Player rating for tournaments across all installments of Heroes.

The formula is quite complex.

Calculating with a bonus that takes into account the results of previous games is more difficult. Moreover, I am sure that there will be, or already are, errors there (possibly not due to you), but it is unlikely that anyone will undertake to recheck. In the results tables from Tournaments, player nicknames are sometimes distorted, and it is difficult to understand whether it is the same player or different ones. Consequently, if the nicknames are different, you will calculate for each one, and then, taking into account the rating of previous games, you will calculate further Tournaments. And after 5-10 Tournaments, some guy will show up and say - listen, the player ***DeMoN*** and DeMoN are me, and you are counting me as different people. And here are two options: 1. You send him away and don't recalculate anything (however, the rating is already distorted for EVERYONE who played with this player in the Tournaments, and if there are not one, but two or more of these guys?). 2. You undertake to recalculate all 10 Tournaments, but then it will be easier to hang yourself :)
Therefore, all other systems are advantageously different from the system with a bonus because they do not take into account the results of previous Tournaments to calculate the results of the current Tournament. In the situation described above, I don't need to do anything except add the results of ***DeMoN*** and DeMoN into one slot in my summary table. Problems may arise with aging. However, in this case, as in your first option, I can send this guy away, since he did not keep track of his rating, or I will only have to deal with him, since his past results are not tied to the results of other players who played with him in the Tournaments, and I do not need to recalculate their results. Do you understand what I explained?

Plus, you can't divide by 0 (and the first number turns out to be exactly that).

I don't understand, how does the first number turn out to be exactly that? And what is it equal to when you divide by 0? :) Kyle, explain this moment of your formula to us.

But in general, it's not bad. But the results are too close, the leaders deserve, IMHO, greater advantages.
If you want, you can calculate using it, but I won't be able to do it anymore ;)

The leaders deserve what they get from their result. Namely, always 100. And if, in addition, their result is very outstanding (that is, they are far ahead of everyone else in terms of days and even far ahead of the player in 2nd place in terms of days), then they automatically reduce the rating of the others, depending on their results. This is the bonus. Everyone gets according to their result. And if the results of the players are close, then I personally don't see anything wrong with that.
Therefore, I suggest that you calculate Kanneghem's Tournament as you are calculating it now, so as not to recalculate anything (according to all three systems).
And in the future, adopt Kyle's method and calculate according to it.
Get rid of the system with a bonus, and in the future, you may have less of a headache ;)
I still think that ***DeMoN*** and DeMoN are the same player, so an error has already crept into your rating with a bonus, which may turn into a snowball in the future, when it will be impossible to correctly recalculate the distorted results of all players, or you will have to spend a lot of personal time on it.