One of the things I enjoy doing during each constructed Pro Tour Qualifier season is reading through the posted decklists, looking for interesting novel choices or just overall trends in successful builds. There are a number of resources for decklists from the current Berlin 2008 Pro Tour Qualifier season:
2008 PTQ Berlin decklists at Wizards
Star City Games deck database
Deckcheck.net
These are partially but not entirely overlapping resources, so it's good to check in with all of them to get a comprehensive view.
One thing I felt I'd been noticing during the current Lorwyn-Shadowmoor block constructed PTQ season was a tendency for Faeries decks to appear more often in the top eights of larger tournaments. But was that just my personal impression, or is there something to it?
Click through to the extended article for the answer.
So what's our fundamental question here?
What I'd noticed was my impression that there were, typically, more Faeries decks in the top eights of events with more people. Note that right away this means I'm sticking with the top eights reported on the Wizards site, as they actually list attendance at each PTQ.
Well, we can start by simply, for our viewing benefit, charting a scatter plot of "Number of Faeries decks in top eight" versus "Number of people attending PTQ." That ends up looking like this:
Well, that pattern does seem to be going up and to the right, which is what we'd expect to see if "Faeries in top eight" correlated with "size of tournament."
But is size really where we want to be looking for our correlation? After all, you don't play everyone at the tournament. Rather, you play a defined number of rounds, which is, in turn, based on the size of the tournament. In effect, the DCI's rules of picking the number of Swiss rounds for a given tournament based on attendance lets us "bin" tournaments into a number of discrete groups. In fact, we see when we do this that we reduce our data sets to four groups, two quite large (seven- and eight-round tournaments) and two rather small (six- and nine-round tournaments). When we chart "Faeries in top eight" versus "number of rounds" we get this:
Note that as we have multiple top eights with the same number of Faeries decks, some of those points represent multiple PTQs.
All of this is very interesting, but still very impressionistic. It looks like the trend is "up and to the right," but is there actually a significant correlation going on here?
To actually test this, I decided to throw out our two small datasets (the six- and nine-round PTQs), and evaluate the remaining two groups via a Student's t test. The means of the two groups are clearly different:
The average number of Faeries decks in the top eight of a seven-round PTQ was 2.46.
The average number of Faeries decks in the top eight of an eight-round PTQ was 3.8.
Our hypothesis, then, is that there is some form of correlation between playing that one additional round and having more Faeries in the top eight. The alternative here is that we're just looking at an outcome quirk that is unrelated to tournament size. The test distinguishes between that.
I let Excel do the heavy lifting here, using it to calculate the p value resulting from a two-tailed t-test run on the two sets of results. The outcome?
p = 0.009
Yeah, stunningly visceral, right?
What this boils down to is that, statistically speaking, yes, the difference between seven- and eight-round tournament outcomes is significant. Neat. Now what does that mean? Does one extra round give the Faeries players a little more time to get value out of their advantage over the field, resulting in more Faeries decks in the top eight? Do larger tournaments occur in areas with a concomitantly larger pool of skilled players, who in turn pick the Faeries deck because it lets them win on skill a greater percentage of the time?
Hard to say. The only thing we can reliably say without some additional way to test the results to date is this:
If you end up in the top eight of an eight-round PTQ, you are more likely to be surrounded by a larger number of Faeries decks than if you had instead ended up in the top eight of a seven-round PTQ.
It's fuzzy, but it's there. Now, back to speculating on the why of it all.