(Updated 29/07/22)
Hello,
This may be useless information for the majority of players, but I thought it was interesting, and I've been in the position in the past where I wanted to improve my rating in one particular category, but wanted to find a certain type of time control (no increment, shortest initial time, longest delay, etc.) which fit into that rating category. To solve this dilemma, I did some extensive backward-engineering, analysing the full range of available time controls, and found the formulae used to determine Hyperbullet, Bullet, Blitz, or Rapid.
x: Initial Clock Time [sec.] - 60 for 1 min., 120 for 2 min., etc.
y: Added Time [sec.] - Increment or Delay, 0 for none.
Increment Games:x÷60+y>7.5 : Rapid
x÷60+y≤7.5 : Blitz
x÷60+y≤3 : Bullet
x÷60+y<0.5 : Hyperbullet
Delay Games:
x÷40+y>11.5 : Rapid
x÷40+y≤11.5 : Blitz
x÷40+y≤4.5 : Bullet
x÷40+y≤1.375 : Hyperbullet
Example: 1|3
Initial Clock: 1 minute ( x=60 ). Added Time: 3 seconds ( y=3 ). x÷60+y=4, which is less than 7.5 (but not less than 3) , so 1|3 is a Blitz control.
Example: ½|4D
Initial Clock: 30 seconds ( x=30 ). Added Time: 4 seconds ( y=4 ). x÷40+y=4.75, which is less than 11.5 (but not less than 4.5), so ½|4D is a Blitz control.