Engagement curves are the curve over time for a particular type of engagement for a particular person (i.e., how much of that type of engagement are they feeling at each moment). The height of these curves is the depth to which each type of engagement was felt, which can can be difficult to nail down precisely (and being really precise here is not necessarily that useful). The set of all engagement curves for a particular person gives a very high-level map of how the overall experience felt to them. This entire set is what we are referring to when the term "engagement curve" is used without specifying a specific type of engagement. The specific engagement type will be referred to ("challenge curve", "accomplishment curve", "sensation curve", etc.) when talking about a single type of engagement. It is generally desirable to have multiple types of engagement peak at about the same time to create really powerful engagement peaks.
The time scale of an engagement curve can be at the micro, macro, or meta scale, but usually it is most useful to focus on the curve across multiple segments or episodes (the macro scale). Only segments and episodes will be talked about below, but engagement curves are fractal in nature and are present at whatever scale you happen to be operating at. For example, the anticipation of a gun firing as you aim and begin to pull the trigger (with the reward being a hit and the punishment being a miss) creates a moment of tension that can drive engagement at the micro scale. Building anticipation for a new release in a series, or for a convention for fans of a series, can help create long-term engagement at the meta scale. Meta scale tension is the slowest building, but creates a strong foundation of engagement to build macro scale tension on. Micro scale tension, which builds very quickly, can then be used to create exciting spikes on top of the macro and meta layers to create extremely high engagement.
Standard Engagement Curves
While there is no perfect form that an engagement curve should take, in practice there is a "standard" form that you will usually want to be aiming for. A standard curve starts with a moderate spike of engagement in the intro segment or episode to get your attention and draw you in to the episode or title. It then drops back down a bit before steadily rising as shown in the chart on the right. The highest peak is the finale segment or episode, while the small peak at the end is the outro segment or episode.
In this chart, each segment or episode has a peak in engagement, while the valleys of lower engagement are between the segments or episodes. These valleys are critical in allowing you to "catch your breath" and prepare for the climb in engagement to the next peak. Without these valleys, you will become habituated to or burned out by the tension driving the engagement of the experience, and engagement will not be able to build, or could even rapidly drop.
Engagement valleys can also be entire segments or episodes. The first chart below shows how you could get the same kind of engagement curve as the one above, but with twice as many segments or episodes. However, in this case, the segments or episodes alternate between "peak" segments or episodes and "valley" segments or episodes. Either method can work well, just as long as the shape of the curve is good (although staying at a peak or in a valley for more than one segment or episode will generally not work). There is also nothing particularly special about the number of segments or episodes (although 6 to 10 is a pretty good default). The second chart below shows how to create a standard engagement curve if there are a lot of segments or episodes. In this case, the peaks will generally need to build more slowly, and the valleys will generally need to be a bit lower, in order to avoid habituation or burnout.
"Perfect" Engagement Curves
It can be tempting to try to create a "perfect" engagement curve instead of the standard curves shown above. This might be a curve that starts at a really high engagement level and stays there (see the first chart to the right) or a curve that builds over time (see the second chart to the right), but still starts at a very high engagement level and doesn't have very deep valleys. The problem with these curves is that the only way to get them is to increase the tension of the experience to such a high level (or so quickly), that overload or burnout are assured, and the desired engagement will not actually occur. As a general rule, engagement can never start at a level above a 6 and can never go up more than about one level at a time.
Short Engagement Curves
If an engagement curve is too short (generally below 6 segments or episodes), it can be very difficult to build the engagement to a really high level. There just isn't enough time, and you may even have to sacrifice the intro or outro segments or episodes to make it work (see the charts to the right). This can be fine when working with an early episode that doesn't need a high engagement peak, but later episodes will generally need to be longer.
Problem Engagement Curves
The charts to the right show the three most common types of engagement curves that have major flaws and need to be fixed. A bad-ending engagement curve is one that was going great, but had a weak finale. Even if the finale had a decent level of engagement, it will feel much worse because you were expecting to get a 9 or 10 in the finale, and you only got a 6 or 7. If the finale is not improved, the engagement for the entire episode or title will be undermined. A flat engagement curve doesn't actually look completely flat--it is just a curve that never built properly in the middle segments or episodes. It may still have a finale, but it won't be very strong because of the flat middle. A weak engagement curve is one that starts out okay, but then just keeps dropping until you finally quit. This is usually caused by repetitive content that does not build up at all or builds up too slowly.
Multiple Engagement Curves
The overall engagement curve for an experience rarely comes from just a single type of engagement. When an experience has multiple core types of engagement, they all add together to create the total engagement (note that they do not add linearly--levels of engagement are best thought of as an exponential scale, like volume or earthquakes). To get really strong total engagement peaks, an experience will generally need to have several types of engagement peak at the same time.
The chart to the right shows an example of how this might be done. A first-person shooter would normally be primarily about challenge, which in this example is the main contributor to the total engagement. But by making sure that accomplishment also peaks when you defeat a set of enemies (getting a new weapon, experience points, rescued hostages thanking you, etc.), and by creating peaks of sensation at the same time (bullet-time for the final shot, big explosions, epic victory music, etc.), the total engagement is pushed higher. This type of synchronization can easily make the difference between a finale being a 9 (very cool and satisfying) and a 10 (over-the-top epic and amazing).
Resonance and Dissonance
Multiple engagement types only actually add together if they resonate with each other. This requires careful crafting to make sure the combination of engagement types feels good and makes them more than just the engagement they would create on their own. It is very easy to have the different types not feel connected to each other very strongly and therefore not actually create the effect shown in the chart above. For example, a game that had you fight the one who killed your father (fellowship), using the combat techniques your father taught you (challenge), then rewarded you with your father's magical sword that your enemy had been using (accomplishment), which you then could use to win freedom for your people (catharsis), would likely have much more resonance (and therefore engagement) than a game that just had you fight unconnected enemies with randomly generated items and no real plot.
In some cases, using the wrong types of engagement at the same time, or just combining them poorly, can result in dissonance, which actively destroys the engagement you would otherwise have. For example, a game that attempted to combine challenge and catharsis might create a finale where you fight the ultimate villain of the whole game. The final fight could be well-crafted, and the plot that has driven you and the villain to this point could be excellent, but if at the final moment of the fight, when you are about to win, the game just goes to a cut-scene (even a very well done one) to show the final blow, then dissonance will be the result. The problem is that the player should be the one who gets the satisfaction of making the final strike, and taking that away undermines both the challenge and the catharsis. Even if it is still engaging, the total engagement will be lower than either the challenge or the catharsis would have been on their own.
Complementary Engagement Curves
Another good way to approach multiple engagement types is to make them complementary (instead of synchronizing them). This is done by creating a peak in one type of engagement (or multiple types) during a valley in another type of engagement (or multiple types). For example, a role-playing game might have peaks of challenge each time a set of monsters is defeated, but have peaks of catharsis in-between those fights that are created by narrative cut-scenes or dialog.
This type of "complementary" engagement is shown on the chart to the right. While the chart shows just two types of engagement, it can actually be a lot more complex. The peaks for the catharsis might only occur every odd-numbered episode, while peaks of accomplishment or discovery might occur every even-numbered episode. Note that the total engagement when using this approach can be more consistent, as you will generally only get habituated to or burn out on a single type of engagement if there are no valleys in that particular type of engagement. It can be harder to get a higher peak at the finale when using this approach, but you can often switch to the multiple synchronized engagement types approach as you get close to the finale.
Tension Drives Engagement
Since tension drives engagement, it is useful to plot the amount of tension over time along with the engagement it creates (as shown on the chart to the right). The peaks in tension match the peaks in engagement. A good metaphor for how this works is pushing a person on a swing. Each push is a spike in tension (which has to be timed right), and the force of the push (i.e., the amount of tension) can be increased with each swing. Note that the engagement does not drop as low as the tension does (there is usually little to no tension during the valleys). This is because engagement has a "momentum" to it; it doesn't just disappear when the tension disappears. Also note that there is a gap between the tension peaks and the total engagement peaks (if the game is well-constructed). This gap is due to resonance with other engagement types and is a good thing, as it means the game is not too tense even when the engagement level is very high.