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Both races have the same limits on their strength, and athletics, but it's hard to imagine why. A Goliath could feasibly lift and throw a gnome, yet the Gnome, following rules as written, can pin down a Goliath, fairly easily, if statted correctly.
Is there an in-universe explanation as to why such dramatically different sized creatures can wrestle on an even playing field?
How might a DM explain a scenario in which a gnome beats a goliath in any kind of test of strength?
I'd like to take a different approach to answering this question: Numbers!
Both races have the same limits on their strength, and athletics, but it's hard to imagine why.
Presumably, this is to allow the role play opportunity of playing a Gnomish fighter who is excellent with a sword. Key stats are key stats, and cherry picking limits actively disincentivises creative character generation. No, it's probably not realistic.
A Goliath could feasibly lift and throw a gnome,
Let's prove it.
Average characters have average stats: 10 across the board. Goliaths get a racial +2 to strength, giving an average Goliath a strength of 12. They also all have the racial trait Powerful Build, making them count as Large for the purposes of moving stuff.
The section Lifting and Carrying on PHB 176 says the carrying capacity of a str 12 character is 180 pounds, and the push/drag/lift weight is 360. However, that's doubled for Large creatures. Thus an average Goliath can carry around all day 360 pounds, and in a pinch lift 720.
The average Gnome weighs 40 pounds. A Goliath would need an impossible -1 base strength plus the +2 racial mod to have a strength low enough to not be able to carry around a typical gnome all day.
It doesn't say anything about throwing, but I think we're in safe territory here.
yet the Gnome, following rules as written, can pin down a Goliath, fairly easily, if statted correctly.
Here, I take 'statted correctly' to mean a strength of 20. You can also get higher with the better Belts of Giant Strength, or by being a barbarian, but I'll stick with the 20.
Is there an in-universe explanation as to why such dramatically different sized creatures can wrestle on an even playing field?
Sure. A 'statted correctly' Gnome can feasibly lift and throw a Goliath.
From the same sources as our Gnome lifting above, a str 20 character (of any small or medium race) can freely carry around 300 pounds without breaking a sweat, and can push/drag/lift a whopping 600 pounds.
Goliaths weigh 280 to 340 pounds. Thus, a feasible grappling tactic for our diminutive grappler is what you might do with a child: pick him up. A somewhat lighter than average Goliath could be carried around all day, in case of emergencies.
Actually throwing the Goliath would be a DM judgement call. If you expand your range of opponents to other humanoids, you should have no trouble tossing around the heaviest humans (weight varies), elves (slender), half-orcs (bulky), tieflings (as humans), or even dragon born (250 pounds). However, it's essential to remember that even at only 150 pounds, nobody tosses a dwarf.
How might a DM explain a scenario in which a gnome beats a goliath in any kind of test of strength?
The Goliaths in question are average and run of the mill. Any gnome with a 20 strength is at least in the second tier (levels 5-10, PHB 15) and thus capable (with a few friends) of handling problems that threaten cities and kingdoms. Thus, such a Gnome is a pretty famous hero and a specimen as rare as any other character with a 20 in one stat.
The problem that you're having here is that, in real life, most people who are 7 feet tall are going to be faster, stronger, and all-around more physically powerful than a person who is 3 feet tall. If you compare two people of similar athleticism, the person who is 4 feet taller is going to be able to physically dominate the other.
However, D&D is not a game built to simulate reality. It's a game built to let you play through stories about heroes who fight against a large variety of evil things. It's built to let players build a wide array of kinds of hero, and let them generally be effective at their role, even if the character options they picked wouldn't work in real life.
This means that the game will let you build a gnome strongman, if that's the kind of character you want to play. The designers wouldn't want your gnome strongman to be much worse at being a strongman than a character of a different race, so the only racial 'penalty' to being a strongman that you get is that you don't get a racial bonus to Strength. All of this is based on intentional design choices to make as many player archetypes as possible viable.
In-universe, they'd explain this just like we would in real life. If a really buff but physically small person wins, say, an arm-wrestling contest with someone pushing 7 feet, we'd be impressed. It would be odd, for sure, but it wouldn't be something impossible. In a world where divine blessings and magic are commonplace, the idea of a strong gnome beating a goliath in a contest of strength becomes less unbelievable, and more possible.
Sure, it's clearly impossible for a little gnome to grapple a goliath in the conventional sense of the word. But in DnD, "grappled" is simply a condition in which the creature's speed is reduced to zero.
It doesn't take too much imagination to have a gnome be able to prevent a goliath from moving. In fact, it's a fairly standard trope in fantasy films - the plucky little guy keeping the big bruiser distracted, confused, tripped and tangled for a few moments during the big fight. You probably wouldn't call it grappling, but if it reduces the opponent's speed to zero, DnD would.
The game is a game, it is based on abstractions and its rules have been written without too much regard for what would be possible in real life.
Basically, the difference between a goliath and a gnome is their size that fictionally justifies a small difference - the racial bonus to strenght.
D&D authors decided to have this bonus way smaller than the range of possible values. One can spend enough points to bring even a gnome to 20, or can decide to spend no points on it even on a Goliath.
The rules give no different limits to their maximum potential. In previous editions, they gave no limits at all, and this sort of solved your problem: the starting advantage was enough to never let a strongman gnome reach a strongman goliath.
Now that the limit is there, aimed at letting players still worry about being able to miss a goblin even at high levels, this looks like an unintended effect. But the game is a game, abstractions are necessary to a game and you can't have both realism and balance at the same time (while playing a game that has stats measured by numbers, that is. In some other games, where the balance is provided by having metagamey resources to influence a story and realism ensured by "you can do what is possible for your character to do" rules, this would be possible.)
There's an aspect of the rules you're overlooking: all situational modifiers exist in a mechanic called Advantage/Disadvantage, instead of a long table of +/− modifiers that would be hard to use or remember.
If a goliath and a gnome are grappling, it would be quite reasonable for the DM to impose disadvantage on the gnome's strength check or grant advantage to the goliath's strength check (or both!), to reflect the major disparity in leverage. As a result, it would not be relatively easy for a gnome to pin the goliath — and if the gnome did, it would be an extraordinary result, meriting an extraordinary narrative description of the phenomenally lucky, clever, and unlikely twist of technique that allowed the gnome to win.
So no, there is nothing lore-wise that explains why a gnome should easily beat a goliath in grappling. In fact, the lore suggests the opposite, and the DM is expected to make those obvious advantages and disadvantages matter by using the rules for handling having disadvantages and advantages.
That's right -- while grappling in the West is commonly portrayed as a matter of brute strength, it really isn't solely determined by that. Many grappling techniques rely just as much on biomechanics as they do strength, in that they attempt to position one or more of the victim's joints beyond their normal range of motion. This gives the attacker the ability to influence the victim's movement, not only through direct leverage, but through pain as well -- joints moved beyond their limits are quite acutely painful, and most of the movable joints in the body are susceptible to this class of technique.
From this, it is not hard to imagine, for instance, a gnome monk getting a hold of the goliath's foot and twisting it sideways on him, sending the goliath off-balance while causing a serious distraction to the goliath in the form of "Yeow! My foot!" From there, it'd be quite easy for the gnome to knock the goliath over, giving our gnomish monk access to many more joints to manipulate to keep our poor goliath pinned to the mat.
There have been a lot of opinions on this matter and often people cite IRL examples but best opinion is "D&D is a terrible reality simulator". I don't think that answers your question though.
Mechanics allow anyone, at any weight, to grapple as long as the target is "no more than one size larger than you and must be within your reach." (PHB 195). It's a game and thems the rulz. Enjoy the game and describing how 'David the shirtless gnome circles the laughing goliath with a twinkle in his eye'.
but it's hard to imagine why. A Goliath could feasibly lift and throw a gnome, yet the Gnome, following rules as written, can pin down a Goliath, fairly easily, if statted correctly.
Stats are key here.
Racial bonuses show a clear favorite with the goliath but if the gnome priorities Str they can hit 20 just like anyone else. The gnome would simply be an anomaly (the jacked gnome at the gym gets gains) verses all the 20 Str goliath warriors running amok. Skill proficiency works the same. Choosing Athletics proficiency gives more points toward success and shows dedication to a (martial) art.
David the gnome has dedicated his life to getting stronger by pushing his body to the limit daily (+Str). He practices take downs, locks, and submission holds constantly between his adventures (+Ath). Facing down his much larger opponent, David sees a lucky opening in his guard and lunges forward at the perfect moment (+Die roll). It may have been fate or with the help of his companion's (+Inspiration/+Guidance spell) but after a flurry of action the goliath was down, wrapped up like a pretzel with David leaning in to put more pressure on his joint.
See above but you can always just answer in one word. "Leverage".
The rules only tell you what happens, not how it happens. Regardless of platform, all game rules have to ignore some reality, or they would become so overburdened as to be unplayable. Imagine playing even a fairly simple computer game like Civilization as a four-player board game; it would take forever!
That said, there are conceivable ways for any creature to grapple another. Wording aside, all "grapple" means in D&D (and indeed, many other tabletop RPGs) is to reduce to 0 speed (initially, at least). "Pinned" means immobile, but not helpless, for 1 round. The rules strictly regulate what can and can't happen in those situations - but it doesn't mean the same actions every time.
If two men grappled, you can easily picture them wrestling back and forth, pinning arms or breaking free. It's easy, because it's familiar. But a gnome and a goliath? They probably aren't wrestling; instead, I picture the gnome darting between the goliath's legs, punching him behind the knee, and sticking a knife up against his delicate unmentionables. The goliath, off balance from the kick and in a delicate situation, does what anyone would do: freeze! Only for a few seconds, of course (1 round), but long enough. If he wins an opposed grapple the next round, he steadies himself, reaches between his legs, grabs the gnome, and hauls him out in front.
The rules tell you that something happened. The GM tells you what.
Read Pratchett, in particular the novels featuring the Nac Mac Feegle. The Wee Free Folk are famously given to fighting, and will happily take on anyone, any size, any time. Common tactics include nutting someone whilst literally "getting in their face", climbing up trouser legs to kick someone in the groin, or ganging up to all lift the "bigjob" and bash them into something.
Grappling is simply close-range unarmed fighting, after all. If a player asks why the gnome can grapple effectively, ask them how they're going to use their wrestling skills on someone who's kicking them in the nuts from inside their underpants. :)
In a similar vein as what pokep has suggested, perhaps they are not grappling using conventional means. When you ask “How can a gnome grapple [lit: immobilize] a goliath?” my gut reaction is “He’s got him by the face.” While I agree with Rene Collins that it is highly possible to utilize the specific weaknesses of a foe to overcome their size advantage, it doesn’t need to be with a “bladed instrument,” the gnome could put the goliath into a thumb-lock*, an armbar, or something similar that works for the narrative without contradicting the game’s mechanics.
*See the thumblock in action in this youtube video: Defend Yourself! "Thumb Lock"
Put your head against a wall, with a chair (or desk, or book, or whatever; anything you can easily lift under ordinary circumstances) between you and the wall. Hold onto the chair, keep your legs straight, and stand up. No man will be able to lift the object from this position, no matter how strong he might be. A woman, however, will be able to lift it easily.
I do not recommend trying this too many times if you are male. You'll only wind up banging your head against the wall, and I mean that literally. Just squat down on your heels, balance on the balls of your feet, and breathe.
How does this work? Because grappling isn't just about strength. In the case of the chair and the wall, it's about your body's center of gravity, which is a little lower in women than in men. When you're bent over with your head against the wall, a woman's center of gravity is still supported by her feet, so she can pick up the chair without difficulty. But a man's center of gravity is supported by the wall, so even if he manages to get off the wall a little bit, he'll just tip over andfall back into it.
Real-life grappling is also largely about center of gravity. There's actually an advantage to being smaller, because you can more easily get your center of gravity under your opponent's, where it is easier to throw them or knock them down. That advantage is not all-powerful -there are limits, and these limits can be overcome- but it's very real.
D&D makes no attempt to actually model the physics of grappling, of course. But at least in this particular case, the mechanics aren't so poor as to be unrealistic. The goliath has many advantages, but the gnome has a very real shot, and the check reflects that.
Grappling in D&D is using Strength to immobilise an opponent. It just means the Grappled creature's speed is zero. They can't move away. This is something that a child can do to an adult in real life, just by putting the adult off balance.
The gnome could for example step close to the Goliath, putting the larger creature off balance and applying a wrist lock from behind.
Real-life martial arts such as Aikido teach their students how to use strength and the opponent's own weight to put them off balance and make them unable to move effectively. If your body isn't on stable footing, it doesn't matter how strong you are. And all things being equal, taller people are less stable.
By RAW, it does not make sense how it works. If you were a smaller person trying to grapple a much bigger and stronger person, you would not use strength or your quickness to your advantage. As a smaller person you have neither of those.
What you would do as a smaller person versus a much larger one is take a bladed instrument and put it to something the other party does not want to lose above all else and control them with that. The threat of the amount of pain an immediate genital evisceration, puncturing an eardrum, cutting off their nose, or the like poses would stop any but the most hardcore of masochists.
