The original Size of Dota’s Skill Brackets has possibly been my most linked to article, so I felt it was time to update it. Unfortunately, the method that I used back then is no longer available, so I have to resort to some more roundabout methodologies.
A few days ago I published Trends in Dota 2 Hero Usage by Skill Bracket using a sample of 10k/12k/12k games. By making that I now had a list of what I thought were the usage rates of every hero. Certainly there’s still some sampling error, but for the most part the error is randomly distributed (Troll Warlord is an exception, but there’s not a lot I can do right now about a hero released in the middle of the sample collection). I also had DotaBuff’s number of games played for the month. By taking that table and calculating the total number of games I have what should be a really reliable usage rate for each hero, and 3 fairly reliable usage rates for each hero divided by the skill bracket.
Individually neither source tells us anything about the number of games played in a particular bracket, but I know that I expect the bracket distribution to be something like 80/15/5. If I create a weighted average of my sample usage rates, I can measure the average error compared to DotaBuff’s total usage rates. From there I can adjust the weighting, and the weighting with the lowest average error should be pretty close to the actual bracket distribution.
So I ran the test. If you want an idea of what it looked like, check out the Weighted Estimate page of Hero Usage and Win Rates — Feb Sample. The best fit I could create was 83%/13%/4%, with the close second being 84%/13%/3%. This is particularly interesting to me since it very closely matches my estimate from last October. It also suggests that there’s not a tremendous amount of rating inflation in the system.
The usual caveats apply. Matchmaking occurs on a continuous scale and matchmaking brackets are just a post-game sorting method. This only estimates the number of matches within the brackets, which could differ from the number of players for all sorts of reasons: new invite waves, a certain bracket playing more games per day on average, group queues pulling players out of their bracket level, hero releases creating more activity in a certain bracket, etc.