Mathematical calculation of current hand, minions, spells card worth

hearthstone

In chess or other similar strategy games you know the value of each piece and can easily calculate the current situation or what will be the best move according to those values.

Is there such a system for heartstone?

Example of what I am asking:
Yeti: 4/5 = 9 total value
Giant: 8/8 = 16 total value
Argent squire: 1/1 + special = 2 + divine shield value

Is something like this developed by players or blizzard?

This question is asked to find out if there is a way to maximize the efficiency of our moves on a mathematical basis.

Best Answer

TL;DR: see summary at bottom

Vanilla Test
I have seen some of the "Pro's" on their streams refer to a minions value by asking if it passes the "Vanilla Test". That is, you can get a textless common card, such as a Bloodfen Raptor that is a 3/2 minion for 2 mana. So when you are looking at other 2 cost cards, you compare it to the other available 2 cost cards.

Mana Cost
That said, your example of value on the Yeti does not take into account the mana cost. If you were going to develop some system like this for yourself, you would also NEED to take into account the mana cost of the cards, as a bare minimum.

For example, Yeti is a 4/5 for 4, maybe a formula like this (4+5) / 4 = 2.25 value.

However, cheaper cards may easily break this system, such as a worgen infiltrator, 2/1 for 1 which would look like (1+2) / 1 = 3.00 value.

Now, having 10 cards that are 2/1 for 1 drops at 3 value in your deck is not necessarily better than 10 cards that are 4/5 for 4 drops at 2.25 value because the amount of cards available to you is limited.

Mana Curve
This puts a much higher importance on "Curving Out". By that I mean, having a good mana curve in deck such that there is a high probability of being able to spend 1 mana on turn 1, 2 on turn 2, 3 on turn 3, 4 on turn 4, 5 on turn 5, etc.

So into the above formula for minion evaluation of (Health + Life) / Mana Cost, you probably also need to take into account how the card fits into your mana curve. The other random variables you would need to account for are Card Text (like abilities) and tempo.

Text
While a Venture Co. Mercenary at 7/6 for 5 mana is very good (7+6)/5= 2.6 value... It has an opportunity cost because while it lives your minions will all cost +3 more. It essentially is adding 3 to the denominator of all your other card values while it is in play.

There are too many different text variables to assign a point range for each, but generally I would say -3 to +3 based on the strength of the text. For example: Ysera has a very powerful ability and would probably get a +2 or +3 based on it, whereas the Venture Co. Mercenary would be in the -2 to -3 range.

Tempo
The other thing to take into account is tempo. Having 30 cards with super high value, even taking into account their text and mana curve, if they all cost 4-10, you will be so far behind on turn 4 when you start playing that many fast decks may have such a lead it is impossible to come back. So a 10 cost card with a super high value, while strong, has a huge cost in not being able to be played early.

An example... Mind Control is often considered to be a super powerful card. If your opponent plays a 12/12 deathwing, wipes the board and discards their hand, and you follow that up with Mind Control, you can often hear the sound of your opponent's soul dying(dramatic exaggeration). However, having 10 Mind Controls in your deck would fortell near certain doom for you.

So the way I value tempo is, will this card get in play and be valuable in time to make a difference? 1-3 cost drops get a +1-2 value. 4-5 cost drops get 0-1. 6+ get -2 to 0 based on my analysis of the cards affect on tempo.

Efficiency
The last and most important part is that you have to meassure card efficiency. A Leper Gnome for 1 mana is a 2/1 and deals an additional 2 damage on dying in most cases. However, while it is great for early tempo, drawing one of these bad boys after turn 6 makes me cry because it has a very small value and takes up an entire card slot in hand and an enitre draw, but most likely it will not even trade 1 for 1 on the board.

So the way I value efficiency is, how much effect will the card have when on the board? Following is a very general guide for how much value a card adds to hand based on cost in my estimation: Cards that cost 1 mana automatically get a +3 for efficiency. Cards that cost 2-3 get a +2 or +1. Cards that cost 4-5 get +1 or +0. Cards that cost 6+ get a -1 to -3.

EDIT:
The above guide should not be true for every case however. Cards like Harvest Golem, Cairn the Bloodhoof, and Sylvanas Windrunner are almost like 2 cards in 1 and in my estimation, that should be represented in the denominator. I know that those are all Deathrattle abilities that should be represented in the "Text" section, but in certain cases the ability is so powerful that I think it needs to be part of the denominator.

New & Ammended examples below are bolded. I tried to add a few examples with efficiency values resulted in non-4 denominators.

SUMMARY

This is not a perfect or comprehensive system and would need more work, but if I were to put together a value formula for minions, it would be something like this:

(D+H+T+M+P) / (C+E)
D = Damage
H = Health
T = Text modifier
M = Mana curve modifier
P = Tempo modifier
C = Cost
E = Efficiency

Examples:
Wisp = (1+1+0+0+1)/(0+3) = 3/3 or 1.00
Leper Gnome - (2+1+1+1+2)/(1+3) = 8/4 or 2.00
Argent Squire - (1+1+2+1+1)/(1+3) = 7/4 or 1.75
Bloodfen Raptor - (3+2+0+2+2)/(2+2) = 9/4 or 2.25
Knife Juggler - (3+2+2+2+2)/(2+2) = 11/4 or 2.75
Questing Adventurer - (2+2+1+1+1)/(3+1) = 7/4 or 1.75
Dalaran Mage - (1+4+1+0+1)/(3+1) = 7/4 or 1.75
Harvest Golem - (2+3+2+2+1)/(3+0) = 10/3 or 3.33
Chillwind Yeti - (4+5+0+1+1)/4 = 11/4 or 2.75
Ysera - (4+12+3-2+0)/(9-4) = 17/5 or 3.6
Deathwing - (12+12+2+-2+2)/(10-3) = 26/7 or 3.71