Oh man, reader. After taking the initial plunge, reviewing data, histograms, values, ratios, and more, I’ve gotten much more excited about the prospect of continuing this research project. I’ll do a quick good news bad news, and readjust our goals after explaining a lot of the data gathered for this step.

Bad news: sample size is a serious, serious problem, and this is more complicated than previously thought.

Good news: There are ways to mitigate sample size error (and in doing so, we can also solve some of the further complications that have arisen).

So, before I get into the nitty gritty, let’s talk about some data:

• There are only 5 non-tribal, no modifier minions in the entire game. These 5 are Wisp, Magma Rager, Chillwind Yeti, Boulderfist Ogre, and War Golem.
• Including tribals, there are only 14 no modifier minions in the entire game. (No modifier means no card text.)

With that in mind, in order to have a large enough sample size, I’ve introduced minions with two extra variables: Tribals (or Creature Types), and Taunt. With these two categories, the number of minions we can draw data from rises to 25. This is still a small number, but it’s better than the 14 we would normally be stuck with. Also, there are some precautions I can take to make sure they don’t cross-contaminate the data. Overall, introducing these extra variables is fine, because they are the two easiest to break down (both logically and relative to the data). But before I can explain why that is, I have to explain something entirely different, something I didn’t expect to have to do for another step, and that’s the value of a card.

This is a little difficult to explain, so I’ll use examples, but it’s not difficult to grasp. When we think about the mana value of a card, there’s a certain amount of “budget” that card is allowed to spend on effects. This budget is a combination of the mana cost of a card, and the intrinsic cost of the card itself. Think of Razorfen Hunter: a 2/3 and a 1/1 boar, attached at the hip. If we consider the 2/3 stats to be “average” (more on that misconception later) as compared to things like River Crocolisk, Mechwarper, etc, the hunter is really only worth 2 of that 3 mana, and the 1/1 boar is worth the other 1 mana. But if we look at other example 1/1’s, that boar doesn’t have haste (Stonetusk Boar), and also isn’t free (Wisp). That boar costs 1 mana for a 1/1 body, which, looking directly at the values, makes little sense. This is because when you add Wisp or Stonetusk Boar to your deck, you’re paying a cost for the slot the card takes up in your deck. With the 1/1, you’re getting it attached to another card, so you aren’t paying that cost for the slot, which means the 1/1 has to cost more than if it was just its own card. So, in this way, any card has an extra cost; the cost of putting it in your deck, which is independent of the mana cost to play it, but adds to the “budget” the card is allowed for its effects.

With that out of the way, we can get on to explaining Tribals, or “creature type” (I call them tribals because of Magic). This attribute has a mana value, as was the entire point of this study; however that value is added to the other side of the equation. Let me illustrate: m + cv = (card stats), where m is the card’s mana cost, cv is the value of a card (as explained before), and these add up to form the aforementioned “budget” for the card’s stats and effects.

So now is the part where we get to the data!!!! WOOOOOOOO!!!!!

*ahem* Anyways, here are some graphs and stuff:

 

There are a couple things to note before we start drawing conclusions. First thing is that we technically don’t need to have a perfectly accurate measurement of the cost of a card: it affects all data equally, so as long as we have a fair ballpark, and we don’t have obscenely high precision figures (which wasn’t going to happen anyway because of sample size), the specifics of that figure doesn’t matter. For good measure, however, I will include my excel spreadsheet here. (For reference, I equated Card Value to 1 mana and a Creature Type to .5 mana, but I made the formulas to determine this data reference those cells, so they can be changed rather easily from the spreadsheet).

Let’s move on to the breakdown of what the data tells us; which is, quite a few things, actually. The first thing that’s immediately obvious is that Taunt has some value, as the difference between the taunt minion and non-taunt minion SPM tells us. This makes sense, but the value is far less than I expected. More on that later. 2nd thing we can tell from the data; if you look at the spreadsheet, you can see that the HPM as compared to DPM (health per mana and damage per mana, respectively) massively differs from BOTH of those figures from Taunt minions. On average, taunt minions devote .2 more mana per point to Health, and .4 less mana per point to damage. (There’s a missing .2 there that is the difference from Taunt itself.) So this means that having taunt on a minion innately makes health more valuable than damage for that minion. This makes logical sense; however, it opens the pathway for two important points that we need to keep in mind as we move forward. 

The first is that effects may modify the mana worth of certain stats or even other effects, as well as having a flat mana cost. Once again, this makes logical sense; there are countless examples of minions with effects that rely on them staying on the board; health, for those minions, is worth far more than damage; you want that minion to stay there. On the flipside, though, if you are a minion with charge, damage will matter far more than health; in fact, one could make an argument that health doesn’t matter at all on charge minions (although I’d imagine this is not the case). This means that the modifiers can go any way for what stats are preferred, and the same is true for the flat mana cost; it can be positive(gives the card an effect that costs mana) or negative(gives the card a detrimental effect like Succubus or Arcane Golem). This is interesting, and makes everything more complicated; not as complicated as the second part, though.

The second is that a card’s mana cost modifies the mana worth of all effects; when I say this , I mean that as you spend more mana on a minion, some stats and effects are going to become more and more worthwhile the larger the minion’s mana cost becomes. This is a little difficult to explain, and is based a little more on my conjecture. If you look at the data separated by mana value:

you begin to notice a trend in the Mana to Damage offset (damage is positive, health is negative) as mana value goes up; it begins to steadily decrease. If you also look at the difference in DPM and HPM in the original data sheet, you’ll see that it favors damage; also, if we use the data from hsrecombobulator.tumblr.com (an average of the stats you should expect to get when recombobulating a minion of a certain mana value), you’ll see that at most values, health is generally favored over damage. This, however, is across such an incredibly small sample size that I can’t really say this is 100% true for all cards; I’ll just have to keep this in mind as I continue.

SOOOOO, what have we learned from all this? Let’s break out that bullet list again.

• Card value doesn’t matter while we’re evaluating minions and not card draw, as all cards will be effected similarly
• 1 Damage = .85 – .9 mana, and 1 Health = .7-.75 mana.
• Taunt has a mana value of about .2 per mana cost of the card, and also has a .8x-.9x modifier to damage and a 1.2x modifier to health
• all effects will have a flat mana value, and a modifier to damage and health
• and finally, all of this data will be subject to change as more work is done.

That last part is the most important; as we examine more and more cards, we can closer and closer to what the “average value” of all these stats will be. I completely expect all of these figures to change to some degree as time goes on. If anything, the difficulty of all these things changing so much has made me even more excited to start crunching more data. On the next episode, time to break down all the other standard minion effects! Hopefully this increases our sample size by a fair amount, and we can start getting more concrete data. See you next time!

P.S. If you look in the tables again, there’s a column labeled”Ratio(-1)”. This stems from a theory a friend of mine suggested, that all minions naturally need 1 health, so in essence, you’re not paying for that 1 health when you play a minion. I recalculated things to see if it changed the data, and it doesn’t; also, you could consider this 1 health the cost you’re paying for this card being a minion anyways. Here is the recalculated data if you want to see it.