What rating value can be considered the "middle" of the rank?

From this picture,
ScreenShot_14_04_2023_10_29_23
your rating is 1607 and your rank is 5k but quite close to 4k.

According to 2021 Rating and rank adjustments the conversion formula from rating to rank is ln(rating / 525) * 23.15.
If ln(rating / 525) * 23.15 is between 0 and 1 you are 30k
If it is between 1 and 2 you are 29k

If it is between 25 and 26 you are 5k

If it is between 29 and 30 you are 1k
If it is between 30 and 31 you are 1d

In your case ln(rating / 525) * 23.15 = 25.9. This is between 25 and 26 so you are 5k. Since this is less than 0.1 rank below the 4k threshold, this explains why “4.1k” is displayed.

In my case
ScreenShot_14_04_2023_10_45_25
ln(rating / 525) * 23.15 = 30.95
This is between 30 and 31 so I am 1d, but less than 0.1 rank below the 2d threshold which explains why 1.9d is displayed.

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