Should You Include Stalking Shadows in Your Runeterra Decks? Diving Into the Probabilities

Hail, Champions! Do you homebrew your own Legend of Runeterra decks? If so, you've probably run into this classic dilemma with your Shadow Isles decks: do you include Stalking Shadows or not? As far as card draw goes, it's one of the best -- for 2 mana you get an immediate draw at burst speed without condition, you get your choice if there are multiple followers in your top 4 cards, and you even get an ephemeral copy of that card. There's just one huge downside: it only draws followers. And if the top 4 cards of your deck contain no followers, the spell will have no effect... often costing you the game.

So, when is it worth running Stalking Shadows and when is it worth running more traditional card draw like Glimpse Beyond? The answer to this question will vary greatly based on what your deck is trying to do. Archetypes like Nightfall really appreciate any burst spells, and Fearsome archetypes really benefit from the extra copy of Frenzied Skitterer or Wraithcaller. However, in case you're just pondering the first-order question, "How likely it is my Stalking Shadows will draw anything?", we're here to help you break down the statistics. Even if you don't play Runeterra you might want to stick around -- we're going to break out the math behind these numbers, which you can then adapt to answer any "What are the odds of X in my top Y cards?" CCG question.

Baseline Probabilities

Assuming a normal 40-card deck, here are the baseline probabilities for how many followers your Stalking Shadows will pull from the top 4 cards of your deck:

Alternatively, here's a graph illustrating the odds of hitting at least 1 option as well as the odds of hitting at least 2. Since it really doesn't help much if that 2nd card is just a copy of the first, we're also approximating how likely it is to draw 2 unique cards. (It's only an approximation since the math gets really hairy if you want to fully account for running 3x of some followers but 2x or even 1x of others.)

Turning Theory into Practice

Let's take a minute to compare some of the most successful meta decklists that run Stalking Shadows. 

We'll start with NicMakesPlays's Nightfall: besides the aforementioned synergies with Nightfall, Nic runs 22 followers meaning he has a whopping 97% chance to hit at least one card and a 75% chance to offer multiple unique cards. Tempo13X's mono-SI deck is a little less lucky: at 15 followers, it only has an 87% chance to hit at least one and 50% chance for multiple unique options. And finally, we have a generic Fearsome spider deck; you'll notice this deck runs 26(!) followers which gives it a 99% chance to hit at least one card and an 88% chance to return multiple options.

So where's the cutoff? I would say that will depend a lot on how much variance you're willing to accept from your deck. Sure, the 13% chance to whiff from Tempo13x's deck looks high relative to those other two decks, but let's compare it to allegiance: at 15 followers, it has roughly the same probability of whiffing as an allegiance deck with 5 off-region cards. Many decks, including the extremely popular pre-nerf Kinkou Elusives deck, are willing to accept those odds.

The Math

Are you interested in how exactly we generated the above values? Let us show you!

Let's start with the example of a deck with 15 followers and the question of "How likely are we to hit exactly 1 out of the top 4?" Picture in your head dividing the deck into 2 piles: one with all the followers (15), one with everything else (25). Since the Stalking Shadows that we're playing can't hit itself, we'll remove it from the "everything else" pile (24). We're going to start to answer this question by calculating the number of permutations with exactly 1 card from the Follower Pile and 3 cards from the Everything Else Pile. Then we're going to combine the two piles back together and calculate the total number of 4 card permutations. Our odds will be NumberOf4CardPermutationsWithExactly1Follower / TotalNumberOf4CardPermutations.

To calculate NumberOf4CardPermutationsWithExactly1Follower, we'll first take that Follower Pile and figure out how many different combinations we can get. It's pretty simple since it's a single card: there are 15 different permutations, the size of the pile itself. Next, we'll figure out how many different combinations of 3 cards we can get from the "Everything Else" pile. If we cared about order, this would be 24 * 23 * 22 since the pile shrinks by 1 every time we pull a card to put it in our combo. However, we don't care about order -- Vile Feast, Atrocity, Vengeance has the same result as Vengeance, Vile Feast, Atrocity. Therefore, we need to compensate for permutations with the same cards but in different orders -- this makes the equation be (24/1) * (23/2) * (22/3) = 2,024. Notice how each time we pull an additional card, the divisor increments as the dividend decrements. Finally, we need to combine these two values to calculate NumberOf4CardPermutationsWithExactly1Follower -- since we are order-independent, this is as simple as multiplying them together: 15 * 2,024 = 30,360. 

Next, we need to calculate the total number of permutations of 4 cards from our deck. We'll use the same order-compensation trick as before, but this time with all 39 cards (again, we're playing a copy of Stalking Shadows so we get to exclude it from the calculations). TotalNumberOf4CardPermutations = (39/1) * (38/2) * (37/3) * (36/4) = 82,251. If we return to our original equation, we'll see 30,360 / 82,251 = 0.3691, or 37%. You can then repeat this procedure to calculate the odds for drawing exactly 2, exactly 3, and exactly 4; the probability of drawing at least 1 will be all these odds added together.

That concludes our analysis about Stalking Shadows probabilities. Did you find this article enlightening? Would you like us to write more like it in the future? Let us know in the comments below!