Written by neosystems on April 15, 2010
Introduction:
Since reading the following articles (http://manamaze.com/special) and (http://www.wizards.com/Magic/Magazine/Article.aspx?x=mtg/daily/feature/65), I have been fascinated with different methods of taking a large number of decklists and making a statistically created decklist. Frank Karsten, the author of both of those articles, popularized this method when he piloted his Faeries deck to a Top 8 finish. I believe there is a lot of room to improve on his methods, as I believe that simply taking the arithmetic mean creates a lot of bad version of decks.
The Mathematics:
The goal in technical terms is to take a large number of decklists (this does work with a small sample size, but works best with a large sample size) in order to analyze card choices and the number of copies of each card played in a deck to create a general “shell”. By shell, I mean that the cards in the deck will include, for the most part, only cards in numbers that are run by a large portion of other decks. In this way, you will not have a finely tuned version of the deck metagamed for an expected field – rather, your deck should give you the best possible chance against an unknown field. More precisely, it will give you the best possible chance against an “average” field where the most popular/best deck would show up in the largest quantity, the second deck in the second largest quantity, and so on. Should you have some knowledge of what you will play against, it is up to you to change card choices appropriately. Here are the statistical methods primarily used for this:
Arithmetic Mean: When someone says “mean” they are usually referring to the Arithmetic Mean, where you take a data set of n points, take the sum of that data set, and divide by n to get a value. I do refer to this as Arithmetic Mean throughout the article, because I will get into the Geometric and Harmonic means later on.
Median: The median is found by taking a data set, and simply finding the middle value. If there is no actual middle, but rather, two data points end up in the middle, simply find the arithmetic mean of the two to get the median.
Mode: For analysis in terms of M:tG decks, the mode is actually more useful than the arithmetic mean. I will get into the pitfalls of simply using the arithmetic mean alone, but for now, just know that the mode tells which number in a data set appears more than the others.
The Folly of Arithmetic Mean:
Many people have used Deckcheck’s “compare” feature to compare a large number of decks and simply using their calculated average to make a deck. This is also the method primarily employed by the articles linked in introduction. I believe that this is statistically inaccurate for a number of reasons.
Consider this first case: Let us say that one is creating a Zoo deck, and according to the data, 25% of Zoo decks played 0 Kird Ape, but 4 Loam Lion, while 75% of Zoo decks played 4 Kird Ape, but 0 Loam Lion. The method of averages would then say that it is correct to play 3 Kird Ape and 1 Loam Lion even though a quick skim of the lists says that this is clearly incorrect, as one should always either play 4 Kird Ape or 4 Loam Lion, as the data suggests.
A second reason why arithmetic mean is bad, aside from the fact that it does not take into account “one or the other” situations, is that it is easily skewed by outliers given a small sample size. Consider this second case: You are analyzing six decklists. Five of them play 2 Islands, while the 6th plays 12
So, how do we then calculate how many of a card to run without making ourselves backtrack and check? The method I use is to calculate the mean, median, and mode for each card. I then compare the values, and use the card number where at least 2 out of the 3 methods agree. For example, say we are trying to see how many Putrid Leeches to play in our Jund deck. The mean comes out to 3.7, the median 4, but the mode 3. The mean and median agree that 4 (always round to whole numbers of course) Putrid Leeches should be played in the deck, and that’s how many I will play. Each one of these three will fail you at some point. This is why it is very important to combine them and not allow one method to decide your card choices.
Putting it into Practice:
I decided to implement this method to create a Vintage deck. After crunching some data of Top 8 lists, I found that the top three best performing Vintage decks in the last 3 months were: Tezzeret’s Vault, Fish, and Iona Oath in that order. Since I was intrigued by the vault deck, and because it was the best deck, I wanted to find a good decklist for it. I have used well performing Tezzeret’s Vault lists from the last three months for the purposes of this article. I suggest you follow along and work with me as I go, if you are interested in this type of thing.
For reference, here are the decks I’ve used.
Cards we can immediately throw out:
Looking at cards which cannot even garner a single copy by method of averages are not cards that will never make it into the deck, but cards that do it make it in our first pass. In this list, this applies to all cards which have an arithmetic mean of less than 0.5.
It is worth mentioning the following two cards you may have noticed by looking at the link I provided above:
Hurkyl’s Recall: Take another look at the card. Deckcheck lists Hurkyl’s Recall and Hurkyl’s recall. The lack of capitalization on the second one, actually, at first glance, skews the numbers enough to tell us that we should not be playing Hurkyl’s Recall at all! In fact, when we add the numbers for the two Recalls together, we get exactly .5, telling us that we should be playing 1 Hurkyl’s Recall in our deck. It’s important to watch out for things like that, it is happens again with Sensei’s Divining Top as well.
Cards that are an auto-include:
A good shortcut to know is that whenever a card is played in only one number across all decks, one will always play that number. For example, every single deck plays a Black Lotus in the link above. Without doing any calculation, you know that the mean, median, and mode will always be one, and thus you will always play one Black Lotus in your deck. Cards that are an auto-include are:
| Auto-Include | ||
|---|---|---|
| Main Deck | Sideboard | |
| 1 Ancestral Recall 1 Black Lotus 1 Brainstorm 1 Mox Emerald 1 Mox Jet 1 1 Mox Ruby |
1 Mox Sapphire 1 Sol Ring 1 Time Vault 1 Time Walk 1 Tinker 1 Tolarian Academy 4 Force of Will |
|
The Mean, Median, and Mode Decklists:
For the sake of comparison, I have created three decklists, each one using exclusively Arithmetic Mean, Median, or Mode. We will then compare and include in our version, each card whose number is agreed upon by 2 of the 3 decks. Usually I do this card by card, but I think for the sake of learning, doing it by three decklists will prove to be beneficial.
First the decklist calculated with Arithmetic Mean:
| Arithmetic Mean Deck | ||
|---|---|---|
| Main Deck | Sideboard | |
| 1 Scalding 2 Polluted Delta 1 Tolarian Academy 1 Tropical 3 Underground Sea 1 Volcanic 1 Flooded 3 1 1 Misty Rainforest 2 Dark Confidant 2 Tezzeret the Seeker 1 Spell Pierce 1 Sol Ring 2 Sensei's Divining Top 1 Thirst for Knowledge 1 Rebuild 1 Ponder 1 Mystical Tutor 1 Mystic Remora 1 Mox Sapphire 1 Time Vault 1 Time Walk |
1 Tinker 1 Vampiric Tutor 1 Voltaic Key 1 Yawgmoth's Will 1 Ancestral Recall 1 Fact or Fiction 4 Force of Will 1 Gifts Ungiven 1 Fire/Ice 1 Hurkyl's Recall 1 Duress 1 Demonic Tutor 1 Brainstorm 1 Black Lotus 1 Mox Ruby 1 Mana Crypt 4 Mana Drain 1 Merchant Scroll 1 Misdirection 1 Mox Emerald 1 Mox Jet 1 1 Variable Slot |
|
The decklist calculated with Median:
| Median Deck | ||
|---|---|---|
| Main Deck | Sideboard | |
| 2 Polluted Delta 1 Scalding 3 1 Tolarian Academy 3 Underground Sea 2 Flooded 1 1 Misty Rainforest 3 Dark Confidant 1 Tezzeret the Seeker 1 Mystical Tutor 1 Ponder 1 Rebuild 2 Sensei's Divining Top 1 Sol Ring 1 Mox Sapphire 1 Thirst for Knowledge 1 Time Vault 1 Time Walk 1 Tinker |
1 Vampiric Tutor 1 Voltaic Key 1 Yawgmoth's Will 1 Ancestral Recall 1 Hurkyl's Recall 1 Black Lotus 1 Brainstorm 1 Demonic Tutor 1 Fact or Fiction 4 Force of Will 1 Gifts Ungiven 1 Mox Ruby 1 Mana Crypt 4 Mana Drain 1 Merchant Scroll 1 Misdirection 1 Mox Emerald 1 Mox Jet 1 6 Variable Slots |
|
The decklist calculated with Mode:
| Mode Deck | ||
|---|---|---|
| Main Deck | Sideboard | |
| 2 Polluted Delta 1 Scalding 1 Tolarian Academy 3 Underground Sea 2 2 Flooded 1 1 Misty Rainforest 1 Thirst for Knowledge 1 Mox Sapphire 1 Mystical Tutor 1 Ponder 1 Sensei's Divining Top 1 Sol Ring 1 Tezzeret the Seeker 1 Mox Ruby 1 Time Vault 1 Time Walk 1 Tinker |
1 Vampiric Tutor 1 Voltaic Key 1 Yawgmoth's Will 1 Ancestral Recall 1 Black Lotus 1 Brainstorm 1 Demonic Tutor 1 Fact or Fiction 4 Force of Will 1 Gifts Ungiven 1 Hurkyl's Recall 1 1 Mana Crypt 4 Mana Drain 1 Merchant Scroll 1 Misdirection 1 Mox Emerald 1 Mox Jet 12 Variable Slots |
|
Now, it is simply a matter of combining the three decklists. Remember, we are looking to find two agreements on number among all three of these decklists. Also, do not worry about variable slots; we will address those in a bit.
Normally, you will either get all three matches, or at the very least, two out of three matches. However, there are times when all three statistical methods will disagree. That is when we may bring in two additional methods: The Geometric Mean and the Harmonic Mean. Since Mean and Median tell us to play two and three Dark Confidants, respectively, and Mode tells us to play none, we can at least say that two out of three agree that we should play some number of Dark Confidants. Thus, we can discount the zeros in our data. This is a prerequisite of finding the Geometric and Harmonic Means. The easiest thing to do now is to input each data point into its own cell in Microsoft Excel and then use the GEOMEAN( and HARMEAN( functions to calculate the values. If you are interested in the mathematics, the Geometric Mean multiplies each data point in a data set of size n together and then takes the nth root of the result. The Harmonic Mean takes n and divides it by the sum of 1/x from 1 to n.
Regardless, for our purposes, we find that both the Geometric Mean and Harmonic Mean suggest that we play three Dark Confidants, which the number I have chosen to use. We could further justify this by discounting the mode (since we know we have to play Dark Confidant) and averaging the mean and median to get 3 as well. This was the only discrepancy I ran into.
The Decklist Thusfar:
| Tezzeret’s Vault | ||
|---|---|---|
| Main Deck | Sideboard | |
| 2 Polluted Delta 1 Scalding 1 Tolarian Academy 3 Underground Sea 3 I 2 Flooded 1 Misty Rainforest 1 3 Dark Confidant 1 Thirst for Knowledge 1 Yawgmoth's Will 1 Voltaic Key 1 Ponder 1 Mystical Tutor 1 Gifts Ungiven 4 Force of Will 4 Mana Drain 2 Sensei's Divining Top 1 Ancestral Recall 1 Tinker |
1 Vampiric Tutor 1 Mana Crypt 1 Brainstorm 1 Demonic Tutor 1 Rebuild 1 Hurkyl's Recall 1 Merchant Scroll 1 Misdirection 1 Tezzeret the Seeker 1 Fact or Fiction 1 Sol Ring 1 Mox Emerald 1 Mox Jet 1 1 Mox Ruby 1 Mox Sapphire 1 Time Vault 1 Time Walk 1 Black Lotus 6 Variable Slots |
|
Recognizing When Statistics Fails:
Going purely by statistics we have six variable slots. However, in reality, we really do not. This is where statistics fails us, and why simple Arithmetic Mean as a way to build a statistical deck is not a very good idea. When we analyze the lists, we see that there are low numbers for large artifact creatures such as Darksteel Colossus. In fact each deck seems to have one of these types of creatures. Every statistical method we’ve used so far has told us to run zero copies of the following: Darksteel Colossus, Inkwell Leviathan, Sphinx of the Steel Wind, Platinum Angel, and Triskelion. However, upon closer examination, we see that every deck seems to have one copy of one of these creatures. This explains why the number is told to us as zero. If each deck were to play one Darksteel Colossus, we would play one as well, but some decks play Inkwell Leviathan, Platinum Angel etc. Recognizing things like this is a skill that must be developed if you elect to use this method. We must now decide which creature to run. Looking at the numbers for Arithmetic Mean, we find:
Darksteel Colossus: 0.23
Inkwell Leviathan: 0.31
Sphinx of the Steel Wind: 0.38
Platinum Angel: 0.08
Triskelion: 0.08
Going by these numbers, Sphinx of the Steel Wind is the most popular choice, which is what we will use for our deck. This is what I mean, when I say that in reality, we do not actually have six variable slots. We must look for the things like this that statistics miss before calculating the actual number of variable slots. In our case, our actual number of variable slots is five. You may stop here and fill them with whatever you’d like, however I will keep going and share what I decided upon.
Filling in the Variable Slots:
I noticed that Mystic Remora was always (save for one exception) played as either a 4 of or not at all. The Arithmetic Mean told us to put one in our deck, but it ended up not making it in at all because the other two methods did not agree with that assessment. I decided to add in 4 Mystic Remora to the deck, because of how well it plays in Vintage. Leaving myself with one more free slot, the best thing to do is to find a card that did not make it in, but was played as a one-of in nearly half the decks we sampled. Being a one of in at least 50% of sampled decks means that the mean, median, and mode would all have suggested to play one. Being a one-of in just less than 50% means that it barely missed the cut. The best card I could find to fit this criteria was Echoing Truth which was played as a one of in twelve of the decks. Being in thirteen decks means that we would have played it in our main deck, but it barely missed out. Adding in four Mystic Remora and an Echoing Truth gives the final decklist of:
| Tezzeret’s Statistical Vault by neosystems | ||
|---|---|---|
| Main Deck | Sideboard | |
| 2 Polluted Delta 1 Scalding 1 Tolarian Academy 3 Underground Sea 3 2 Flooded 1 Misty Rainforest 1 3 Dark Confidant 1 Sphinx of the Steel Wind 1 Thirst for Knowledge 1 Yawgmoth's Will 1 Voltaic Key 1 Ponder 1 Mystical Tutor 1 Gifts Ungiven 4 Force of Will 4 Mana Drain 2 Sensei's Divining Top 1 Ancestral Recall 1 Tinker |
1 Vampiric Tutor 1 Mana Crypt 1 Brainstorm 1 Demonic Tutor 1 Rebuild 1 Hurkyl's Recall 1 Merchant Scroll 1 Misdirection 1 Tezzeret the Seeker 1 Fact or Fiction 1 Sol Ring 1 Mox Emerald 1 Mox Jet 1 1 Mox Ruby 1 Mox Sapphire 1 Time Vault 1 Time Walk 1 Black Lotus 4 Mystic Remora 1 Echoing Truth |
|
Sideboarding:
Sideboards are messy, to be honest. They vary so wildly that you will never be able to construct a decent 15 card board without a bunch of one-ofs that do you no good. You can find good sideboarding information, but I urge you to combine statistics with maybe one or two well performing decks to figure out a good sideboard. For example if we were to make a sideboard with purely Arithmetic Mean for this deck, we would get:
| Sideboard | ||
|---|---|---|
| Main Deck | Sideboard | |
| 1 Duress 1 Hurkyl’s Recall 1 Ingot Chewer 1 Leyline of the Void 1 Pithing Needle 1 Ravenous Trap 1 Sower of Temptation 1 Tormod’s Crypt 1 Yixlid Jailer 6 Variable Slots |
||
What actually makes this more difficult is that there are four cards in this board which could be classified as “graveyard hate” so honestly, I would first combine all the “graveyard hate” cards into one lump sum and calculate how much hate people are playing, as it’s unlikely that playing one of each card is a good idea.
For anyone wondering, I more or less compounded those numbers and looked at the sideboards of a few good decks and made the following sideboard.
| Suggested Sideboard | ||
|---|---|---|
| Main Deck | Sideboard | |
| 1 Hurkyl's Recall 2 Extirpate 3 Pithing Needle 1 Yixlid Jailer 1 Ravenous Trap 1 Tormod's Crypt 2 Sower of Temptation 4 Leyline of the Void |
||
The Final Deck and Closing Thoughts:
neosystems on 2010-04-15 01:30 CET test
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mchosa on 2010-04-15 03:45 CET cool story bro
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Drayen on 2010-04-15 07:06 CET Nice.
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SteveMan on 2010-04-15 07:09 CET Math iz hard
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neosystems on 2010-04-15 08:10 CET Here's the conclusion, because apparently, adding it in makes all the page tables to go hell. The final deck is just the final maindeck listed + the suggested sideboard.
For this deck, we used sound statistical methods at every step of the way and made our own additions where statistics failed us (i.e. the step when we added Sphinx of the Steel Wind, which still had its basis in mathematics) to construct this deck. I can confidently say that this deck is one of the best versions of the deck to play at a Vintage tournament with an unknown field. It is not metagamed except against the “average” field one could expect. I hope this method serves you well. Let me know in the comments or on IRC if you have anything to add, any good statistical methods I’ve missed out on, or if you’d like to see an article like this every so often where I will create a deck in this way for T2, Extended, etc.
Thanks for reading!
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coboney on 2010-04-15 13:54 CET Very good article and a good read Neosystems.
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Nickname7 on 2010-04-15 18:36 CET extremly useful
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GoneBananas on 2010-04-16 18:59 CET i keep trying to google translate this into english but it won't work!
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warpg8 on 2010-04-19 09:19 CET are you secretly walter wagner? reference:
http://www.thedailyshow.com/watch/thu-april-30-2009/large-hadron-collider
summary: "you don't really know how probability works, do you?"
ignoring the two biggest factors in deckbuilding, namely metagaming and synergy, creates a pile of cards based on, in this case, cleverly disguised bad math.
in short: terrible article, people are now worse at this game for reading it.
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neosystems on 2010-04-19 20:15 CET 1) I've addressed metagaming in the article already. This method is useful for creating a good version of an archetype versus an average field (the average field being the field faced by the decks you chose to sample). If you choose well performing decks indiscriminately as I did, you will truly have a good version for an average field. If you have a good idea of what you will face, as I said, it is up to you to make the changes yourself, or sample decks which did well in the field you expect to face. In theory you should stick with Classical Statistical thought, but you should be Bayesian in practice and know when statistics will fail you.
2) Synergy: As I said the in the previous sentence, know how far your statistics will take you. That being said, synergy, given a sufficiently large sample size (I predict ~20 based on having done this so many times), will almost always take care of itself. In fact, arithmetic mean is the biggest culprit of betraying synergy if you look at Frank Karsten's Jund article (linked at the top of my article).
I am sorry you are unable to see any value in this. Clearly the fact that you think your quotation of "you don't really know how probability works, do you?" has any relevance shows you lack a basic understanding of the difference between prediction based on random chance, and data analysis (though I admit they are not mutually exclusive).
Please let me know if you need explanation of anything else, and I will try to help you out.
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warpg8 on 2010-04-19 21:00 CET Mean, median, and mode are measures of central tendency, so this statement:
"This method is useful for creating a good version of an archetype versus an average field (the average field being the field faced by the decks you chose to sample)."
is erroneous. You will create an average (not good) PILE against and average field. ie, expect to 2-2 drop. And the only reason "synergy" looks like it takes care of itself is because so many cards are common to so many decks in vintage. This method completely falls apart in every other format.
You're violating all sorts of basic statistical requirements when you bias your sample, e.g. "...it is up to you to make the changes yourself, or sample decks which did well in the field you expect to face." Is the population normally distributed? What is known about the population variance? Are the samples all taken from a homogeneous card pool? None of these MAJOR assumptions for your methods are discussed. Additionally, assuming you could predict with any accuracy the field you are about to play against, can you predict within an acceptable margin of error the NUMBER of people in the field alongside the %makeup of the heaviest played decks? The size of the sample makes an incredible impact on the statistics. And assuming both of those things could be predicted with some accuracy an acceptable amount of time ahead of the tournament start (at least one, if not both cannot, so an invalid assumption), the following statement shows your incredibly rudimentary understanding of statistics. "(I predict ~20 based on having done this so many times)". Interesting. YOU predict ~20. Unfortunately, Stephen Colbert's "gut" isn't a statistical tool, so neither is yours. However, there is a wonderful statistical tool that can tell you, based on certain information (information, by the way, YOU do not have), called a binomial nomograph, that will tell you exactly how many samples you have to take in order to achieve desired results within your tolerances for statistical accuracy.
Binomial nomograph:
http://tinyurl.com/y37bctw (google images)
So basically, use the cards that everyone else uses heavily, then make judgment calls based on your knowledge of the metagame and synergy between cards in the given format. Or, you could just pick a deck that performed well at a recent tournament from deckcheck, which will almost certainly produce better results than this rubbish.
By the way, please do your homework before arguing with an engineer/statistics grad student, who is going to analyze this and then completely rip apart, in minutia, every single flaw in your method.
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neosystems on 2010-04-19 21:58 CET "Interesting. YOU predict ~20."
It was implicit that my prediction of optimal sample size had no basis. Obviously the point was that that particular statement had no mathematical back-up, just an off-handed statement I made. I didn't care to calculate it, because I didn't make mention of optimal sample size in my article.
"This method completely falls apart in every other format."
Actually it doesn't. As long as you don't choose conflicting sub-archetypes (for example, decks are classified as "Zoo" on sites such as deckcheck in fact cover a variety of sub-archetypes), you can get good data.
"Is the population normally distributed? What is known about the population variance? Are the samples all taken from a homogeneous card pool? None of these MAJOR assumptions for your methods are discussed."
Gaussian distribution is quite irrelevant since, with the exception of basic lands, you're (on a card by card basis) worrying about a closed interval of [0, 4]. It most represents Triangular Distribution or an extension of Beta Distribution (use appropriate formulas for variance calculation). It's a homogeneous card pool in the sense that each player (in theory) has the card pool of every card ever printed for Vintage, with the exception of decks sampled before WWK's release. I should have mentioned that, because in narrower formats such as T2 it makes a -huge- difference, but less so as you approach more eternal formats. These things are time sensitive, ans I will gladly concede that.
"Additionally, assuming you could predict with any accuracy the field you are about to play against, can you predict within an acceptable margin of error the NUMBER of people in the field alongside the %makeup of the heaviest played decks?" "You will create an average (not good) PILE against and average field. ie, expect to 2-2 drop."
I am not worried about that. That is for the player to decide. Like I said, I care about making a good "shell" of a deck from which one can make appropriate modifications. Should a player choose to play the deck, the deck should perform well against the average of the field of all sampled decks. The point I was trying to get across is that if a person knows what they were going to face (which isn't a statistical exercise at all) they could instead sample decks that faced a similar field.
Let me know if you have anything to add. I'll do my best to explain.
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warpg8 on 2010-04-20 10:40 CET "Gaussian distribution is quite irrelevant since, with the exception of basic lands, you're (on a card by card basis) worrying about a closed interval of [0, 4]."
Gaussian distribution of the individual cards, yes, but what about the distribution of archtypes? Certainly the deck choice of the individual is a factor of what information they have available about the metagame. As for the homogeneous card pool, that is a necessary assumption that must be met for statistical accuracy. The introduction of 1 or 2 new cards into the vintage card pool can completely warp the metagame. Using your analysis technique, older cards are going to appear much more prevalent due to them existing in the card pool longer and therefore being played more. Basically, the restrictions you put on your sampling are going to negate the entire purpose of the statistical analysis, assuming you want to do research on the versions of major archtypes which take into account the entire legal card pool.
"The point I was trying to get across is that if a person knows what they were going to face (which isn't a statistical exercise at all) they could instead sample decks that faced a similar field."
Right, so basically if a person is clairvoyant or has access to virtually limitless information about the decks a statistically relevant portion of the population is going to play, then they can apply this incredibly convoluted approach to tune a deck after they've already decided on an archtype. And hopefully they know how to pilot said archtype (ie, they've already been testing with it or against it) or else play errors will abound and all the time spent doing the analysis will have been wasted anyway.
There are literally thousands of players doing something that is far more relevant than this approach ever could be, and that's actually building decks and playing games. Simulation on a massive scale with innumerable variables and interactions (no small part of which is human error and decisions made without knowledge of the future) in each and every game. Pick your archtype, tune it to what you think your field might be, and then TEST. Why waste your time doing this kind of analysis, which at its root, is analysis of the judgment calls of other people? Because that's exactly what the decklists you sample from are. Archtypes with judgment calls.
At this point, I'm not even going to debase your math anymore. You've done that enough yourself, and anyone with the time and motivation can do the research and see that it's faulty. However, for the amount of time it takes to collect accurate data and then perform this analysis, there is very little return. "The Minimum Wage Job Approach to Deckbuilding, by neosystems." Because of the complexity of this game, discrete and optimal decisions cannot possibly be made by this simple of statistical analysis. For systems as complex as even a single game of magic (let alone entire tournaments), simulation software packages are the preferred method (Arena is the package I am familiar with, but there are numerous others). Equally relevant decisions to your analysis can easily be made after playing 4 or 5 matches with a friend on his card table in his basement while munching on some nachos and Dr. Pepper, which brings me to my final point:
The quality of the player playing the correct archtype (even a sub-optimal list) has a much larger affect on the game than whether or not to cut your 3rd bituminous blast for the 3rd broodmate (and similar tuning) ever could. Doing this analysis is not making you a better player. It's not teaching you what the most probable correct plays are in the critical turns before your control deck stabilizes. It's not showing you what conditions you should meet before you decide to combo off. It's not showing you that if you burn your opponent at the end of his/her turn that you have to draw Lightning Helix and only Lightning Helix to win, and that making any other move guarantees you lose the match and therefore $20,000.
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darkwizard42 on 2010-04-20 15:52 CET hey noob/skathe
its an article, you are obviously the bigger idiot by wasting your time arguing about a magic-league article...
for an 21+ year old engineering/statistics grad student, you are clearly not doing too well in the world if you have time to waste analyzing this article...
the article was written well, describes an interesting process, and simply takes a different approach at creating a deck shell, its just as much a good deck analysis as those article you probably pay for on starcitygames, good thing we have writers like neosystems who don't mind sharing some interesting things from time to time
lastly, you will probably never earn $20,000 playing magic, or working after you earn your graduate degree
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Tcleberg on 2010-04-20 17:38 CET Good prediction, darkwizard. Hey, Skathe, you make more than 20k, just barely, right?
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warpg8 on 2010-04-20 20:54 CET @darkwizard: you're right, taking 10 minutes to put together a coherent argument about something i am a) knowledgeable and b) enjoy doing in my free time is obviously directly indicative of my yearly salary. and i've wasted far less time reading and critiquing this article/technique than the author did writing it or actually performing this process.
Nice attempt at trolling, though.
simplyhired.com search of my occupation:
http://www.simplyhired.com/a/salary/search/q-industrial+engineer
@Tcleberg: yes, just barely. LOL
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initD on 2010-04-22 21:15 CET "oohh, this is just too goo" - syndrome
