Tiers

Because Minecraft's physics is tick-based, the player's movement is not updated continuously.

Therefore, some jumps are identical in difficulty, despite having different heights. For example, +0.5 and +0.75 jumps of the same length have an equal difficulty, beause the player lands the jump at Y=0.7532 either way.

The range of heights matching to the same difficulty corresponds to a Tier.

By convention:


 * Tier 0 corresponds to the range containing the default height (+0.0)
 * Positive Tiers correspond to positive heights
 * Negative Tiers corresponds to negative heights

On flat ground (Tier 0), a jump lasts 12 ticks.

To convert duration to tiers, there is a simple formula:   $$Tier = 12 - Duration$$

https://youtu.be/1tWXifGkNVw

Jump Heights per Duration
The following table lists the player's jump height at every tick until -256b.

The reason the height peak is higher in 1.9+ is because the momentum threshold has been lowered to 0.003, and no longer affects jumping.

Some jumps are easier in 1.9+ because their tier has been lowered: those are indicated in "Tier Updates".