REVISION (3/10/17, 8:51 pm EST): The numbers were updated after this was written, so all the numbers listed are wrong. Chakki’s feat becomes even more impressive.
I have been getting immersed into statistical analysis more and more now, and I couldn’t help but notice the anomaly in the Hearthstone NA Top 100 Arena Leaderboard for February 2017. Hearthstone professional memer, Chakki, grabbed the top spot in NA with a 8.65 average. The notable thing about this average is that it is a whole 0.55 games higher than the #2 ranking. Let’s look at a few stat things and check out how amazing this is.
This is Stata output of Average Wins of the top 100 players. The main takeaway here is that Chakki got 8.65, which is well above the 99 percentile in this list of the top 100 players. If you dabble with standard deviation, he was over 4 standard deviations above the mean for the top 100.
Check out this box chart. This box and whisker shows the quartiles and inter-quartile ranges. Everything in the shaded box represents the 25 – 75 percentile, and everything past the upper hash is considered an outlier. Chakki is way up there, and the other outliers were scores 2-4. Remember this population is just the top 100 again.
And finally a scatterplot showing how many runs were done versus average wins. It’s no secret that the highest achieving scores stopped right around the minimum 30 wins, while some of the grinders shooting for the top 100 spot had to put in 90 or 100 runs in the month. This graph is likely what will lead to this being the last cumulative arena leaderboard, with March starting the first “best of 30 consecutive” counts.
Of note, Chakki had a 0-0 run counted against him, so he would have a more ridiculous average of close to 9. This was an amazing performance, and provided a statistical outlier that showed how well he did, even in the subpopulation of the top 100 players.