For the past few weeks, we’ve been looking at applying mathematical models to Magic’s vast set of creatures. We started out two weeks ago by creating a function that mapped power and toughness of vanilla creatures to a “par” mana cost that would be appropriate for each combination. Then last week, we took our model to the next level by going through the list of evergreen keyword abilities and modifying it for French vanilla creatures with each keyword on the list. Today, we’ll finally get to finish going through the evergreens, and we’ll wrap up this topic with some final thoughts and next steps.

In case you forgot, here’s our graphical model for a par vanilla creature:

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As I mentioned last week, you can read the graph by picking a power on the P-axis and a toughness on the T-axis, then seeing where the plane intersects the vertical axis at that point- that’s your mana cost. For example, our model puts the appropriate cost for a 1/7 at a hair under four mana, which you can observe by looking at the far back corner.

Indestructible

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We get to start this week’s list off with one of the more potent evergreen keywords, indestructible. Remember how creatures with deathtouch didn’t get much better the more power they had, as long as they had at least one power? Indestructible is like that, but opposite. As long as a creature with indestructible has at least one toughness, it doesn’t get much better at all once you start piling more on. (At least with deathtouch, more power equates to more damage dealt to players- indestructible only cares about toughness when it’s dealing with -X/-X effects!) As a result, the graph for indestructible creatures is going to look very similar to the mirror image of the graph for deathtouch creatures, except more exaggerated.

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Lifelink

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Lifelink gets better the more damage you deal, right? But lifegain is also better in defensive strategies where the game lasts longer, and those strategies prefer creatures with higher toughness. It might sound like a paradox, but the reality is that these opposite forces probably land lifelink as one of the rare mechanics that’s just good on all bodies. In fact, I’m not sure whether I’d rather have a 4/2 lifelink for 4, a 3/3 lifelink for 4, or a 2/4 lifelink for 4; each is strong  in its own way. For this reason, the lifelink graph looks like the vanilla graph, with a little extra bonus cost for the ability.

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Menace

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Menace is one of the newest additions to the evergreen keyword list. I’ve seen menace be most effective on creatures heavily skewed toward power. This is because menace creatures are good at getting their damage in until eventually you’re forced to 2-for-1 yourself just to get rid of them.

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Prowess

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Prowess is tricky, as the only triggered ability on this list- all the rest are static abilities. What that means is that prowess is going to be more relevant in certain situations than others, and this is going to be more common for prowess than all the other evergreens.

I like to think of prowess as turning every instant in your hand into a combat trick, but only a marginal one. Prowess creatures want to set up what looks like it’s going to be a mediocre trade, then suddenly blow your opponent out with an instant they weren’t expecting. What this means is that prowess creatures want enough power to incentivize attacking, but they also want high enough toughness to survive a multi-block. (This won’t be the case for every strategy that utilizes prowess, but from my experience it’s generally how things end up in limited.) We’re going to see on the prowess graph that the best prowess creatures are well rounded but slightly heavy on toughness.

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Reach

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Outside of Mwonvuli Beast Tracker shenanigans, the only reason a creature might have reach is so it can block fliers. That means that creatures with reach want to have high enough power to be able to trade with fliers consistently, or high enough toughness to be able to survive bumping into fliers consistently. On top of that, the latter case is going to be useful somewhat more often than the former case, as reach lends itself to pillow-forting strategies.

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Trample

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What do Charging Badger and Darksteel Colossus have in common? They both have trample. Obviously, they wield that trample in different ways, and it’s no debate that Darksteel Colossus uses it better. The bottom line with trample is that more power = more pain for your opponent, while toughness doesn’t interact with the ability much at all.

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Vigilance

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When a creature has vigilance, it wants to be able to both attack and block. That means that like prowess creatures, it wants enough power to get some damage in, but it also wants enough toughness to be able to survive combat. All that adds up to a situation where the ideal vigilance creature has well-rounded stats with a slightly above average butt.

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Moving Forward

Well, fifteen keywords in, and that’s our list! While this exercise has been fun, and the knowledge can be important unto itself, I feel like we’re only scratching the surface of this type of theoretical thinking in Magic. While I won’t be covering these kinds of models here any more in the near future, I would not be surprised if anyone wanted to expand upon this. In fact, a few people have reached out to me looking to do just that. With them in mind, I would recommend the following:

1. Get some data to back this up

While I go pretty deep on some of my analyses here, my perception of what’s good or bad is based solely on my own experience and card evaluation skills. I would love to see someone crunch the numbers over a large set of games to figure out which sets of stats are the true champions of card quality.

2. Improve upon my lousy math

As I mentioned in my first article in this series two weeks ago, a lot of my math is kinda janky, and while it approximates the values I’m going for, I know that there are probably better mathematical formulas that exactly mirror my intuition.

3. Extend the model to include all creatures, perhaps via a neural network

We’ve come up with models for vanillas and French vanillas, but we can go even further. For one, we can create models for all keywords, not just evergreens. (Skulk comes to mind as a recent example that would fit right into the pattern of our models.) To encompass all creatures into our model would be pretty difficult. We can try out developing a neural network that reads in all creatures ever printed and attempts to create its own model based on what it sees.

4. Put in your own two cents

Think I’m dumb as rocks when it comes to card evaluation? I don’t mind! I would love to hear some alternate opinions with regards to my claims over the past few weeks.

5. Apply this knowledge to your play

It’s one thing to know a lot of things, but it’s another thing entirely to make use of them in real situations. I hope that if you’re reading this, you’ll go back to your next prerelease and make a more informed choice between that 2/3 vigilance and that 2/3 menace.

I hope you enjoyed our journey to mathematically model Magic’s creatures! Check back with me next week, when I take my first look into the exciting new Modern Masters 2017 limited format. Have you seen those crazy spoilers?!

Looking for some more bits of Aether Revolt limited analysis? This article from Charlie Rinehart-Jones gives us some of the surprise successes of the format so far.

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