[HMM III OFF TOURNAMENT] "Race for the Leader"

Here, I'll suggest a formula for calculation:

R = (R_1 + R_2 + ... + R_i) / i * K_i,

where i is the number of games the player participated in;
K_i = {0.7, 0.8, 0.9, 1.0} or {0.55, 0.70, 0.85, 1.00} - a bonus/reduction coefficient (the more games, the fewer points are reduced)

Example.

some1 (1 game) = 1000 + 0000 + 0000 + 0000 = 1000
some2 (2 games) = 0500 + 1000 + 0000 + 0000 = 1500
some3 (3 games) = 0800 + 0900 + 0400 + 0000 = 2100
some4 (4 games) = 0700 + 0800 + 1000 + 1000 = 3500

Let's calculate the average:
s1=1000/1=1000
s2=1500/2=0750
s3=2100/3=0700
s4=3500/4=0875

And now - BONUS (or reduction, if you prefer)
R1=1000*0.7=700 (550)
R2=0750*0.8=600 (525)
R3=0700*0.9=630 (595)
R4=0875*1.0=875 (875)

The advantage of the system is that each stage of the game is taken into account; the main thing is to choose the coefficients correctly.