Monday, 15 March 2021

The Kill Index

I was trying to think of a measure for how powerful a threat is and the "kill index" is what I ended up with. This is not unlike an article Top X list in which I covered cards that had text closest to "win the game" on them. This however extends the idea beyond big things that win and lets us examine midrange cards too. The idea is simply how long a threat has to stay in play on average before it has effectively won the game. Ideally I would be able to pull on thousands of games of online data for this rather than just guess based on a significantly smaller pool of experience. The kill index of a card that literally said win the game would be 1, the best possible. Cards that usually win right away or force a concession such as Ugin or Craterhoof would have a kill index near 1 such as 1.2 or something. As you would hope when you are paying for an 8 mana card! It is the low cost cards that are more interesting however. I have always thought the sign of a good four + mana planeswalker is one that is passable with one activation, good with two and game winning with three. That is essentially saying planeswalkers with kill indexes of 3 or less are really good. You do really want to take CMC into account as well. A three mana planeswalker with a kill index of 4 is very probably better than a four mana one with a kill index of three. Certainly that will be the case for curving although it is a different story when it comes to top decking it.

The kill index is a measure of threat, not of survivability. You need the card to survive in order to assess how effectively it is contributing to the win! As such you can just assume a card stays in play in order to calculate the kill index. A Monastery Mentor has a pretty low kill index. Typically untapping with it leads to a win giving it an effective kill index pleasantly close to 2, say 2.5 for the sake of argument. This is better than most planeswalkers, certainly in the same cost range. The difference however is found in the value generation and ease of removal. Planeswalkers generally do at least one of these things, often both. Mentor, especially on curve typically does neither. A shocked Mentor leaves you well behind. Other cards with worse kill indexes than Mentor will either leave behind more when dealt with or resist being dealt with significantly more effectively. A kill index is not therefor an overall measure of card power but more of threat level. When faced with a choice of what to kill the card with the lower kill index is the best choice on average. When curving into a situation where you know you don't face removal then playing your card with the best kill index is generally the best line. When building your deck or curving out normally however just playing the cards with the lowest kill index is not going to be the optimal strategy with value and durability being of importance.

The threat of a card helps to make it powerful but the power of a card doesn't always relate to how threatening it is. Threat is a component of power. Not all cards have threat at all, certainly not in a direct way. A Counterspell might be a threat to your game plan but it isn't directly a threat to your life by itself. While not all cards need to have threat level all decks do need to contain some cards with it. This makes it more important that decks packing fewer threats play ones that have that have a low kill index, or at least incredible resilience and inevitability. I often rule out top end cards that are clearly powerful overall simply because they lack threat. 

Aetherling is a funny customer. You could argue for a kill index close to one, or could have done so back when it was the premium win condition for blue. You simply need to resolve it with some mana up and that would be the game won. The issue is speed and defence. Aetherling is slow to kill and puts up a relatively poor defence. As power in cube rose and tempo became ever more crucial Aetherling fell out of favour. The kill index of Aetherling is basically just tied to how long you can survive. If you have your opponent locked out of the game then sure, call it a kill index of one. If not then even four might be generous. Not an overly relevant tangent what with the card no longer being all that potent but it is worth noting. Ugin has some similarities to this but it is much more matchup dependant. Ugin locks a lot of players out of the game hence so often securing the immediate win. Some decks however win with burn or mill or things Ugin can't bolt or exile out of the game with ease. In those cases Ugin's kill index is much closer to how fast he can win by doing three to the face, sometimes gaining 7 if against burn. 

If we want to get super technical looking we can say that the threat of a card is a product of it's kill index and a measure of it's survivability. The latter would be determined by ease of resolving it and difficulty in removing it. This would help us to determine the power of the card but we would need to take into account a few other factors to fully arrive at the power level. You could slap "draw a card" onto something and make it a lot more powerful but you wouldn't have affected the kill index or the survivability. Things like value, disruption, information, and options, all also contribute to the power of a card. As does the way those elements synergize with the overall card. How much of a swing, or how much board presence a card has is a big factor too. Cards like Whirler Rogue are great because they cover a lot of ground on this front. Things that stop you dying are just as important as things that kill your opponent. All these things are considerations for power level, the kill index is just a small slice of that. 

It is important to make the distinction between how many turns a card goldfishes in and how many turns on average it needs to be in play and active before the game is over. The former is less useful in that it takes no account of how robust a card is nor how good it is at getting through defences. Ugin is actually pretty slow to goldfish doing just three a turn. In practice he seals the deal very rapidly (in most cases, exceptions previously discussed). The reverse is true of Phage the Untouchable who looks to take the game in one hit giving her a goldfishing kill index of two. Due to her lack of evasion or extra pressures and effects her kill index is going to be way way higher. Sadly it is very easy to work out how quickly a card kills in a goldfish while pretty tricky to estimate the average duration in play a card needs to have before it equates to a win. 

A useful measure of a card is to add it's converted mana cost to it's kill index, we could call this a kill speed. A Goblin Rabblemaster comes in at a respectable 6 being a 3 mana card with a kill index of around three. Yes, Rabblemaster kills in four turns by itself in a goldfish but it has done critical damage and value in three. If we generously give a Grave Titan a kill index of 2 then it is still two turns slower at getting the job done than Rabblemaster. This is why aggressive decks play cheaper cards that kill slower rather than pricier ones that kill quicker. That of course combined with the cumulative effect of multiple threats. 

So what is the point of all this? Basically it is just a tool to assist with understanding, decision making, and comparison. The more you understand underlying mechanics and concepts the better placed you are for all of those important elective and comparative aspects of magic. I find that formalizing things and putting numbers to them, even if they are estimates and hard to measure, very helpful in doing this. Every time you have a removal spell and a close choice between multiple targets you are essentially working out the kill index of those cards in the context of that game. The same is true when trying to curve out in an informed way with good reliable tempo. It lets you examine a cards strengths and weaknesses in card evaluation which in tern lets you better select things for appropriate roles in deck construction. Working out goldfishing kill indexes and kill speeds is very easy. Estimating them accurately for real games is something that likely takes some experience and practice.

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