HearthMath: Druid

Today we continue our series on how to better understand the math behind Hearthstone and how you can bend it to your advantage, by looking at Druid!

Introduction

Hey, guys. It’s RaFive. Today we continue our series on how to better understand the math behind Hearthstone and how you can bend it to your advantage, by looking at Druid!

Malfurion has several class cards that have a significant impact on the way to calculate mana curves and build toward the best draws. Innervate effectively multiplies your resources during early turns. Wild Growth transforms your mana curve. These let you scale your curve upward, but it’s still necessary to have enough on the low-end that you’re insured if you don’t draw into your ramp-up cards. This article will examine some of the math behind all that, so you can make more informed decisions on how to build your Druid decks.

As usual, while the topic is math-heavy, I’ll try to make it as easy on the less quantitative brains as possible and crunch numbers only when needful. For reference on draw probabilities, please see this chart I’ve prepared and make sure you’re familiar with my previous articles on the topic. Early turns are the most important for Druid’s ramping strategies, and it’s always better to build for a game where you go first, so I’ll generally be supposing you’ll have at least one card in your opening hand you want to hold, giving you an assumed six draws by the time the game starts on turn 1.

I’ve also included a recent, quite powerful Ramp Druid decklist for easy reference to the curve and the core / common cards in the list. There are a couple of interesting choices in the card selection, but the curve is reasonably representative and it gives us a good framework for discussing how to think about probabilities in Druid deckbuilding. Let’s begin!

The Hero Power

The first important thing to consider when doing the math on a hero is the hero power. For example, Priest’s lifegain power means that even control variants typically only run a single middling burst heal, Holy Fire, and that as much for burst damage as anything else. Druid has a fantastic midrange hero power: 1-damage removal for 2 mana but no card cost — effectively Wrath’s effect in terms of card advantage(since you don’t draw a card but don’t use one, either), with the deck slot replaced by (X – 1) of your health total. If you don’t attack a minion (or attack a 0-attack minion), you effectively add 1 to your health total each time you activate. It’s a fantastic ability, flexible in the very best sense of Druid, leaving it up to you to value it in individual situations.

The removal aspect of the hero power means you can afford to put slightly bigger minions in and run slightly less early-game removal. Combined with ramp cards, this means you can actually get away with running Wrath as your only 2-cost minion or removal, as you can see in the decklist. Since the hero power is effectively “in your hand,” it can probably be valued equivalent to 2-3 copies of a card with a similar effect (Wrath, Shiv, maybe Elven Archer), and can also be considered as running a slight heal.

The Ramp Cards

First, a word on draw odds to better contextualize how the cards are evaluated below. Most Ramp Druid decks run double Innervate and double Wild Growth, and that’s it. If we look at the probability table, we see that running four cards and drawing six, our odds of at least one success are a little over 60%. Even if we’re only drawing four (i.e., mulliganing one card when going first), our odds are only slightly lower than even. This means Druid is basically banking on ramping extremely favorably about half the time, and the other half of the time scraping by using Wrath and the hero power while hoping to draw into ramp. If you add Wrath to the ramp cards, the odds of drawing into one by turn 2 is 83% — plenty consistent enough for the hero power to fill in the probability gaps.

(Incidentally, this is one reason why Grove Tender hasn’t proven popular with Druid — at 3 mana it’s a slow card for early ramp, and even running two copies, you only improve your probability of being able to ramp by about 15% at most generous.)

Now, the ramp cards.

• Innervate is one of Druid’s most important cards, since it effectively lets you skip two turns in terms of what tactics are available to you. This gives Druid tremendous flexibility when it comes to populating the board.Mathematically, it’s better to think of Innervate as basically a Preparation with global effect: “all cards cost (2) less.” In other words, if you have Innervate in hand, Chillwind Yeti is a 2-drop. Looking at the decklist, you see 2-3 3-drops (depending whether you count Mind Control Tech), 6 4-drops, 5 5-drops, after which time ramp starts to encounter irrelevancy through diminishing returns (since you’ve certainly drawn strong plays by then).

With Innervate, however, that becomes 3 at 1 mana, 6 at 2 mana, and 5 at 3 mana. If you look at the table, you’ll see your odds of drawing those by their respective playable points are quite good (and also suspiciously similar to a standard midrange mana curve — although with Innervate, you’re effectively spitting out superpowered minions). You have about 2 to 1 odds to draw into your ramp by turn 3, and slightly better odds to draw into a 5-mana card by turn 3, as well, by which time you’re also almost certain to have pulled a 4-drop for the next turn, and can snowball from there!

• Wild Growth is another card that’s better to reframe slightly for mathematical purposes. For most Druid play, it’s used to effectively reduce 4-5 mana cards to be able to play them on turns 3-4. The sweet spot to play Wild Growth is turn 2 (or possibly turn 1 with the Coin if you’re going second); it’s awkward to use on future turns in such manner that you have enough mana to make a credible play. As a general rule, if you get Wild Growth after turn 2 (and don’t have some kind of weird Innervate wombo-combo that lets you gain a mana crystal to efficiently ramp into another play without falling behind in the game) you should seriously consider holding it until you can get card draw value from it. Again, if we look at Wild Growth as giving us 6 turn 3 plays and 5 turn 4 plays, we can see that we have extremely favorable odds of timely drawing into the particular cards we’re running in those roles.
• Grove Tender is basically Wild Growth, a turn later. This is actually a lot worse than it sounds, because it does not affect 4-drops (unless, of course, you coin Tender out). Druid has some really solid class cards at 4, like Keeper of the Grove, and also tends to play beefy minions that can wreck an opponent’s early game if ramped out, like Chillwind Yeti. Considering Druid’s other ramp cards let you ramp much earlier — thus enabling those quick, powerful 4-drops — and considering Tender’s effect is symmetric, it’s hard to justify building her in around the assumption that an entire mana tier (and 4-drops are very strong, comparatively) may be useless orsuboptimal in any given game.Instead, Tender is better as a 1-mana Innervate on the turn you play her, for a later-game board flood against aggression (or extremely late-game against control, for card draw). Instead of being used to set up a ramp play, Tender is much better used for something like a Wrath into a Tender on turn 4 to regain board presence. Although she looks like a ramp card, she’s really not.
• Nourish, sadly, is a draw spell. For competitive purposes in Druid, it has no impact on the math of the mana curve. Barring the extremely rare case where draw a double Innervate together with Nourish in your opening hand, the soonest you can play it is turn 4-5, by which time you’re almost certainly already ramping into the most powerful Druid threats. As if that weren’t bad enough, sure, it gives you two mana crystals, but that’ll ramp you up to 7+ mana, and Druid can ill afford to run a half-dozen cards that fat with class cards that are strongest in midrange. (It’s worth noting that Nourish, much like Grove Tender, actually gives you two filled mana crystals, effectively costing 3 if you play something else on the same turn, but this just encourages you to play it even later in the game when its effect is even less useful.) Nourish can’t be played until midgame, eats up your whole turn, and you have about a 60% chance to draw into it on curve with a good mulligan, so there’s just no way to build an ultra-rampy Nourish Druid that plays fatty after fatty; you just can’t make the numbers work on the first few turns without cards that then swing your gameplay faster enough that Nourish comes too late. (I may eat my words on a future Tree of Life Druid.) The bottom line here is that you either play one for draw, or, more likely, you just don’t play it at all.

Conclusion

Druid provides a number of excellent examples for how to think mathematically about unusual deck curves due to ramping effects. Innervate is a one-time significant cost reduction which, together with the Druid hero power, removes the need for most early-game cards in ramp decks, and Wild Growth’s more permanent effect requires you to think in terms of your whole curve, so you can land ramped minion after ramped minion while your opponent is unable to efficiently respond. However, we’ve also learned how to spot signs that a card may be unsuitable for a rampy deck, even if it looks like a ramp card in theory; Grove Tender and Nourish are excellent case studies.

Best of all, this learning is transferable! You can easily apply similar reasoning to Mechwarper and Preparation, which are the other commonly run ramp cards — for example, a little over half the time, Sprint costs 4 mana in decks running Prep. See? Rampology is easy, and it’s just one more fun way to build a better metagame!