Glass City by the Numbers
I’m sure everyone’s going to do some re-caps of Glass City, but I want go a different route. I wrote the premise portions - each paragraph preceding the data - before Glass City, then added in comments afterwards today.
Swiss is supposed to guarantee even match-ups. That’s its premise. I’m going to try to see if there’s an answer to that question. First thing, we all have to agree on what constitutes an even game. This is one of those problems a human is much better at solving than a computer (http://xkcd.com/1425/), but I can probably take a stab at a metric which is close. I’ve thought about this a little, and I’m going to say that plain old QPD (in this case, the absolute value of it) is as good of an indicator as anything available to say if a game’s an even match-up given what I have to work with (I’ve got a complete breakdown of the scores by team, RT/OT/2OT, and quaffle/snitch). I’m going to say that a low QPD means a good game. The expected pattern if Swiss gets us good play is that QPD will trend downward for the second, third, and fourth rounds. Here’s the data:
Round 1: 68.6 average QPD
Round 2: 52.9 average QPD
Round 3: 55.7 average QPD
Round 4: 60.0 average QPD
Yikes! It would seem that Swiss gives us WORSE play, if anything. The first round saw UM blow out UD by a QPD of 170, other than that the average QPD would have been 51.7 - even if their QPD had been a modest 80, that’s still 55.7 average QPD. Either way, the QPD has trended up the farther along we go. Note that the QPD has increased by a total of less than one goal, though, meaning the games didn’t really get that much farther apart. I’m not sure if this means that Swiss isn’t a bright idea, but there’s certainly no evidence that Swiss guarantees even play. The last round was spread out - a couple big blowouts and at least a few close games.
Here are the box-and-whisker plots of each round, if you’re curious. I’ll leave the numbers here and let the analysts do their work. (Get a hold of me if you want some numbers ran - if you know SQL, though, I can make your life a LOT easier for number crunching.)
The next thing I’m going to try is to see if Swiss play sorted the teams into the bracket the correct way. For this, I’ve punched the data into Excel to get the pretty little graphs you’ll see below. The X-axis is the QPD of the game relative to the higher seed (if the higher seed scored fewer quaffle points, this’ll be negative), and the Y-axis is the numerical difference between the seed numbers of each team. There are two graphs - one for the first round, and one for all rounds. If the teams are seeded where they should be, then the QPD should be some function of the seed difference where the leading co-efficient is positive - that is to say as the seed differences increase, so does the QPD.
I guess? I added a linear-order trend line (a straight line that best fits the data). The R² value is a comically-low .34 (.80 is considered decent, and it goes from 0 to 1), and the other trend lines (logarithmic, exponential, power) were worse. There’s the -150 QPD for the #3 Marquette vs. #6 Blue Mountain game, indicating that one or both should’ve been seeded elsewhere.
In conclusion, Swiss, from a pitifully small sample size of fourteen teams, nine of which were official, doesn’t seem to hold much promise for quidditch. Maybe I’ll re-evaluate the data after World Cup, where I’ll have a sample size of approximately twenty-five per cent of the official teams. If anyone’s got good data for a pool-play style tournament with similar team in a format where I don’t have to hunt and dig through 500 Facebook comments to get at it, send it my way and I’ll compare it to these data.
Next up, after I talk to some people to get some feedback, is a recap of Glass City from the point of view of a Tournament Director looking to plan a tournament - what went well, what went badly, and what went wrong and how to fix it.
Again, if you want me to run the numbers with a different variable other than QPD, let me know.
