Player rating for tournaments across all installments of Heroes.

Let's start in order... The constant **a**, which you introduced, represents the average rating of a beginner and is equal to 20, and in principle, it can take values in the range [0; 100]. Did I correctly understand its physical meaning? Now, let's try to justify why you shifted this value towards the zero end of the scale? After all, it is possible that it should be closer to 50. I suggest simply referring to the tournament statistics...