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On PHB p182:

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.

I understand the RAW, but my question is, what does that mean really? What portion of the jumper's body is clearing the obstacle? Do the rules mean that a halfling of average strength with a runup can jump up onto a table and land on their feet, then keep going? Or does it mean only the center of the halflings body is clearing the obstacle? Or maybe they are doing the olympic style flop high jump (which no-not really but is funny to consider)?

The idea that it is the height of your feet off the ground is supported by this portion of the jump rules:

You can extend your arms half your height above yourself during the jump. Thus, you can reach above you a distance equal to the height of the jump plus 1 1/2 times your height.

If it is the height of your feet off the ground, then a person of average strength (36") should be an NBA player. And a person with 18 strength is in the superhuman range (72" vs. the record for a running vertical jump in the NBA of 46"). At the other end of the spectrum, a 6'8" human with a 20 strength and a decent Athletics roll can jump up and grab the top of a 20 foot wall. Or, you know, just jump up and stand on the rim. Just like the gnome with a 20 strength can.

To summarize:

Are the jumping rules under the High Jump section really describing a running vertical leap wherein your feat clear the height listed in the jumping rules?

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    \$\begingroup\$ I'm kind of confused. If you understand the RAW and have already cited enough evidence to answer your question, what do you want us to do? What exactly are you confused about still? \$\endgroup\$ – Rubiksmoose Apr 3 '18 at 15:30
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    \$\begingroup\$ @JWT If you're wondering whether D&D's jumping rules are realistic, I might remind you that D&D is not a simulation... \$\endgroup\$ – Speedkat Apr 3 '18 at 15:39
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    \$\begingroup\$ Yeah. I know that, but it also should be reasonable (even if it is "heroically" reasonable)- else what is magic for if the average bloke is capable of olympic caliber feats. At a certain point it breaks Suspension of Belief. \$\endgroup\$ – JWT Apr 3 '18 at 15:42
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    \$\begingroup\$ Look at a standing jump for a character with 12 strength. It's 2 feet (half of 3+1 feet). By definition, if you jump two feet into the air, every part of you is two feet higher than it was when you were standing. If it was measured by where your waist ended up, for example, a two foot jump would be a squat for most adults. \$\endgroup\$ – Zeus Apr 3 '18 at 19:45
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    \$\begingroup\$ @GreySage 12 is not superhuman, it's simply above average. \$\endgroup\$ – Zeus Apr 3 '18 at 19:46
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Yes, the jump is the distance from the ground to the bottom of your feet

When you make a high jump, you leap into the air a number of feet equal to 3 + your Strength modifier [...] Either way, each foot you clear on the jump costs a foot of movement.

Intuitively, a vertical jumping distance makes the most sense as the distance between your shoes and the ground but really your entire body is moving the same distance upwards. The rules' language talks of the distance you "clear" and "leaping into the air" both of which evokes the imagery of the gap between ground and shoes. More direct evidence can be found in the following passage:

You can extend your arms half your height above yourself during the jump. Thus, you can reach above you a distance equal to the height of the jump plus 1 1/2 times your height.

So it is clear from the rules that when you jump, the distance is measured from the ground to your feet and that means that the rest of your body moved vertically that same distance.

If the PC can jump X feet, their feet reach X feet

If a 6' tall character jumps up 8' it means that their feet are 8' above the ground and their head is 6' + 8' = 14' above the ground. If they raise their arms the tips of their fingers would be 1.5 * 6' + 8' = 17' feet above the ground.

In this case, if a character jumps up at a 8' wall with a jump of 8', then the assumption is that they land on their feet on top of the wall.

The way the jump looks narratively is not defined

How all this jumping and leaping looks is completely situational and also not at all defined in the rules. In cases like these, the DM must fill in the blanks.

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