Wednesday, February 17, 2010

Is it random?

This is a spreadsheet that totals up all of my Heroic runs on all of my characters.  I can't believe I've run 315 heroics.  You will see that the probability that my dungeons are distributed evenly is less than 0.01%.  That's not good.  Why the hell is Drak'tharon Keep so high?  I knew I was running that place too much.

Now, there are tons of things at play here, and the dungeons that I'm getting are also a result of player behavior. Perhaps players often drop out of Drak'tharon Keep?  It's important to remember that the Dungeon Finder is subject to player behavior and isn't just taking 5 people and tossing them into a dungeon.

If you are savvy enough with spreadsheets, here's how to make your own.
  1. Make a column for each of your characters, and a row for each Heroic.  I only used the old dungeons in the randomness calculations since the other ones are new and thusly I should have fewer runs of.
  2. Calculate the total number of times that you have run each Heroic.
  3. Calculate the total number of (old) Heroics that you have run and divide that by 12.  That is the number of times you would have run each dungeon in a perfectly random world.  That number will go in every cell in the expected column.
  4. Difference is the absolute value of expected minus total ( eg:  =ABS(F4-G4) )
  5. Chi-partial equals the square of difference divided by expected (=Difference^2/Expected)
  6. Chi square is the sum of all the Chi-partials   =SUM(H2:H13) on mine
  7. Degrees of Freedom is 11    (12-1, it's a statistics thing)
  8. Go to and enter Chi-square under X^2 and 11 for 2.
  9. Calculate and multiply by 100 to get your percentage.  
My actual percent chance that this was completely random was 0, but I knew that was a rounding error so I changed it to what I put there.