Super Mario World's Historical Context
This section will explain how we measured Super Mario World and what conclusions we drew from those measurements. Everything that can be said about the smallest level of Super Mario World’s design comes down to one question: how difficult is this jump? Obviously, it’s a question that is going to be asked thousands of times. Players don’t always consciously ask themselves this question, but it’s definitely at the back of their minds—especially on the really tricky jumps. Players have to predict the motion of Mario (or Luigi), the motion of their target, the distance they have to cross, any enemies they need to avoid while in flight, and numerous other factors that affect the challenge of each individual action. Experienced players can do this in an instant, so it’s clear that these elements form a very cohesive whole. The problem for us as designers is: how do we figure out numerically how hard the jump is? Can we unpack the dense, intuitive understanding so many players have of this classic game? Can we break down into pieces something that is beautiful and seamless as a whole?
Fortunately, the answer is yes. In fact, Super Mario World breaks down quite nicely into its component design elements. From jumps we were able to deduce challenges, and from challenges we were able to realize the presence of cadences, and cadences fit together into skill themes. But, going back to the beginning, our first task was to figure out ways to meaningfully measure everything in the game. Once we had measured everything, things like cadences and skill themes came together quite quickly. This section tries to assemble the same line of thinking and process of discovery that we experienced while researching. The conclusions come in the next section (part 3) but that section and the definitions in it will not make much sense without reading this one.
The first and most important key to understanding the design of Super Mario World is the coin-block.
This block is the basic unit of Super Mario World—the “atom” of the game. The Super Mario World team did themselves (and us) a huge favor by standardizing all of the distances in the game. There are no playable surfaces anywhere in the game which are not made up of an integer block length. There are no heights which are not made up of a whole number of blocks. Some moving platforms pass through heights which are not evenly divisible by blocks, but even these come to rest at block-level. Some objects appear to sit in spaces not evenly divisible by a coin-block too, but their “hit box” is always at an effective integer mark. Therefore every jump event in the game, even underwater events, can be measured precisely.
Mario’s ability to jump to any given height is dependent upon the amount of momentum he has. With no momentum, Mario can jump on top of a platform four blocks above the position of his feet. With one block of lateral momentum he can jump to a platform five blocks above the level of his feet. With eleven blocks of momentum, he can jump as high as the top of the sixth block above his feet.
If he has the cape, eleven blocks of momentum will enable Mario to soar high enough that measuring that height is mostly pointless. You’ll notice, of course, that these momentum levels correspond to block-lengths. The eleven-block momentum benchmark is important because it frequently prevents Mario from using the soaring cape ability to bypass levels (or sections of levels) which lack platforms of sufficient length. The designers of Super Mario World made level design easier on themselves by doing this; as long as they restricted platforms to lengths of less than 10, they could exert some control on how the player would approach a level.
There’s also the issue of how far laterally Mario has to go when jumping. Most jumps involve a lateral distance, which also breaks down nicely into block-lengths. At no momentum, Mario can jump from block one to block six, a distance of five blocks.
At any level of momentum before a full run, he can jump from block one to block nine (distance of eight), and at a full run he can cover 12 blocks. All of this, of course, assumes a flat area; any vertical distance involved in the jump will change the figures significantly. None of this takes into account the use of the cape powerup. The cape extends the fall time on a typical jump to about three times its normal length. It doesn’t significantly affect the speed of the lateral motion (what we’ll call the x vector), but by allowing the jump’s vertical motion (y vector) to last longer, jumps can go farther laterally before Mario hits the ground again. And of course, the player can use the cape while at a full run to go so far across the level that measuring is pointless; only a wall, ceiling or enemy will stop him.
There are three important statistics that come out of this: delta height, delta width and d-distance. (Delta means the change between two or more points of data.) The most obvious place to start measuring jumps is the danger distance, or d-distance for short. The d-distance is the amount of lateral distance that Mario has to cover in a single jump event. In the screens below, you can see how we measure this.
You’ll notice we don’t measure diagonally. Because of the way that vectors, intercepts and powerups in Super Mario World work, diagonals aren’t any more meaningful than the mere lateral distance unless there’s another element like an intercept present, and then it’s the intercept that’s really meaningful. D-distance measures the size of deadly obstacle Mario is trying to avoid, whether it’s a bottomless pit or some kind of damage floor (or, in some cases, a fall that forces the player to tediously climb back up).
The next most obvious point of study is changes in heights during a jump event. In the jump pictured here Mario is ascending from height. A number alone doesn’t explain if the jump is difficult, however, so let’s break it down further. This jump goes up; jumps that go up are more challenging than jumps that go down. The reason for this is that Mario loses his momentum when he’s going up (unless he’s flying with the cape or Blue Yoshi), but his downward momentum tends to stay the same, and can be easily controlled with a cape-glide. Anyone who has played the game will instantly know that the right hand jump pictured below is easier—even with a larger d-distance—because it is descending.
When Mario begins a descending event, he usually has a lot more time to get into the right X position, and the Y position will take care of itself because of the y-vector (the game’s gravity) and the floor. He’s falling the whole time, so the player doesn’t really have to worry about falling—especially if he has the cape, which will greatly extend the fall and give the player a ton of time to guide Mario downwards. There are exceptions to the rule, but it’s almost always harder to jump upwards than downwards. This will be reflected in the numbers when there is a negative delta height (starting height – target height = negative number). Like with everything else, the height of an average jump doesn’t go up much across the course of the whole game, but it’s fairly common for successive challenges within a single level to feature increasing positive delta heights.
The trickiest measurement we have to make is the width metric. First, we should define what we mean by width. The jump event width is the amount of horizontal space, measured in blocks, that the player has available to them to begin a jump event. Starting platform width matters mostly because it determines how much momentum Mario can accumulate before jumping. Starting width is pretty easy to measure, but landing width is often complicated by factors other than the size of the platform.
There’s an enemy approaching Mario, which will damage (and possibly kill) him if the player doesn’t avoid it. Can the player simply drop Mario onto the head of the oncoming Koopa? Maybe, but the problem is that when this jump begins, the Koopa is offscreen, and so by the time the player sees it, Mario won’t have enough height to bounce of its head. Therefore we say that the real target width of this jump is in fact a width of four, because that’s the width available for landing between the edge and the enemy. Most of the time, the starting and target widths are not so complicated, but it can become so.
Just as it is more difficult to perform a jump that ends higher than it began, it is more difficult to perform a jump that ends on a platform smaller than the one Mario jumps off. The width-specific difficulty of a jump is usually determined by the size of the landing platform. It’s not altogether that hard to jump from any platform of width greater than 2 (unless the delta height is high too, but this rarely happens), but it’s definitely harder to land on a narrower target because of momentum and overreactions to intercepts that might get in the way. The general idea is that the wider the target width is, the easier the jump will be. That said, the hardest jumps of all are the ones that begin and end on very small platforms. Platforms narrower than 3 blocks are tricky to jump from because they don’t allow much room for gaining the right momentum and timing. We’ll get to talking about that momentum in just a moment, but what we found overall with widths is that across the course of a level, the starting platform for a jump event doesn’t need to change to make that jump harder. It’s the landing platform’s width that reveals if there are any really meaningful changes in the sizes of things. (Although starting platform width matters in a few levels that require lots of momentum and don’t provide space for it, like Outrageous or Forest of Illusion 4.)
There is one last point of concern for measurement, and that is the use of soft sizes. An object with a soft size is any object for which the disparity between the graphics and collision box favors the player. That’s a little wordy, so let’s use an example. The big bullet is an obvious case: although the animated object is quite large, the part of it which can hurt Mario is smaller than it seems like it ought to be, as you can see below.
When it comes to platforms, however, the sizes are almost always larger than they appear to be, as you can see above. The size of the object is almost always more favorable to the player than it looks like it ought to be. Shigeru Miyamoto was a pioneer of this technique, going back as far as the barrels in Donkey Kong. Play a few other arcade games and you will see what a difference soft sizes can make to a player’s feelings of euphoria or frustration.
An intercept is an enemy timed and placed so that it interferes with a jump that Mario needs to make. The prototypical intercept is a Wing-Koopa that patrols a vertical path above a bottomless pit. If Mario jumps at the wrong time, the Koopa will intercept him along his path, sending him to his death. The general rule for intercepts is that the more of them there are, the harder the jump and/or challenge will be.
This rule of quantity is only true up to a point. Eventually the screen can become so saturated with Wing Koopas that Mario can’t help but land on one after another, earning him points and possible extra lives. This is rare, however. It’s also true that different kinds and speeds of intercept are more difficult than intercepts that are uniform in quality.
The last important thing to know is what intercepts are NOT. This enemy is not an intercept:
This enemy is causing Mario to jump. Essentially, the enemy begins the jump event, and therefore cannot be an intercept that alters the jump event. The enemy in the paragraph above, on the other hand, is not the cause of the jump event, but rather an obstacle that modifies the jump event. The gap between the platforms is the cause in the earlier example; the Wing Koopa merely makes it harder.
The last element which we measured that turned out to be meaningful throughout the game was the penalty factor. Penalty simply means the guaranteed result of a failed jump event. That is, if Mario needs to jump from platform A to platform B, and he fails, the penalty is the guaranteed result of that failure. Now, the penalty must be guaranteed—that is to say, if there are enemies in a pit below, there’s a chance Mario could land in that pit without taking damage. This is merely a risk that the player has to deal with in several ways, rather than a guaranteed problem to avoid. The most iconic penalty comes from the bottomless pit, which will definitely cause the loss of a life. Not all jumps penalize the player with death, however. Some jumps merely do damage, and some have no penalty except having to do the jump over.
We rate these penalties with numbers for the sake of judging the changes in penalty across challenges with simple nomenclature. If the penalty for failing a jump that the player has to try that jump over again, and Mario doesn’t lose a life or take any damage, the penalty rating is a zero. Jumps whose penalty is guaranteed damage but not necessarily death are rated one. Instant death pits are rated two. This is a very obvious metric, in that anyone can look and see what level of penalty a failed jump event carries. We nevertheless include it in our metrics because the penalty level of a jump event says a lot about the kind of challenge it is, which explains a lot about the design of the level and the skill theme, which we’re going to discuss next in the next section. It’s important to keep in mind, however, that for any given challenge there is a standard penalty. Deviations from that standard penalty are what signal to us, as players, that the designer is pressuring us to learn and perform in new ways.
Although vectors only need to be measured once, they’re nevertheless very important to the game—and they’re also important because in Super Mario World they’ve changed significantly from earlier Mario titles. For our purposes, we can define vectors as the forces of momentum a moving object has in the world of Super Mario World. Real world vectors are significantly different from Super Mario World vectors, so disregard your current knowledge of physics, because it will not help you understand this game. Mario’s vectors in Super Mario World have two properties: magnitude and direction. Acceleration and deceleration are totally unrealistic from a real-world point of view, but they make complete sense from the point of view of game design. As we saw above, Mario doesn’t gain running speed in a linear, asymptotic or gradual fashion. Rather, Mario has three speeds and he switches from one to the next after passing a certain number of uninterrupted blocks of distance. This is our x-vector, the side-to-side motion of Mario in the game. As for the other direction, it’s important to note that Mario’s jump speed is completely static. His jumps simply rise and fall without real acceleration or deceleration physics. He jumps at one speed, and falls at the same speed, with a very slight pause (about three frames long) in between ascent and descent. The only things that can modify his jump velocity are the presence of water, a springboard, or the use of the cape powerup in a glide.
The x-vector and y-vector are of enormous importance to the design of the game, because one of them always has a fixed magnitude. In most levels, the y-vector has a static magnitude; just as noted above, Mario’s upward jump motion only has two speeds. Even when soaring upwards with the cape or falling from a great height, Mario only ever moves along the y-axis at either jump speed or at cape-glide speed—that’s all. Even soaring up onto the highest platforms is a manipulation of the x-vector; Mario can only gain that extra height by increasing his x-vector magnitude (run speed) to its maximum. This is the reason why platform width is such an important datum: Mario needs that width to gain height. Once Mario is in the air, however, there are only two speeds at which he can move up and down: fall speed or cape speed. (Some master players can “blink” the cape glide in certain situations involving longer falls to fake a third fall speed, but this is very hard to do. There is a built-in cooldown on button presses that will start a glide, and so most players cannot switch back and forth between falling and gliding with meaningful results.) This means that in most levels, most of the problem-solving work of the player consists of these skills:
- Getting Mario to the right momentum
- Standing at/jumping from the right place
- Jumping at the right time
- Avoiding the sudden appearance of enemies
Those four skills correspond to the skill themes in the game, respectively: the preservation of momentum theme, the periodic enemies theme, the moving targets theme, and the intercepts theme.
Of course, there are also the water levels, and as you might expect these levels place a much greater emphasis on solving problems via the y-axis, but this doesn’t meant the necessary skills have changed. What’s really happened is that the game has literally turned sideways. In a water level, the vector scheme is reversed; now the x-vector magnitude (speed) is static and the y-vector speed can actually change. In a water level, the player has control over Mario’s ascent and descent speeds, and can zoom along the y-axis quite quickly and with a great amount of control. The player is unable, however, to change Mario’s x-axis swim speed in a meaningful way. There are only two speeds that Mario can move laterally in these levels: walk or swim.
Many of the challenges in a water level have to do with quickly going up or down in the water so as to avoid enemies or other obstacles. You can see how enemies in water levels are staggered so that Mario can ascend or descend between them.
Shooting these gaps in a dry level would require some serious jumping skills, but in a water level it’s not hard. What’s really happened here is not that the designers have removed platforms, but that everything has become a platform. Mario can jump at any time, he just can’t run. Naturally, this strips away the possibility of the designers using the platforming-declension themes (all water levels are either intercepts, periodic enemies or outside of the themes altogether). The moving targets and preservation of momentum themes are built upon the fact that Mario has to commit to a jump in the right way. The water allows Mario to “jump” (in a loose sense) at any time. The only problem with these challenges is that with fewer inherent design possibilities, the levels can become a bit repetitive. Each water level is different from the others, but they can feel slow and same-ish throughout because less is possible design-wise.
THE BIG CHANGE IN MARIO HISTORY
Now, despite all the detail laid out about vectors, the momentum mechanics present in Super Mario World are actually a simplification from earlier titles in the series. In SMB and SMB3, when Mario was moving at full speed, he was unable to come to a complete, sudden stop on an open plane. Instead, he would “slide” about half a block in the direction his momentum had been carrying him. This made for some frequent problems when landing on a narrow platform, since Mario’s momentum could easily carry him straight over the edge into pits and enemies. In order to compensate for this, many players would do a momentum-breaking back-jump in order to land on a platform.
As if the momentum weren’t enough, there is a very short (but potentially deadly) input lag/cooldown on Mario’s ability to jump. This has been eliminated from Super Mario World. The player’s ability to stop Mario’s horizontal momentum is now about as close to perfectly precise as human and technological limitations would allow at the time.
The second major change is in the arc of Mario’s jump. In SMB and SMB3, Mario’s jump arc was clearly divisible into sections. It’s easiest to understand if you see the diagram below.
The first part of Mario’s jump is a rapid ascent; the second part slows that ascent down, and then turns over into the beginning of the descent. The descent starts off slowly, and then returns to the initial speed. The reasoning behind this two-speed arc is that by giving Mario more time at the peak of his jump, it’s easier to land on a target like the head of a Koopa. (There may also be technological reasons for this, but we can only account for the design effects here.) The problem is that a two-speed jump makes the hardest jumps harder. Jumps that feature things like intercepts or moving targets are complicated by the fact that a player doesn’t just have to predict Mario’s landing point, but also how the slower, second stage of his arc might collide with the obstacles between the start and end of the jump event. Eventually the player will learn to do these things, but wouldn’t it be more straightforward just to have a uniform jump motion everywhere? Super Mario World changes things so that the motion of Mario’s jump is uniform throughout. In Super Mario World, when Mario jumps, he ascends at the same speed he descends, with only a tiny pause (about 3-4 frames) at the apex of the jump.
The meaning we find in a study of the vectors in Super Mario World is less obvious than d-distance or delta-height or any of those measurements. The highly refined, obvious and intuitive vector system in this game is in place to make this game not just accessible to an ever-broader audience, but also to give that audience the full experience of deep mastery while taking away the inherent problems of such. The Super Mario World team saw that they could accomplish more in their game by simplifying their basic mechanics and building up their advanced mechanics. The changes in Mario’s momentum and jump arc means that most of the deaths will occur because of a failure to understand things at the level of the challenge or skill theme, not at the mechanical level. While players who grew up on the earlier games might complain that this makes the jump mechanics more noob-friendly, it ultimately allows the designers to come up with more elaborate and inventive challenges. It’s much more rewarding for the player to fail at timing their jump between a spike and a fireball or bouncing off the head of an intercept than it is to simply slip off the same cliff five times. The simplification of the basic mechanics—specifically in how vectors work—allows for higher heights in player mastery for a greater number of players. Instead of sacrificing depth, it merely shifts the depth into the big-picture skills instead of the tiniest mechanics.