Victor van den Broek
1/2/2003
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Happy New Year! Gelukkig Nieuwjaar!

First of all, I wish you all a happy and fruitful 2003! As for my resolutions this year, I hope to have a better Magic year than I had last year, and I hope to finish this series. Also I hope some of the readers of it will actually have improved their game by the end of it. I'd love to hear if any of you find you suddenly look at the game differently. And last of all I hope that all of you reach the goals you have set for this year, either goals that have anything to do with Magic, or those in your personal life.

Now without further delay, today's article:

Getting Better IV - Deck Construction and Evaluating Test Results

Once you hand in your decklist at a constructed tournament, you have set your tools for that tournament in stone. You're not allowed to change it anymore, and you have set the parameters you have to work with. If you only registered 15 lands for your 60 card deck, that means you have only 25% land in your deck. If you decided to play UG Madness in your Pro Tour Qualifier, and the majority of the people there decided to play Oath, you're in for some trouble. Adding four Waterfront Bouncers main deck changes that matchup though - how are you going to make sure you have your deck the way you want to during the tournament?

Before you know your final decklist, there are a lot of choices to be made. First of all you need to know what kind of deck you want to build. This choice is made based on the field you expect at the tournament you're going to attend. In the beginning of all testing, you should play against your teammates or any opponent for that matter, with the main decks of the format. That way you get a feeling for the format, the speed it has, the power it has and the possibilities that are currently being exploited. Often you just take one of the tier one decks and intend on playing it, in that case you skip all the way to fine tuning the deck. If you decide to design your deck from scratch, you're going to have to have a good idea what your deck is going to do. Through this article I'll take the design of a UG Madness deck as an example. I'll show the design process as if it was from scratch... so some choices that are made later on are rather obvious with the knowledge we have now, it's just to illustrate how the process works. Also the list I'm working with here is not a tuned Type 2 UG Madness deck. It's an illustrative example as to how I started deck construction on this type of deck when the Standard rotation just took place.

The Idea

The idea of the UG Madness deck is to be an aggro/control deck with very efficient creatures. It finds these efficient creatures in the green Torment creatures with madness that require to be discarded so they can be played for this cheap cost. Blue provides control measures as a standard feature of the color, but can't deal with creatures permanently.

The Rough Sketch

The madness creatures in Torment have a converted mana cost of G, and 3GG respectively, and a madness cost of 0 and 2G respectively. Especially the cost of 2G on Arrogant Wurm points in the direction of getting a way to discard the Wurm for free on turn 3, so I can play it then. A 4/4 trample without drawback on turn 3 is pretty efficient. Cards that allow a free discard on turn 3 in blue and green are Wild Mongrel, Aquamoeba and Merfolk Looter. Other spells or creatures that allow discarding are Careful Study, Grafted Skullcap, Jalum Tome and Tolarian Winds. Others seem to be too expensive or require other colors. For control of the board, blue provides Aether Burst, Essence Fracture, Equilibrium and Unsummon. For counterspell measures blue provides Counterspell, Circular Logic and Memory Lapse. The first list includes all the cards I could possibly want in there. All the green creatures go in, along with all the madness outlets, Careful Studies, Aether Bursts, Unsummons, Counterspells and Circular Logic. That provides the following list:

4 Basking Rootwalla
4 Arrogant Wurm
4 Wild Mongrel
4 Aquamoeba
4 Merfolk Looter
4 Careful Study
4 Aether Burst
4 Unsummon
4 Counterspell
4 Circular Logic


That's 40 cards total. As a starting rule, I always put 24 lands in a rough sketch. That means 4 cards will have to go. 12 Madness outlets and 8 bounce spells seemed a bit too much, so I cut 2 of each - in this case 2 Aquamoeba and 2 Unsummon to see the effect. After I get a list like the above, I scribble down a quick way of determining the mana you should put in the deck. I just look at the cards in there and see how many colored mana symbols they have in their converted mana cost. A madness card counts as half regular, and half madness cost. In this case, there would be 12 green and 28 blue, so about 1/3rd should be green and 2/3rd should be blue mana sources. Along with 4 City of Brass, this gives us 13 Island and 7 Forest.

First Testing and the First Iteration

After having done the above, it's time to put together the deck and run it against the main decks of the format. If it loses to everything without having a decent chance, discard it. If it does win sometimes, but doesn't feel right, try and put a finger on what's wrong. In testing the above list, I noticed the deck was pretty good against control decks if it drew its mana right, but weak against creature decks as it didn't have enough staying power. So one weak point is the mana base, and the other weak point found was that I needed more creatures and a way to break through. 24 lands did seem like the right number, though it could go down to 23 for a bit more risky build. As the contents of the deck are continuously going to change, the mana base will too. Another search in the card sets that were available brought up the following efficient creatures: Ravenous Baloth, Phantom Centaur, Ernham Djinn, Roar of the Wurm and Air Elemental. Roar of the Wurm gives most power for invested mana, but Phantom Centaur gives a better deal against control decks. When making room for cards that are better against aggressive decks, I'll have to cut stuff that's good against control, so it's best to try and find cards that are good against both. I added 4 Centaurs to the list, and took out the 4 Counterspells to see how it worked. Another card that caught my attention while going through the binders was Wonder, and I added 4 Wonder instead of the 4 Unsummon. The mana base also changed to 4 City of Brass and 10 Island and 10 Forests.

Finetuning and the Remaining Iterations

After changing the deck for the first time, I played it against the main decks of the format again and saw how it performed. I took note of improvements, and of results that deteriorated. The Wonders turned out to be very good in the deck, Phantom Centaur worked very well too, but I found having two could be too much. Also Aether Burst seemed to too expensive for the deck. When playing, I also thought that a couple of Counterspells should be added back into the deck, and the mana base was too painful with 4 City of Brass. After a few more changes, the first real version of the maindeck looked like this:

2 Aquamoeba
4 Wild Mongrel
4 Merfolk Looter
4 Basking Rootwalla
4 Arrogant Wurm
3 Phantom Centaur
4 Wonder
4 Circular Logic
2 Counterspell
2 Unsummon
4 Careful Study
3 City of Brass
9 Forest
11 Island

Adding a Sideboard

After having a good idea what the main deck should look like, it's time to start testing sideboarded games. The above list had some weaknesses against control but was very strong against creature decks. I found that it did have trouble against Sligh with Sparksmiths though. A quick scribble gave the following sideboard:

2 Quiet Speculation
2 Ray of Revelation
2 Deep Analysis
2 Roar of the Wurm
2 Unsummon
3 Stupifying Touch
2 Counterspell


That improves the matchup against control by quite a bit, and it has an answer to Sparksmiths, albeit a tad shaky. Again, just playing after sideboarding gave me an idea what the rest of the decks in the format were going to do against me, and what answers I could provide to counter theirs. For example, the GW deck sideboarded Silklash Spider, as they expected the UG deck to keep in Wonders. By continuing to make changes to the deck, in the end I was bound to find a list I was happy with.

The Iteration

So apparently the design and testing of a deck is an iterative process. There are three steps in it: designing or changing the deck, playtesting it, and seeing how it affected the deck and its performance. This iterative process is shown in the graph below.

When you change your deck, you need to playtest those changes again. During playtesting you should keep track of the game scores before and after sideboarding and use those as input for the evaluation process. In the evaluation process you have to fill out the expected field table again, with the new information you have. All three of those steps need additional explanation. I'll start with discussing how to evaluate your playtest results. The reason I'm going to discuss the last step first, is because that way you know what input that step will need from playtesting, and what output it gives for deck design. As will be shown later the link between Evaluating Results and Deck Design is the weakest one, so this seemed like a logical place to start for me. Be warned: the rest of the article has some math and theory in it. Some readers have let me know they find the math boring or hard to follow. For this reason I included some excel sheets with today's article to help you with it. If you don't want to read the math skip to the conclusion.

Evaluating Playtesting Results

I chose to discuss how you should evaluate your playtesting results before discussing how you acquire reliable results. This is to illustrate what output you'll want to get from playtesting, and what input you'll get for deck design.

Say that there are three decks in a format, decks A, B and C. You're playtesting a new deck, and your rough sketch got the following results. It won 40% before sideboarding ( = p(A_nosb)) and 70% after sideboarding (=p(A_sb)) against deck A. It won 80% before sideboarding and 60% after sideboarding against deck B. It won 50% before sideboarding against deck C and 20% after sideboarding. You expect the three decks to be 50%, 30% and 20% of the field respectively.

Out of the six different results (WW, WLW, WLL, LWL, LWW, LL) you can have against any opponent in a tournament there are only three results that give you a win. The match win percentage for that matchup is calculated as follows:

P(Match_vs_A) = P(A_nosb)*P(A_sb) + P(A_nosb)*(1-P(A_sb))*P(A_sb) + (1-P(A_nosb))*P(A_sb)*P(A_sb)=0.4*0.7 + 0.4*0.3*0.7 + 0.6*0.7*0.7 = 0.658

Along with your predictions you can fill this out in the following formula to get your expected overall match win percentage:

P(Match_overall) = P(Part_of_field_A)*P(Match_vs_A) + …

If you do that for all the decks you expect to be a good part of the field, you end up with your expected overall match win percentage. In this case, that would be 0.5*0.658 + 0.3*0.744 + 0.2*0.2 = 0.5922.

Suppose that if you change the deck, your game win percentage before sideboarding against deck C goes down 10% and the game win percentage before sideboarding goes up 10% vs deck A. Also the game win percentage after sideboarding goes up 20% against deck C, but down 20% against deck A. How does that affect your overall match win percentage? If you go through the above math again, you'll find out that the overall match win percentage went down to 0.5686. That makes the changes that were done to the deck a bad decision.

Theoretically speaking, you should do the above for every single card you change in the deck. That is quite a lot of work to do, especially if you realize that determining the game win percentage reliably is a lot of work. If you only play 10 games you do get a game win percentage, but it's very unreliable. Statistics aren't my strongest point, but if you play 100 games you can't predict the game win percentage with an accuracy of 1%. So if you fill out the excel sheet I provided with the exact game win percentage you got from testing, keep in mind that you're filling in unreliable results - that also makes the end result unreliable. If you test 20 games and find that you won 16 of the 20, which makes the 80% you fill in a lot more reliable than if you won 8 out of 10 games.

The overall Match Win Percentage shouldn't be trusted blindly though. Suppose you're going to a tournament that has the field described above with decks A, B and C present. C appears to beat decks A and B pretty convincingly. If you want to take the deck that sports the game win percentages described as above, you only win 20% of the matches you'll play against deck C. If your goal for the tournament is to win it, then the deck is not acceptable. After all, you expect decks C to rise to the top of the standings based on the way the metagame works and you'll have to beat those deck C's!

The overall match win percentage predicts how likely you are to win against a random deck from the entire field. If you expect deck C to rise to the top of the standings, and you want to win the tournament as well, you'll have to change the percentage of the field you expect those decks to represent there. For example, if deck A is a bad choice in the metagame, its percentage will drop at the top of the standings, and rise at the bottom part. Deck C will have more decks present there. Instead of 50% deck A, 30% deck B, 20% deck C, the 4-0 field of that tournament you're going to might be 20% deck A, 20% deck B and 60% deck C. This effect is what makes sure you rather have a deck that has a 60% chance of winning against each of those decks, rather than beating decks A and B 100%, and losing to deck C all the time. If you see something like this could happen, it's best to play deck C. After all, it beats the two decks that are most present in the field and still has a 50% mirror matchup against itself!

In Conclusion

Deck Construction is an iterative process. You make a deck, playtest it, evaluate, make some changes, playtest it again, and so on. During the evaluation stage you make the choice of either discarding the deck as a viable choice, or continuing with it. The evaluation process can be aided by math, but its use is limited because it's hard to get reliable input for it. How to make sure you don't do a lot of playtesting and still get unreliable results and what intricacies there are in deck design itself will be up next.

Most of all, be creative!

May 2003 be a good year for you.

- Vic


PS: In the excel sheets, the only parts you have to fill out are greyed. The rest all have calculations in them, so the rest of the sheet will fill itself out. Also I included the examples I gave from today's article and the previous one to show you how they work.

The Metagame Crosstable

Determining Overall Winpercentage