Emergent Mathematics pt.1

Emergence is wonderful, mysterious, and unpredictable. Like with Conway's Game of Life, a few rules and the right core gameplay dynamics can produce infinite unexpected possibilities that may even reflect the truth of the universe. The reason emergence can produce such surprising results is because humans aren't very smart. Our limited cognitive abilities and our poor ability to consider all factors allows the result of a step by step process to seem like it has a life of its own. So if our limited understanding of emergence gives it that surprising "anything-is-possible" feel, then as we deepen our understanding of emergence we should come to new insights. In this article I present 3 such insights that work to make the emergence of gameplay a little more predictable. The ideas are pretty high concept. I suggest being familiar with the concepts of DKART skills, design space and wrinkles, interplay, tactics and strategy, metagames, and emergence to fully grasp the ideas.  

 

Reflex Range

I came up with the concept of a reflex range in response to comments on how slow the combat is in Street Fighter 4 and Super Smash Brothers Brawl compared to other fighting games. I think the gameplay of these games is quite fast. The characters may not move across the screen as quickly, but the windows players have to react within are just as tight and possibly more frequent. Supporting this stance is more difficult than comparing frame data. Speed and time in video games is a lot more complex and nuanced than many realize. I don't think there is a better way of approaching this topic than using the DKART skill system, which explains the sensation of speed as well as our conscious limitations as we understand it in real-time.

To understand time, we must examine how we perceive it moment to moment. Time awareness is basically our reflexes constantly firing. To understand reflexes best we must first start with knowledge skills. According to my theory, all successful, long running competitive mutiplayer games stress knowledge skills the most out of all the DKART skills. Not only does the knowledge skill ceiling increase as a game's metagame evolves, but knowledge enhances every other facet of the DKART skills. Because how quickly we process images and how well we can respond in a given situation is largely dependant on our knowledge of the stimuli, it becomes clear how our sense of time and speed are connected to our knowledge. I explained this here when I covered reflex skills. One key thing to note is the more stimuli we have to process and the more outputs we have to match up with the stimuli, the slower our reaction times. You can test this for yourself by playing our free game Reflex.

It turns out most people have fairly similar reflex capabilities. The difference between gamers with really quick reflexes and gamers with slow to average reflexes is merely a fraction of a second. Furthermore, the effect that increased stimuli and matched responses has on slowing our reflexes also seems to slow down everyone proportionally. The likely explanation for these results is that our brains and biology are mostly the same. Because of our physical similarities we have similar reflexive abilities. Unlike dexterity skills where facets like strength can be increased by building muscle, we can only enhance our reflexes with our knowledge. In other words, knowledge is the biggest reason why the pros are so much better at hitting targets in FPSs than non-pros. They know where to look ahead of time and combine this filter with other match and metagame specific data to decrease the aiming reticle travel time and simplify the reflex challenge as much as possible. Pros call this pre-aiming.

Here's where the concept of the relfex range comes into focus. The idea is there are 3 specific ranges of reflex based interactions; too fast, skill based, and too slow. Some of the fastest reflex times land at around 10/60ths of a second or 10 frames. In these situations, the user is most likely completely focused on the test, which is a simple, one-stimulus one-response test. Knowing this, we safely assume that any mechanic or challenge that must be countered in under 10 frames is in the "too fast" reflex range. So, 10 frames marks the lower boundary. 

The upper bounddary is an amount of time that nearly 100% of players can comfortably react within given sufficient knowledge of the challenge. Remember, we're not concerned with the time it takes a player to encounter a new stimulus, learn the complexities involved, and then react accordingly. We're only looking at the fastest stimulus and response times. I don't have any data to mark the upper bound, so let's just say 1 second is enough time. 

The reflex range is the upper and lower bounds of time where reflex skills can be stressed. And it turns out it's approximately between 10 frames and 60 frames. This is where conscious, real-time, speedy action gameplay occurs. Anything below the lower bound nobody can react too. Attempting to counter anything this fast at best is an educated guess. Anything longer than a second, everyone can react too with little problem. This explains why so many mechanics in action games have counter windows within the reflex range. See Smash Bros Brawl character frame data here. See the frame data for many other fighters here.

Designing mechanics or challenges above and below the reflex range boundaries is  a great way to add variety to gameplay. If you think the -10 frame mechancis would be too powerful and the 60+ frame mechanics would be useless, think again. There are countless ways to balance the effectiveness of a mechanic. Faster moves often have less power and range. Slower moves tend to be stronger (read more on the mechanical balancing formula here). And there's always recovery frames to make it harder to defend yourself afterwards. So, as long as there is a risk-reward balance the emergent gameplay should have variety.

With mechanics and other elements players cannot react to (below the lower bound) the only way to counter them is with prediction. Getting "reads" and the concept of yomi are greatly enhanced when a game features mechanics and strategies that cannot be countered with reflexes. Blind mixups are just a few types of mixups that can only occur when one or more players cannot react to a threat to make a proper counter. By using -10 frame mechanics to force your opponent into reacting preemptively, you can gain more time to execute very slow moves. The idea is, if the opponent focuses on what might happen and reacts to a possibility, then he/she will be "blind" to your actual moves. Get your opponent to react the wrong way and you can land moves in the 60+ range. Influencing and reading expectations like this is what many refer to as making hard reads. I fully explain such emergent gameplay in my article series Complex Time Simplified.

In conclusion, game speed in the way that it matters to gameplay has little to do with action frequency. You can press a lot of buttons and feel like you're crawling along (Metal Gear Solid 4 ending). Or you can hit a few buttons and feel like you're rocketing along at high speeds (Super Meat Boy Naija). It also doesn't matter how fast the animations look. One of key takeaways about the reflex range is that when gameplay actions/challenges are too fast, we play preemptively based on our knowledge (ie. educated guesses). When gameplay actions/challenges are within the reflex range we play actively, in the moment, and by using our knowledge skills to filter stimuli. And when gameplay actions/challenges are too slow, everyone can react accordingly processing the task in STM. If the STM gets overloaded, we'll either freeze up or revert to the same kind of guesswork that we use when the gameplay actions/challenges are too fast.

So, simply by looking at the range of timings for mechanics and general gameplay challenges, you can now make stronger predictions on how the emergent gameplay will turn out. In part 2, we'll look at the line between tactics and strategy.