Official Website of KYOTO ESPORTS
LOG IN SIGN UP

Boiling it Down: A Mathematical Analysis of Hearthstone Mechanics

3 months ago

Well met, and welcome to Boiling it Down with HardBoiled, the segment where your host, HardBoiled, does a mathematical analysis of Hearthstone mechanics and uses these numbers to analyze individual cards! Today, we’re going to be attempting to prove something that has been assumed by players since the beta - the stat distributions of vanilla minions, and as a result, the amount of value we should be expecting each minion (and therefore, spell) to have.

There are a few factors here to consider when attempting to take on a task like this. One of these is that class cards are often better than neutral cards, which can throw off our calculations. A good example of this would be Murloc Raider and Enchanted Raven - they cost the exact same amount, but Enchanted Raven has one more Health. This comparison can be made with other class cards - why does Voidwalker have one more health than a Goldshire Footman, when they’re otherwise the exact same card?

Other issues similar to this one are challenging us as well. What do we do about power creep? Should we be counting both Ice Rager and Magma Rager in our calculations, or just one? If just one, which one? In order to prevent these issues, I will be making my calculations without class cards, and any cards that directly power creep another card, or are power crept by another card, will not be counted. This means that Magma Rager, Ice Rager, and Enchanted Raven are all out of the picture. However, I will be counting vanilla minions that are power crept by non-vanilla cards. In essence, I will be counting all minions with no text that are neutral and do not have a minion either objectively better or worse than them. I’ve also removed minions that wouldn’t represent the numbers properly - the minions I’ve taken out are Wisp, because it technically has infinite value, and Puddlestomper because it’s a near clone of Bloodfen Raptor.

Oddly enough, this cuts out a lot of minions. With the eighteen minions, we have to remain, I will be trying to find how much Health and Attack are to be expected from certain Mana costs. Using this, I want to find a formula for creating Vanilla minions. The first thing to do is find the average minion. By averaging their stats, I have created a minion that represents the average vanilla minion. The Wisp Mother, as I like to call it, is a 5 Mana minion with 5.2 Attack and 5.4 Health. Through the power of rounding, and with the knowledge that most vanilla minions are slightly worse than an average card, I’m going to put this at about a 5 Mana 5⁄6.

 

Now that we have this minion, what’s next? Well, this minion is representative of all of the vanilla minions, and thus all of the regular minions, in the game, so we can use it to create a formula to build your own vanilla minion! Assuming M = mana cost, A = Attack, and H = Health, this is what I came up with -

M = 1⁄2((A+H)-1)

In short, this formula means that the Attack and Health of a minion should average out to the mana cost of the minion, plus one-half. This means that our 5 Mana 5⁄6 works perfectly in this

formula - 5 = 1⁄2((5+6)-1). Most of the other vanilla minions work perfectly with this equation - the minions that don’t are all either really big minions, which can make them a little bit more practical, and thus keeps them from being overpowered, or are meme cards, like Magma and Am’Gam Rager.

Of course, we can’t draw too many conclusions from this data alone. However, we can form a hypothesis on the value of Class Cards, which is that they are worth one-half Mana Crystal more than the neutral cards. Of course, we can’t exactly prove this yet, but hopefully, we can gather more data on this as we continue to work.

Thanks for reading Boiling it Down, with yours truly, HardBoiled! Maybe if we do enough math, we can stop missing lethal?