# Hearthstone Theory and Math

HEARTHSTONE THEORY AND MATH: MINION STAT VALUES

Blizzard Entertainment has begun releasing Hearthstone expansions at a rate of 3 every year. With this new influx of content entering the game, more new cards with never-before-seen effects and uses are being implemented. However, when a brand new effect is introduced, it is difficult to evaluate its impact on the game and its actual value in comparison to pre-existing cards. This becomes much easier once you notice the patterns behind Hearthstone card design and apply the rules of card value across expansions.

Consider Hearthstone’s vanilla statted cards. Some of these minions include Goldshire Footman, River Crocolisk, Spider Tank, Chillwind Yeti, and Boulderfist Ogre. The average card follows the rule where mana cost (m) is represented by [(TS)-1]/2 = m, where TS is “Total Stat Value”. Take chillwind yeti for instance. By implementing its total stat value into the equation, we find:

We can deduce that the average 4-drop is worth 9 total stat value. Using that information, we can evaluate cards such as the Piloted Shredder, another 4-drop, and a former staple in most meta Hearthstone decks. Inputting its stats into the formula, we find a total stat value indicative of a 3-drop card. However, by considering its deathrattle, we see that the secondary effect ties the card together. With “Deathrattle: Summon a random 2-cost minion,” and knowing that the average 2- cost minion has the average stats of a 2/3 or 3/2, we find that the Piloted Shredder is actually an extremely efficient card. By paying 4 mana, the player is receiving 5 mana worth of stat value.

With card such as the Piloted Shredder setting an example for value, we can evaluate the worth of more secondary effects. Keeping the stat values of an average 2-cost and 3-cost minion in mind, we see the stat difference of +1/+1. With that information, we can infer that the additional stats of +1/+1 is worth approximately 1 mana. We see evidence of that inference through the card: Shattered Sun Cleric. Its total stat value represents a 2-cost minion, but at 3 mana, with the additional Battlecry: “Give a friendly minion +1/+1”. That allows us to reaffirm the hypothesis that +1/+1 of stats is worth approximately 1 mana, and that the Shattered Sun Cleric still totals a 3 mana value.

FRACTIONAL MANA VALUE

This technique is not only limited to just stat values, but also more ambiguous secondary effects and fractional mana value. Looking at the Gnomish Inventor, we see a 4 mana 2/4, with a secondary effect of “Battlecry: Draw a card”. Inputting its stats into the equation, we see a total stat value representing 2½ mana.

By subtracting its represented stat value from its total mana cost, 4 – 2½, we get = 1½. We can infer that the effect of Battlecry: Draw a card, is worth 1½ mana. Again, we see this reinforced by the Novice Engineer, a card with ½ a mana worth of stats that also contains an identical Battlecry.

Utilizing this formula, we can evaluate cards you are considering putting in your deck. It allows us to know just how much value we are gaining or sacrificing when running one minion as opposed to another. It is deck building challenges like these that make Hearthstone and math (relatively) fun.

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#### Devon

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