This article is intended to be a guide to help understand the OBC statistics spreadsheets,"GP Cleveland Statistics" and"Combined Summary OBC Statistics" that are available for downloading. These spreadsheets contain information on the prevalence and performance of the different OBC deck archetypes at all of the major events (Worlds Day 3, GP Sapporo, GP London, and GP Cleveland). This article is not intended to provide conclusions that can be made from those statistics, but I have written such an article,"Conclusions from the OBC Statistical Data" and is already posted on CardShark. I encourage you to check that article out after you have read this. This article should enable you to look at the spreadsheets and read the data yourself, use the data for multiple purposes, and even modify some of the parameters if you so desire.

If enough people find this useful, I hope to do this sort of analysis for other constructed events in the future. Please feel free to email me at adam_mba@yahoo.com to let me know what you think and if you have any questions or suggestions.

The best way to understand how to read the spreadsheets is to understand how I prepared the data. For the remainder of this article, I suggest reading it and referring to the spreadsheets provided at the same time. Individual worksheets within a spreadsheet will be denoted by italics.

Setting up the players and categorizing their decks:
To start with, refer to the"GP Cleveland Statistics" spreadsheet. I copied various information from the Sideboard's coverage of Grand Prix Cleveland into Excel. The Player Records and Decks sheet (near the middle in the ordering of worksheets) contains the names of all players who made Day 2 at Grand Prix Cleveland. Then, I looked at the deck lists given for each of the players and categorized them by deck type. I used deck types similar to the ones the Sideboard used, but I customized them to provide what I felt was a more accurate categorization of the metagame. The deck types I used, in rough order of their prevalence at Worlds, were:

1. Mono-B Ctrl:
   Classic creature-light mono-Black control decks.
2. UG QR-Mad:
   Blue-Green decks that utilized the madness mechanic extensively (e.g. Arrogant Wurm, Circular Logic) and also had at least a couple of Quiet Speculations.
3. UG QR-Fate:
   Blue-Green decks that were more threshold-based and/or used Grizzly Fate. These decks also included Quiet Speculation as well as - in most cases, anyway - Catalyst Stone.
4. UG Thresh:
   Blue-Green decks that were threshold-based but relied more on quick threshold-dependent creatures such as Nimble Mongoose and Werebear than they did Roar of the Wurms. These decks did not include Quiet Speculation, but did include Standstill most of the time.
5. UG Mad:
   These were Blue-Green decks that were madness-based, but did not include Quiet Speculation and often included no (or few) Roar of the Wurms.
6. BU Braids:
   Black-Blue decks that were focused on using Braids and creatures and control spells that supported Braids. The Blue was generally just a splash for cards such as Shadowmage Infiltrator and Aether Burst.
7. GW Mad:
   Aggressive Green-White decks that used very efficient creatures along with the madness mechanic to provide a quick beating backed up by Glory.
8. WU QS:
   White-Blue"Quiet Screech" decks, based on a design by Team Punisher for Worlds. These decks include lots of cheap White creatures, along with Battle Screech and Divine Sacrament. The Blue is mostly a splash for Deep Analysis, Quiet Speculation to get the Battle Screeches and Deep Analyses, and Envelops.
9. UB Zombie Upheaval:
   Blue-Black decks that were mostly creatureless and were based abound Zombie Infestation, Upheaval, and lots of control spells.
10. Mono-B Braids:
    Mono-Black decks that relied more on Braids and other creatures for the win. A variant of this decktype is the"Pirates!" deck that debuted at GP London.
11. Ugw Wake:
    Blue-Green-White decks based on surviving the early game until they get out Mirari's Wake and then generate obscene amounts of mana to set up and go fetch one of a few win conditions.
12. Other:
    Everything else not covered by one of the above types.

Calculating each player's performance:
After setting up the Day 2 players and deck types, the next step was to list each of their performances on both Day 1 and Day 2. I used the R8 Standings sheet to capture each player's standing at the end of Day 1. In addition, I used the pairing information from the Sideboard to capture how many byes each player had. I converted the standings and byes to wins, losses, and draws and then included on the Player Records and Decks sheet (and yes, I know I ignored the possibility of three points equaling three draws instead of a win - but this should be rare enough to not matter). In addition, I calculated the winning percentage for each player, treating a draw as 50% of a win.

Next I captured the results for each Day 2 match on the Day 2 Match Results sheet. I included all matches, including the Top 8, with the exception of byes and intentional draws. I then included win-loss-draw information and winning percentages for Day 2 as well as overall (Day 1 and Day 2 combined) on Player Records and Decks. The players are ranked not by their"final standings" as reported on the sideboard, but rather by what percentage of their matches they won overall, followed by what percentage of their matches they won on Day 2.

Summarizing the performance of each deck type:
I summarized the performance of each deck type on the Deck Performance sheet (the first worksheet in the workbook) by combining the performance of all players who played a given deck type. Thus, the"Avg. Win %" gives the percentage of matches that a particular deck type won, taking all players who played that deck type into account. Also, I provided a raw count of each deck type so it is apparent what the makeup of the field was.

The"Avg. Win %" number can also be interpreted as the best available estimate for the percent of the time that a particular deck type can be expected to win. Yellow highlighting denotes percentages greater than 50% but less than 60%; green highlighting denotes percentages greater than or equal to 60%.

The estimate for a given deck type is more accurate when more data is available (i.e. more copies of that deck type were played). In order to provide a measure of confidence in the estimate, I also broke out my MBA stats book and calculated the minimum value of the 60%"confidence interval" for each deck type - basically, the percentage that we can be 60% sure the"true winning percentage" of the deck type is. This number factors in both the winning percentage of the deck type as well as how many matches that number is based on - the more matches played, the more reliable the number and thus the lower the margin of error.

For example, Mono-B Ctrl has a minimum of the 60% confidence interval of 41%, which is quite close to the 43% best estimate. This is because 135 matches worth of data is available for Mono-B Ctrl.

However, B/U Braids has a minimum of the 60% confidence interval of 26%, which is a good deal below the 33% best estimate. This is because only six matches' worth of data were available for BU Braids.

Calculating the percentage of matches each deck type won against each other deck type:
On the Matchups worksheet, I took each deck type and computed its average winning percentage against each of the other deck types. In the first table, each number represents the percentage of matches Deck 1 (the deck type in column A) won when paired up against Deck 2 (the deck type listed above the percentage). In the second table, each number represents the number of matches that were composed of each deck type pair (note that the table is symmetrical about the diagonal, as each pair is listed twice - once in the upper-right and once in the lower-left; thus the total number of matches included is actually 188, half of the 376 value listed).

For example, if you look in Row 3, Column E and Row 19, Column E, you can see that BU Braids played 3 matches against Mono-B Ctrl and won 33% (i.e. one) of them.

I used Matchups - Adjusted worksheet to calculate how a given deck type could be expected to perform in a given metagame. To do this, I first had to have a complete table of deck type matchup winning percentages. Unfortunately, some pairs of deck types were just never matched against each other at Grand Prix Cleveland and so no data was available. In these instances, I decided the best thing to do was to just assume that the matchup was 50-50. Luckily, this was less of an issue for the most prevalent deck types.

The first table uses a metagame exactly equal to the metagame on Day 2 at Grand Prix Cleveland. The number in the Grand Total column represents the percentage of matches a given deck type could be expected to win in a metagame that was exactly like that at Grand Prix Cleveland.

For example, continuing with BU Braids, you can see from the first table of the Matchups worksheet that the deck type won just 26% of its matches. However, this was in large part to it winning 0% of its matches against UG QR-Mad. Moreover, as can be seen in the bottom table, two out of BU Braids's six matches were against UG QR-Mad. In other words, the"metagame" that BU Braids happened to face at GP Cleveland Day 2 was 33% UG QR-Mad - which is a horrible matchup, according to the data!

However, as can be seen on the Deck Performance sheet, UG QR-Mad was just 8% of the field at GP Cleveland. In other words, it can be said that BU Braids had a string of bad matchups. The top table on the Matchups - Adjusted worksheet adjusts for this and looks at what the expected performance of BU Braids would be if it instead faced its"fair share" of 8% UG QR-Mad. In fact, it does this for all the deck types and comes up with an expected winning percentage of 42% for BU Braids - considerably higher that the deck type's actual performance of 33%.

This information is also summarized on the Deck Performance sheet in the"Hypothetical Record Based on Event Metagame" column and the minimum of the 60% confidence interval is also shown.

However, there's no need to limit ourselves to assuming a metagame that is the same as the GP Cleveland metagame. For instance, what if you expected the deck types that did well at GP Cleveland to be a higher percentage of the field at the next PTQ than they were at GP Cleveland? Or what if you expected your local metagame to be substantially different? That's what the second table on the Matchups - Adjusted worksheet is for: Simply plug in a percentage for each deck type that represents how much of the field you expect it to be; make sure the numbers add up to 100%, and then the numbers in the Grand Total column represent the percentage of matches each deck type would be expected to win in the assumed metagame. This information, along with the minimum of its 60% confidence interval, is also summarized on the Deck Performance sheet in the"Hypothetical Record Based on Example Metagame" column.

Combining the results from multiple events:
The data from GP Cleveland is good because it is the most recent available - but to be honest, it would be much better to have more data, especially for the individual matchup winning percentages. Thankfully, more data is in fact available - as Worlds Day 3, GP Sapporo, and GP London were all OBC events. In the"Combined Summary OBC Statistics" spreadsheet, I combined all the information from the 238 decks and 674 matches at Worlds, the 64 decks and 190 matches at GP Sapporo, the 64 decks and 194 matches at GP London, and the 64 decks and 188 matches at GP Cleveland - that's 430 decks and 1246 matches in total!

(Can you tell I like numbers yet?)

The Deck Performance sheet lists each deck type's prevalence and performance at each event, its combined performance taking all events into account, and its expected performance in a sample metagame. (Note that the much-hyped"Ugw Wake" decktype has been rolled into the"Other" category due to its small numbers).

The Matchups sheet lists the percentage of matches each deck type won against each other deck type. The Matchups - Adjusted sheet summarizes the metagame information from all the events and assumes a particular metagame composition. The percentage of matches each deck type could be expected to win in this metagame is then calculated and shown.

Where To Find Answers To Your Questions:
To summarize, the spreadsheets can be used to answer the following questions (among others) about OBC results for either GP Cleveland (more detailed) or Worlds Day 3, GP Sapporo, GP London, and GP Cleveland combined (more summary-level).

What has the metagame looked like? What deck types are being played and in what numbers?
Either spreadsheet, Deck Performance worksheet, first set of columns

How has each deck type performed? What percentage of matches has it won? How sure is it that these winning percentages are relying on enough data?
Either spreadsheet, Deck Performance worksheet, middle set of columns

How can each deck type be expected to perform in a particular specified metagame?
Either spreadsheet, Matchups - Adjusted worksheet for both metagame specification (across the top of the table) and expected winning percentages ("Grand Total" column); expected winning percentages (along with confidence level information) are also on the Deck Performance worksheet, last set of columns, of either spreadsheet

How does each deck type perform against each other deck type? How much data is this based on?
Either spreadsheet, Matchups worksheet

How did individual players do? What deck types did they play?
"GP Cleveland Statistics" spreadsheet, Player Records and Decks worksheet

I hope you find this information useful, and good luck!

Adam Fischer
adam_mba@yahoo.com
Team CardShark