IronAxe
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I will do the following:
I will calculate the rating according to your system and according to mine. Just for comparison.
And I will use the ^ symbol to denote exponentiation; I think it fits there. I will post everything soon...
Added 3 hours 0 minutes ago
So, here are the results:
The basis is:
Number of players = 10, so there are 10 places.
A round-robin tournament with 10 people was taken, meaning everyone played against everyone else.
Also, the initial rating for all 10 is 100.
Here is the calculation:
According to the system proposed by IronAxe:
Player 1 - 3521.67
Player 2 - 2708.07
Player 3 - 2046.14
Player 4 - 1516.91
Player 5 - 1101.43
Player 6 - 780.73
Player 7 - 535.86
Player 8 - 374.87
Player 9 - 197.79
Player 10 - 66.67
According to my system
Player 1 - 200.00
Player 2 - 185.00
Player 3 - 177.33
Player 4 - 171.50
Player 5 - 166.40
Player 6 - 161.67
Player 7 - 157.14
Player 8 - 152.75
Player 9 - 148.44
Player 10 - 144.20
(Comment on my system: 1st place was taken by the player who played 10 games, 10 wins, 0 losses; 2nd place - 10 games, 9 wins, 1 loss, and so on. If a player who took last place did not win a single game, then he is not awarded a rating, but if he won at least one, then the count begins:) )
(Comment on IronAxe's system: Player 10 received a rating lower than the starting one by 43.33 units. Why?)
P.S. I attached my system just to see:)