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An Examination of Skill pt.17

The skill spectrum is a complex system. Essentially, it's a combination of the the "human machine" and interactive design. For the purposes of this article I will focus on video games as the primary interactive system. To illustrate how the several parts of the skill spectrum affect each other I will use a bit of math logic to explain what happens to each of the 5 facets of skill as a game's speed increases to infinity. 

For those who generally experience anything close to a slight trepidation in the face of a mathematical equation, allow me to alleviate your fears. Not only are the math like expressions I'll present fairly intuitive, but I'll explain everything clearly in words. 


To start we have to declare/understand a few things.

  • t = game speed. How every frame of a game relates to real time. A game running at 60 fps means that each frame of game time takes up approximately .017 milliseconds of real time. 
  • k = the constant of agency. This is a conceptual figure that frames the upper rage of player agency, or the player's capacity to to act. The figure is based on the following truths. 
    • A game can only be played or interacted with to a degree equivalent to its fps. In other words, time and space are not infinitely divisible in a virtual world. The frame is the quantified measure of existence and therefore interactivity. We can refer to this truth as the law of frames. This law mostly applies to simple, singular game systems as opposed to networked system with multiple coordinated CPUs. 
    • Depending on the controller type, how quickly one can manipulate the controller is another limiting factor. If the system can only register if a button is pressed or released every frame, in a 60fps game, one can only press a button a maximum of 30 times/second. For analog sticks and motion controls there's additional potential for limitations some of which are set by the amount of force it takes to break the unit. This skill ceiling, maximum level, is denoted by a capital D.
    • Knowing that the brain has physicochemical limitations that are well beyond the scope of this blog and this investigation, we can simplify things by stating that all mental activity and knowledge processing is equivalent. This factor is denoted by K. As long as one is thinking, one exercises their agency outside of the game system. When it comes to outputting (manipulating the game according to mental processes), such an act falls under other skills and like dexterity and adaptation. 
    • The capacity to adapt (A), respond reflexively (R), and time actions (T) are all very dependent on game time. Though humanly impossible, the fastest reaction time one can have to a stimulus from a game system is 1 frame. Interestingly, the fastest one can adapt to a situation in game is 0 frames, which essentially requires one to accurately read or guess the situation and act in anticipation.
    • Because varying examples of timing elements are game time dependent, each timing element in a game is unique. This means that the different timings can't be compressed or optimized. To get an accurate measure of the range of timings a game has, one must define a range and collect data (in frames) of all the different possibilities and mechanics. More on this later.


Now we can consider what happens to k (the constant of agency) as t increases approaching infinity (--> ∞).

as t --> ∞, D --> 0

  • As the game time increases approaching infinity the skill ceiling of dexterity shrinks proportionally to 0. Think about it this way. The faster the game moves the harder simply inputting becomes. It's like trying to play a video game while moving in slow motion (unless the game is turn based). Even your fastest inputs will become father and farther apart from the game's perspective. Interestingly, if we zoom in to the facets of dexterity skill, as the game time gets faster only the speed facet is shrinks. Power, control, harmony, efficiency, and stamina all stay the same. 

as t --> ∞, K = K

  • As the game increasingly becomes faster one's knowledge skills remain constant. Like I described above, what goes on in your head is outside of the game system. This means that whether the game is zipping by really fast or at normal speed, your mind is largely unaffected.

as t --> ∞, AK --> guessing

  • When it comes to taking in information, processing, and outputting, such knowledge based (tier 1) adaptation skills diminish to nothing as a game increases in speed. If you think about it, after you take in the information from the game, the relevancy of that information begins to fade. The faster it fades, the less effectively one can adapt. For example, if you see a Goomba walking at you there is a limited amount of time before it kills you. In that time you can come up with all kinds of strategies and ways to handle the situation. But, if the game moved forward at a very fast speed, by the time your brain even "sees" the Goomba you could already be dead. As t increases, challenges that you had plenty of time to think of solutions, you have to react to. As t increases even more, situations you had to react to can only be overcome with a pure guess. Yes, luck, guessing, or "reading" is a part of one's adaptation skills. 

as t --> ∞, R --> 0

  • Good reaction times are around 10-12 frames (at 60 fps). If a game challenge has a reflex window that's smaller than your best reaction time, then you can no longer react to it. 

as t --> ∞, T --> 0

  • As the game speed increases, all of the timing elements (∑T) get compressed into increasingly smaller amounts of real time. Unfortunately what's unique about timing elements in a game is that they take up consistent amounts of real time. Because each timing element is unique and uncompressable, the potential range of skill shrinks as the game speed increases. On the plus side, as the range of skill shrinks, the timing challenges fundamentally change creating new challenges. 


From these expressions we can understand that t (game speed) affects how effective our skills are in disproportionate ways. This is a perfect example of how tier 3 adaptation comes into play with video games. Whenever you have a change in game speed, adjusting involves tier 3 adaptation. 


In addition to the above effects, we can also look at the ways players can augment one skill for another with tier 2 adaptation as t (game speed) increases to infinity. 

  • Reflex can be augmented with Knowledge. Like in the StarCraft static defense example, there are precautions and strategies that can be used to aid in a lack of reflex skills even if it's due to an increase in game speed. 
  • Reflex can also be augmented with Adaptation even if the adaption is pushed to a point when one must correctly guess to be successful.
  • Timing can be augmented with Dexterity. If you don't know the timing necessary or you get out of sync, depending on how the mechanics are designed you can increase your success by button mashing (rapidly hitting buttons). In the best cases, you can do better by intelligently mashing than you can trying to play it straight.
  • Dexterity can be augmented with Knowledge. If you can't input accurately enough because of the increasing game speed, there may be strategic workarounds. Whether you add/drop a few moves or change your entire strategy, the better you understand the game system the more successful the augmentation process can be. 
  • Knowledge cannot be augmented with another skill. The capacity to use knowledge to adapt only degrades as a game increases in speed. Though the long running, learned information stays constant, the new moment-to-moment information more quickly becomes irrelevant as the game speed increases. 


If you'll notice, all of the augmenting that can be done with tier 2 adaptation puts a great emphasis on knowledge and adaptation (guessing) skills. While design wise this trend can be a key part of a game's challenges and the overall gaming experience, from my experience there are many games that suffer from featuring game speeds that work against the full skill spectrum. 

Notice how the time to play each micro game gradually shrinks (see video above). You can feel it in the gameplay, and you can hear it in the music. The point of the tempo increase in the WarioWare series is to push you to your limits by making seemingly easy/simple games deceptively difficult. 

It is not common for games to feature increasing game tempos. The following is a list of games, modes, or levels that have successfully designed challenges around the disproportionate decay of the skill spectrum as the game speed increases.


In part 18 we'll check out the flip side, ie. what happens to the skill spectrum as the game speed decreases. I think you're in for a surprise. 

« An Examination of Skill pt.18 | Main | An Examination of Skill pt.16 »

Reader Comments (2)

You are really doing all my work for me with this series here. It's genius stuff and stuff that I've been meaning to write about more. I'm very interested in breaking down skill in games, especially physical skill, and figuring out how to add it (I love hardcore actiony games with good feel).

November 30, 2011 | Unregistered CommenterJohn Mawhorter

@ John Mawhorter

Thanks. I'd like to know more about your research and thoughts. We should talk. I'm usually online in the evenings.

November 30, 2011 | Registered CommenterRichard Terrell (KirbyKid)

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