first unit of consumption of a good or service carries more utility than later units.

For example if a person consume bread for the first time, he will fain the full satisfaction from the delicious taste on the first bite. But when he continue to consume the 2nd, 3rd, and 4th bread; the satisfaction become less and less, because his appetite started to full, and the taste already expected.

Now then, if levelling up a card give you the benefit of increasing certain status. Which looks more beneficial between gaining 1 health for Tusk The Wide or Goblin Psychic? If you agree with me, gaining 1 health Goblin Psychic looks better. But why? Thinking back to the concept; Tusk The Wide already had 12 health at Level 1, an additional 1 health doesn't seemed to make much difference wasn't it? You expect the 12 health enough to sustain Unicorn Mustang 3 damage up to 4 round, what difference would 1 additional health make?

In contrary, Goblin Psychic could had everything from the additional health. It now able to survive 3 damage attack, it could offset any Weaken ability effect, and it could survive another round if faced against 1 damage attack.

CONCLUSION

For some time, I've been wondering about choosing the card that I would focus to level up. Sometimes I pass on from leveling up just because the growth doesn't seemed to change my chance of victory that much. Sometimes I saw some controversies, take for example the progression chart for Demented Shark (you can find my post here); where some growth seemed imbalanced between level. This propel me to write further post which take deeper look into the growth we gain from levelling up each card.

One final note for this post. The First Reason and Second Reason are not applicable equally for each status aspect. Armor, Health, and Damage status will grow higher, scaling up with the higher the value of cards mana. But Speed is an absolute value ranging mostly between 1 - 6 value, where low or high mana card invariably might have any value of speed. Ability are somehow a semi-absolute value, since low or high mana card will also invariably possess same ability. But certain ability, especially Support Abilities (for example buff and debuff), would looks more valuable if possessed by lower mana card, since they benefit card other than the owner itself (here, you could find further explanation on Striker, Tanker, and Support Abilities)