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Here are the rules about jumping:

Your Strength determines how far you can jump.

Long Jump. When you make a long jump, you cover a number of feet up to your Strength score if you move at least 10 feet on foot immediately before the jump. When you make a standing long jump, you can leap only half that distance. Either way, each foot you clear on the jump costs a foot of movement.

High Jump. When you make a high jump, you leap into the air a number of feet equal to 3 + your Strength modifier if you move at least 10 feet on foot immediately before the jump. When you make a standing high jump, you can jump only half that distance. Either way, each foot you clear on the jump costs a foot of movement. In some circumstances, your DM might allow you to make a Strength (Athletics) check to jump higher than you normally can.

Here are the rules about moving a grappled creature:

When you move, you can drag or carry the grappled creature with you, but your speed is halved, unless the creature is two or more sizes smaller than you.

What I don't know is whether your maximum long/high jumping distance is also halved by grappling. For example, would someone with a Strength score of 20 (granting a normal maximum running high jump of 8 feet) be able to jump 8 feet up with a grappled creature, or would he only be able to jump 4 feet up?

This assumes the 20 Strength grappler/jumper has made the running start beforehand and has enough total speed, even if halved due to grappling, to make the maneuver.

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It may be shortened if you run out of movement.

You can either:

  • move 10 feet and then long jump [Strength score] feet
  • long jump [Strength score/2] feet
  • move 10 feet and then high jump [3+Str mod] feet
  • high jump [(3+Str mod)/2] feet

And each jump foot is deducted from your leftover movement. Therefore, if you have a high enough speed, then grappling doesn't really bother you.

For example, with 20 Strength and a speed of 60 feet, grappling a creature makes you have a speed of only 30 feet. You can move 10 feet and long jump 20 feet, or high jump 8 feet, which is the same distance you could jump without grappling a target. If, on the other hand, you had a speed of 30 feet, grappling halves this speed to 15 feet. Now, you can move 10 feet and then long/high jump only 5 feet, less than the original amount.

TL;DR: It depends on how much Strength you have, and how much speed you have.

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    \$\begingroup\$ In other words, if you have enough movement speed to pay the "foot price", your maximum jumping distance is not affected by grappling ? \$\endgroup\$
    – Gael L
    May 7, 2019 at 17:06
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    \$\begingroup\$ @GaelL Precisely! Either by having a high enough speed, or a low enough strength score. \$\endgroup\$
    – BlueMoon93
    May 7, 2019 at 17:06
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    \$\begingroup\$ I would add the explicit clarification that there aren't hidden rules - neither the rules for jumping nor the rules for grappling state that jump distance is reduced, so grappling does not directly affect your jumping ability. \$\endgroup\$
    – Carcer
    May 7, 2019 at 17:10
  • \$\begingroup\$ It may also be worth noting the difference between your speed and your movement - even with a speed of 15 feet (halved from 30), you can take the Dash action and get another 15 feet of movement, allowing you to jump the full distance. \$\endgroup\$
    – V2Blast
    May 7, 2019 at 19:17

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