Mario responds SMOOTHLY and INSTANTLY but not physically accurately to the analog joystick controller and buttons, which was the genius of Miyamoto's "outside-in" physical-world-first design methodology, which he describes in his GDC keynotes, that I quoted and linked to here:

https://news.ycombinator.com/item?id=28814555

>In an earlier talk, he explained that he designed his games starting with how you physically interact with the controls you're holding in your hand, and then inwards into the computer, instead of the other way around like so many other people tend to do.

Also there's some great stuff about the controller and physics design here:

https://shmuplations.com/mario64/

>Super Mario 64 – 1996 Developer Interviews

>—Mario 64 is the lead-off title for the new Nintendo 64… but how did the project first get started?

>Miyamoto: Well, in the beginning… we were working on something really simple—deceptively simple, even, from the perspective of the team that would go on to finish the huge, final game. (laughs) There was a room made of simple lego-like blocks, and Mario and Luigi could run around in there, climb slopes, jump around, etc. We were trying to get the controls right with an analogue 3D stick, and once that felt smooth, we knew we were halfway there. And so, along the way, we realized wanted to create a slightly larger area for them to move around in…

>—I don’t know if “slightly” is the right word there…

>Miyamoto: Well, that’s how it is with all our developments. (laughs) For this game things were especially vague in the beginning, because we developed it in tandem with the N64 hardware, and we didn’t know exactly how powerful the hardware would turn out to be. That’s why, at the very beginning, we actually did our work on a large, powerful computer that simulated what we guessed the N64 hardware specs would be… then, well, we got things to a point where the controls were nice and responsive, and we thought this could be the foundation for a game. But the problem was, it had all been made on this massive computer that cost tens of thousands of dollars. No one yet believed that we’d be able to make something like this on a little 250$ machine like the N64. (laughs)

>However, once the N64 prototype was finished and delivered to us, we saw that it handled the movement and controls almost perfectly. That was the moment we first realized this was going to work, so we quickly dashed off a planning spec sheet for the game. When the staff saw how long it was, they said they’d been lied to—no one told them they would have to make this massive game! (laughs) That’s how we make games at Nintendo, though: we get the fundamentals solid first, then do as much with that core concept as our time and ambition will allow.

>—And in this case, that fundamental basis was the model you made with Mario and Luigi running around that room.

>Miyamoto: Yes, it was being able to move Mario and Luigi around with the 3D control stick, and being able to change the camera view with the press of a button. One of our big development themes was letting the players move Mario around any way they wanted. We wanted to make a game where just moving Mario around was fun.

>—People have described Mario 64 as “interactive animation”, and I think that term fits perfectly. Mario is truly a joy to control.

>Miyamoto: That’s why I think it would have been great if we’d been able to make it two-player, with Mario and Luigi. But if we had done it wrong, it would have turned into a fighting game or something (laughs), so we’re leaving that challenge for next time.

>—I really like all the nuance to Mario’s movement. It looks very natural.
Miyamoto: That was all done by Nishida and Koizumi. I should have told them to make the jump look cooler though. (laughs) About all we told them in terms of guidance was to create as many different movements as they could.

>Koizumi: I didn’t think it would end up being THAT many. (laughs)

>Nishida: Koizumi created the animation data, and I did the programming. I counted them all up, and there were 193 different animation patterns! And if you include the 50 or so animations that we created but ultimately rejected, it comes to nearly 250.

[...]

>—I got used to the 3D stick’s analogue controls very quickly, and it felt completely natural to use in Mario 64, but I’m guessing it was actually very difficult to get right?

>Miyamoto: It was a huge challenge, definitely. Now that they’ve had time to play it, people tell us it feels natural, but when we exhibited Mario 64 at the expo in November, we heard a lot of people say “I don’t know about this, the controls feel really wobbly and slippery…” We weren’t about to back down that easily, though. We dug in and pushed forward, knowing that this kind of response is to be expected if you’re trying to change the culture. And yet, while we were all telling ourselves “walking around leisurely can be fun too!”, I have to admit that internally, I was a little worried… normally games have a faster pace. (laughs)

>Ultimately, though, we really did want to change the culture of gaming, and it was in that spirit that we made Mario 64. And that’s reflected in the controls, and how long it takes to accelerate.

>—When I played that version in November, if I can speak honestly, my first impression was that I wanted the controls to be a little more responsive. But when I played the final version, I felt the responsiveness fit the game just right.

>Miyamoto: We tightened the springs a bit on Mario, maybe? I don’t know. (laughs) In any event, though, Mario 64 required a lot of difficult physics calculations. This is an exaggeration to make my point, but when Mario is moving like a car, or moving like a human, or moving like an airplane… all those require different physics calculations. His different jumps all require different calculations too. It was very annoying.

>—I remember you remarking that Wild Trax (Stunt Race FX) involved a lot of car-related mathematics too. Mario’s movement likewise has a proper sense of centrifugal force and “braking” friction… I noticed it when I was playing, and it reminded me of that conversation about Wild Trax.

>Nishida: It’s not actually “real” physics, of course—we’ve fiddled with them a bit. Gravity, friction, resistance… these have properly set parameters, but if you rely on the actual laws of physics too much it doesn’t really make for a good game. The floatiness of Mario’s jump, for example, works great in a game, but a real airplane would never be able to fly at that speed.

>Miyamoto: Yeah, it really was difficult! It was like we had to go back to middle school and learn basic physics concepts all over again—like what does it mean for a substance to be at rest? I never thought I’d have to study those things again at my age. (laughs) But that was also part of the fun. [...]

Also:

https://www.gamasutra.com/view/feature/2322/game_feel_the_se...

>Game Feel: The Secret Ingredient

>[...] There are lots reasons for this, but the main one is that game feel is slippery. It’s mostly subconscious, a combination of sights, sounds, and instant response to action. It’s one of those ‘know it when you feel it’ kinds of things. If it’s off by just a little bit, a game’s goose is cooked. If it’s “responsive”, “tight”, and “deep”, it can be magical.

>As a canonical example, consider Super Mario 64. The feel of steering Mario around in Super Mario 64 fills me, to this day, with thoughtless joy. Especially in Bomb-Omb Battlefield where there’s very little pressure or structure, I love to just run and bounce and spin, experiencing the sheer kinetic joy of controlling Mario. Control, intent, and instructions flow from me into the game as quickly as I can think.

>Feedback returns just as quickly, letting me adjust and fine-tune my instructions. When a game feels like this I’m hooked, ready to spend endless hours discovering every nook and cranny. Considering the near-universal reverence for Mario 64 among both players and creators of video games -- to say nothing of the millions of copies it sold -- I think it’s safe to say I’m not alone in enjoying the feel of Mario 64. As a developer, though, I have to wonder: wherein lies the magic? What’s behind the curtain? A huge part of it is the feel. [...]

>Breaking the game down by “granules” this way, it seems that Mario 64 is a game about feel. The thing you spend most of your time doing is moving Mario around, interacting through the controller at a tactile, kinesthetic level. It’s the fundamental activity of Super Mario 64 and it feels great. It has its quirks and input ambiguities, but this sensation is the foundation the rest of the game sits on.

>“Before any of the levels had been created Mr. Miyamoto had Mario running around and picking up objects in a small ‘garden’ which he uses in all his games to test gameplay elements. “A lot of the animation was actually in there before any of the game” explains Goddard. “The Mario that he had running around basically looked the same as he did in the final version. Mario’s movement is based on good physics, but you have bits on top that you plug in so you can do things you shouldn’t be able to do. They spent a lot of time working on the swimming, it’s harder than running to get the feeling right, they didn’t want you to avoid the water, the wanted to make it an advantage and fun to dive in.”