Player rating for tournaments across all installments of Heroes.

...but I couldn't have imagined that someone would interpret the entry differently...

Well, I guess I'm the only one who thought that way... But it's not rocket science; it's your invention, and who knows the meaning better than the author? Our task is to read the words and understand their essence, not to guess what was meant... Apparently, that's really the case... :) Let's continue.

1. Tournament difficulty coefficient.

K=(∑(Ri+a))/1000 - where a is a certain constant that determines the contribution to the tournament category of a participant who does not have a rating.

I think we'll have to adjust this as well. Why is the constant a under the summation sign? The number of players without a rating is not equal to the number of players in the tournament... And in your case, it turns out that this coefficient will be taken into account exactly N times in the final sum... Something is not right... Maybe it was meant to be ∑(Ri)+a*n(a), where n(a) is the number of players without a rating?

2. What does the divisor 1000 represent? Why exactly that value? And what range will this coefficient be in, in your opinion? For now, it seems to me that it depends exclusively on the number of participants, and not on their average rating. Why not divide the sum by N? If you compare a tournament with 5 players (all of whom are aces) and a tournament with 50 players (all of whom are beginners), the difficulty of the second will be almost an order of magnitude higher! That doesn't make sense...