A Nerdy Look at Chakki Blowing Up the Arena

A Nerdy Look at Chakki Blowing Up the Arena

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.

Summary

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.

Graph box.png

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.

Linear Fit.png

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.

 

Hearthstone Minion Averages and Radar Charts

My educational background and work experience thus far has allowed me to work with data all the time and has showed me how to evaluate things with numbers. While using numbers typically have a work or research-related application, numbers have been increasingly used to look at hobbies. I decided to look at some basic numbers with stats involving Hearthstone minions.

For this exercise, I just decided to look at averages for minion cost, attack, and health.

Hearthstone minions by class

averages_class

What this tells you is that the average minion in Hearthstone is a 4 mana 3.5 / 4. The average neutral minion also has a similar cost and stat distribution as all overall cards.

It is pretty obvious that Druids have the highest cost minions, and biggest minions, consolidating their status as the ramp class. Rogue cards are the cheapest and have the lowest health. Shamans have a low attack total, tainted by 0-attack totems.

Hearthstone minions by set

averages_set.PNG

The Basic set are clearly the weakest cards around, as they are the cards you get for free. Naxx and GvG were known for ushering aggro into dominance, as evidenced by their relatively low costs. BRM was a set that had a lot of beefy dragon minions.

Hearthstone minions by rarity

averages_rarity.PNG

Finally, a view of rarity, which primarily has implications in the arena. You see a clear linear trend in the upward slope of cost, attack and health, as a card gets rarer.

Radar charts

I was doing some work on Microsoft Excel when I realized that Excel could create radar charts. Intrigued about this, I thought about what possible visual applications radar charts had on conveying information. This all led to me creating some Hearthstone-related radar charts.

For minions, I decided to categorize all class minions into “what they did.” To account for all the different types of effects, I had to put them into broad bins of what they did.

  • Spellpower – Pretty clear, e.g. Kobold Geomancer
  • Taunt – Pretty clear, e.g. Frostwolf Grunt
  • Damage – Something that deals extra damage, e.g. SI: 7 Agent
  • Charge – Pretty clear, e.g. Kor’kron Elite
  • Buff Self – Something that only helps itself, usually continuous, e.g. Lightwarden
  • Buff Other – Helps other minions, e.g. Blood Imp
  • Reinforcement – Summons something to the board, e.g. Dr. Boom
  • Cost Mod – Reduces or increases costs, e.g. Shadowfiend
  • Mana Mod – Affects mana crystals somehow, e.g. Grove Tender
  • Minion Mod – Affects minions in a non-damage way, e.g. Water Elemental
  • Hero Mod – Affects own heroes in a non-damage way, e.g. Fallen Hero
  • Cycle – Draws cards from deck, or gets you new cards in hand, e.g. Tomb Spider
  • Heal – Heals hero or minons, e.g. Earthen Ring Farseer

all_minion.png

The graph of all classes is a mess, but if you look at individual classes, like Paladin, you see their minions focus on buffing each other (Argent Protector), and minion modification (Aldor Peacekeeper).

paladin_other

Also for minions, I looked at basic stat distribution, and classifying them as aggro minions (more attack than health), defensive minions (more health than attack), or even.

all_stat.png

Very aggressive minions, those than have 2 or more attack than health are quite rare. You see Rogue class minions almost always have more attack than health or are even. Shamans and Warlocks have minions that typically have more health than attack.

Priests seemingly have no card that has 2 more attack than health.

priest_stat.png

Finally I made some graphs for the spells of Hearthstone, and what they do.

all_spell.png

Paladin spells are primarily focused on buffs, and have all but one source of hard removal.

paladin_spell.png

Meanwhile, Warlock spells are all about doing damage, but have some areas of decent hard removal and AOE.

warlock_spell.png

All in all, this was just to help me learn to use radar charts to display visual data for Hearthstone. In the future, I may incorporate such charts when analyzing certain decks or even arena runs.