There were another two Kotei this weekend, but the non-reports are starting to build up (by the time things were wrapped up last year, I think there was only one Kotei that we aren’t able to get full data for, so hopefully we’ll get there again this year).
If you’re tracking the data closely, you’ll that the total number of players in this week’s data actually went down compared to last week’s. This is because, in last week’s data, I somehow managed to pull the Atlantic City data a second time, instead of the Szczyrk data. The Atlantic City Kotei was so big that one copy of it is more players than adding back in the Szczyrk data and the Louisiana data from this weekend (as of the time I’m writing this, we don’t have the full data for the Athens, Greece Kotei).
You may note that there is now a chi-square value in the table, replacing the “relative chance of making cut” column, but serving a similar function (note that all calculations in this column exclude unaligned players). The number is the standardised residual, or the square root of the chi-square value for that clan’s number of players put into the cut (taking into account player population). A higher absolute value in this column indicates a greater deviation from an average rate of making the cut – positive numbers means the Clan had a higher rate, negative numbers mean the Clan had a lower rate (note that the mean chance for a player to make the cut is not the same as the number at the bottom of the “% Made Cut” column, as that number is the average by Clan, not by player). The range from -1 to 1 is within 1 standard deviation of the mean. Anything above 1 or below -1 is an indication that the deviation is more than chance. Anything at or above 1.96, or at or below -1.96, indicates a 95% confidence that the deviation indicates that the faction is question is not balanced. Note that this test of statistical significance will tend to show fewer “unbalanced” clans than many players would identify. Numbers with a 95% (or better) confidence as “unbalanced” are marked in bold – with this data set, it only applies to Crab (on the high end) and Crane (on the low end).
There is an additional number in the final row of the column. This is not any sort of average or sum of the numbers above it. It is, instead, the standardised residual for the environment as a whole. Because the environment as a whole, across all nine Clans, has many more degrees of freedom, a higher number is required to achieve the same degree of confidence. For this data, a number of ~3.94 or higher indicates a 95% confidence that the environment is not balanced. When the number in this data block meets this threshold, it wll be marked it bold (it does not meet the threshold this week).
I have said it before, but let me say again that what, exactly, one makes of this data is up for discussion. In particular, I think it takes some thought what exactly it means to say that there is a 90 or 95% confidence that there actually is an unbalanced environment. This particular threshold may not mean a ton, since it’s not like the null hypothesis of a perfectly balanced environment is one that (IMHO) one could reasonably expect to be possible, much less true. So, for this number in particular, there may be more to be gleaned from comparing the number across environments than in looking at the particular value for a particular environment. And for particular Clan values, there is still a potentially useful comparison point – even if neither one crosses the threshold, you’re still probably on safe ground within this context saying that a Clan with a value of 1.9 is stronger than a Clan with a value of -1.9.
Of course, if any of the math-savvy in the audience spot any errors in my math below or explanation above, feel free to correct and/or clarify.
|Emperor Edition Environment|
|Players||% of Field||Made Cut||Won||% Made Cut||Chi-Square Standard Residual|
Make the Cut Rate Rankings
1) Crab – 30%
2) Lion – 26%
3) Phoenix – 26%
4) Dragon – 23%
5) Mantis – 21%
AVERAGE – 21%
6) Scorpion – 19%
7) Unicorn 17%
8 ) Spider – 15%
9) Crane – 11%