The problem with these “physics of [video game]” articles


Super Mario Bros is a popular case study in discussions of physics and gravity. The acceleration of gravity in the Mario universe has been studied extensively in relation to fan theories in Youtube videos by Game Theory and PBS Spacetime, articles in Wired, Business Insider, and Techradar. It has even been frequently used to teach physics in actual classrooms, some of which has resulted in publications in education journals.

The results obtained by all these studies give us something that is hardly surprising. The gravitational acceleration in the Mario universe is not the same as in the real world, which should be 9.8 m/s^2. The obvious answer to this is that video games are not supposed to represent the real world. If we apply real-world laws of physics to a video game, it is inevitable we will get non-sensical results. So why do physicists keep trying to apply Newtonian mechanics to 2D platformers?

In the case of classroom teaching, the reason is obvious: it gets students to learn a hands-on approach in calculating and measuring kinematic quantities. The results they do get can be compared to real-life values and how they differ from each other could launch interesting discussions about the design principles and decisions that led to programmers to code this specific behaviour in the game.

Of course, there’s nothing wrong with using a video game like Mario as a tool to teach physics. In fact, it is a brilliant way to engage with the students. However, outside the context of education and exploration, there are three issues inherent to the mindsets and attitudes of these articles:

1. Applying the physics from “our world” to the “game world” crosses between two contradictory logical systems.

That statement sounded quite formal, but think about this example: In football, the most goal scored in a game by Cristiano Ronaldo is 5 in a game. But in the LA Lakers, Kobe Bryant has once scored 81 points in a single game. Obviously Bryant is a better player than Ronaldo, right?

It hardly needs to be said that we cannot compare a football player with a basketball player because they are different games, following different rules. The reference points are different for each game. For football, scoring 3 or more goals is usually an impressive achievement. While scoring over 30 points is normal for a basketball match.

By the same token, it doesn’t really make sense to imply “Mario can run faster Usain Bolt” (Techradar), or that “Mario has amazing leg strength to jump the height that he does in the game” (Business insider). Let me pose an alternative statement instead: if Usain Bolt lived in Mario’s world, how fast would he run on screen?

Super Mario operates within a different reality to ours. And I’m not just talking about the existence of Goombas and fireballs. In Mario’s world, his jumping ability isn’t that particularly unique, since Luigi, and Peach in the later games have mostly similar abilities. It is because of our tacit understanding of their different reality that we accept that their anatomical proportions are grotesquely different from real-world humans, much in the same way we accept anime characters with huge eyes within the context of their anime world.

It would cause an alarming cognitive dissonance if we smash these two realities together. This actually happened to a Mario game, where its latest game, Super Mario Odyssey recently released a trailer back in January showing our cartoon plumber bursting into New York Donk city with normally-proportioned inhabitants. There has been plenty of negative reactions to this trailer. Check out the bewilderment of everyone in this mashup when Mario pops up in the “real world”. Hbomberguy has made an excellent video explaining the psychology behind this cognitive dissonance.


Odyssey is not the first game that crosses this cognitive boundary. The image above is from the 2006 installment of Sonic the Hedgehog. It actually went further than Odyssey and gave Sonic (…a Hedgehog) a human love interest by the name of Princess Elise. Just like Odyssey, the visceral reaction to this image seems weird, grotesque, or just uncanny. This is probably because our brain feeling discomfort over processing two contradictory realities within the same space.

Of course, we don’t feel the visceral revulsion when we apply real-world physics because equations and mechanics are more abstract, and thus protects our instincts from perceiving the dissonance of the two realities. But as Odyssey and Sonic ’06 has shown us, we are not supposed to process these two worlds within the same framework.

Trying to apply real world proportions to the world of Super Mario may lead to disastrous results. Case in point:



2. This practice implicitly assumes that “game world” physics is an objective reality.

To analyse the physics of Mario games, the Wired article used a data logger on a gameplay capture, the PBS spacetime video used stopwatches and tapes to mark time and distance, and hypertext physics article analysed the video footage frame-by-frame.

These are methods familiar scientists, as they are developed from the philosophy of the Scientific Method, which is to understand objective reality through experimentation and theory. Quite often, we here the mantra that “the Universe doesn’t care about us”. (The full quote is attributed to a Times reporter David Levithan, which goes like this: “Ultimately, the universe doesn’t care about us. Time doesn’t care about us. That’s why we have to care about each other.”). This is partly to convey the idea that the universe exists independently of our wants and needs.

Except for Earth, every place in the universe is lethal to us. That flu virus you have doesn’t care if you have a runny nose that annoys you the entire day. Why does traveling from Asia to Europe take so many hours? Why is the internet speed so slow? Why isn’t there enough hours in a day? The laws of physics exists in the way they do whether we like it or not. (This is ultimately related to why people say they “hated studying physics at school” – though that’s a whole other article.)

And that fundamental principle is almost the opposite of the “game world” physics because games are intentionally designed to satisfy a user.

It is not surprising to state that the “game physics” is NOT an objective reality, but is intentionally designed with human users in mind. So applying the data logger and tracker measurements to extract the physical parameters of a game seem strange, unless you are in a classroom to teach students about these methods.

The parameters of the game physics is decided by someone, or a group of people. They have already written down the parameters in the programming of the game. So the obvious way to figure out the details of the game engine is to look at the code, which brings us to the next point.

3. These articles ignores the intellectual accomplishments behind the design principles and decisions that created the “game world” physics.

These “physics of Mario” articles are sometimes written by physicists – people whom our society has decided to be respected and treated with reverence. If not, they are written based on data obtained by methods we’ve learned about in physics class (data logger, tracker, stopwatches), which brings in another association with physics.

Of course there’s nothing wrong with applying these methods from physics, but if an actual scientist or engineer is serious about extracting accurate parameters of the game, they would be looking at the source code. A search leads to a Github page posted by a team who reverse-engineered the code, and below is a section involving Mario’s jump mechanics:


The code is hard to read, especially since the game is written in the NES assembly code in the 80s. So a further search reveals that user jdaster64 has studied the code and translated it into understandable quantities. In particular, they determined the exact jump and gravity parameters under various situations. The image below shows a section relevant to the jump mechanics: (Numerical values presented in hexadecimal, length scales are in units of (16)^(-3) pixels, and the unit of time is 1/60 s)


One of the most interesting results to me is that jdaster64 discovered that Mario’s gravitational acceleration is piece-wise velocity-dependent, in addition to whether the jump button is held throughout the motion or not.

In the video “Mechanically Speaking: Jumping in 2D” by [game array], jumping in 2D games are designed to be responsive and fair to the player. According to that video, the reason why Super Mario Bros. feel so much better to play it’s because the player can alter their trajectory mid-jump, and the variation of gravity based on the button presses gives the illusion of a pressure-sensitive input. Both of these features are markedly different from the basic assumptions of projectile physics, where the motion is completely determined by the initial conditions. [game array] pointed out that earlier games which does have jump trajectories fixed by initial condition will feel less satisfying, and sometimes frustrating. That’s because once you’ve jumped, you’re committed to the act, and when an enemy or obstacle pops out, there’s nothing you can do about it, and you die.

Dying frequently is a source of frustration to many players, and designers tend to want to circumvent that to have gameplay that is responsive to player inputs at all times. Players are more acceptable to fail-states that result from their own actions, so they can learn to avoid the same mistakes in the future. This video by PBS Game/Show makes a similar argument citing a more general idea from the book Game Feel by Steve Swink.

So the jumping physics are intentionally designed to be different from real-world physics. Even though we would naively think that we want video games to simulate real-life situations as much as possible, some of these simply do not lead to satisfying gameplay.

Again, I emphasise that there’s nothing wrong with applying real-world physics to a game like Super Mario Bros. It’s just that there’s so many of these articles that we seem to be missing an interesting conversation on why games are designed in the way they do. Of course, none of these articles imply that game developers are idiots and do not know physics, but the thing is they don’t even acknowledge the existence of the developers, and we’re missing another interesting conversation on how user considerations like our perceptions and responsiveness forces them to make the physics of their games different from the real world.

Of course, there are almost as many technical analyses of Mario from the programming community. But these seem to be so disconnected from the academic physics community that everyone is stuck within their own bubbles and we never learn anything new or interesting.


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