Early iterations of the grey box demonstrated a fundamental flaw in the design. Although play was becoming intensified as it reached the center of the map, a secondary mechanic was emerging; players became aware that it was possible to farm the outer ring of the map and rack up numerous spawn kills. As a result of testing, edges [corridors] 1 and 2 were raised to create one-way gates, allowing them to feed players into the map but not allowing players already within the map to access the spawn points. The elevated corridors were re-conceptualized in the physical space as maintenance shafts, as can be seen below in Figure 33.

Figure 33

The placement of pickups also benefited from the molecule design approach and followed a similar symmetrical layout to the level geometry. Although the use of symmetrical molecules creates an easy workflow for designing the map, too much symmetry is often boring and even confusing for players.

To address this issue, asymmetry was used to create navigation landmarks for the players as well rooms that highlighted different types of weapons and game mechanics. Differences in each room's layout served two purposes: to aid with player navigation and to create "perceived" advantages to each room. Perceived unfairness suggests no matter how fair or balanced a system is, players will be drawn to elements of the game that they believe are broken, even if they are not.

In essence, each room in the second ring contained a different type of spatial molecule. The molecules differed by varying choke points and cover elements. The result of this can be seen in the comparison between Figure 34 and Figure 35; both are rooms in the second ring and both offer different types of play experience within them.

Figure 34

After further iteration and testing, it was found that players were entering the primary room more than the second ring / medium rooms, but not at the expected proportion. The intensity of the play experience needed to be very high in the center room and there simply was not enough player traffic to achieve the desired experience. Of course, this could have been addressed with revising the space to make it smaller, however as much of the level art had already gone into production, it became necessary to look at alternative option.

To amplify this experience, a second ring of player spawn points where created on the mezzanine floor of the secondary ring. The walking distance to the center room from the upper spawns was shorter than the ground floor and therefore encouraged far more traffic to the central room and as such created the desired effect.

Figure 35

The two stacked spawns in Figure 36 did not have the same spawn-to-engagement times to the mid rooms. In other words, the edges above were not equal to those below when they should have been. By changing the position of the spawns in line with the revised molecule design, time to engagement was negligible when compared with the existing spawn points.

Figure 36

Symmetrical molecules create fair distribution of stairs and elevators in the map; however, the actual design of each of these three elevators is varied intentionally (Figure 37). The rationale for this approach was to highlight the psychology of perceived unfairness. Via testing, it was shown that most players thought that the stairs near their spawn point gave them the advantage, and that this advantage was not used against them. Asymmetry was also used in the design of stairs themselves, again this served two functions: to assist with navigation and vary the play experience in the medium rooms.

Figure 37

Another strategy that was used for balancing was not in the graphing theory itself, but highlights how graphing theory can help read player behavior. A Kismet script was created where every three minutes the game would compare the number of players that have passed through each of the six medium rooms and determine which one had the least traffic. The room with the least activity would then spawn a trigger.

When pressed by a player, this trigger would vent every other player into space, killing them and scoring multiple kills for the instigator. (Figure 38 is a view from above the map, and the last thing a player would see before dying.) This encourages "heat" where there is least, therefore creating a dynamic balancing system through mechanics rather than the static graphing. When presented with this scenario, players are given a choice to exercise Steiner point solutions to resolve the spatial problem -- what is the shortest route to the target.

Figure 38

Once the script had identified the room with the least traffic, all players in the map receive both an auditory and a console announcement letting them know which medium room the trigger is available in. Depending on the player's current location, they are presented with two main choices. They can use the risky, but shortest path through the center OR they can navigate the longer, but safer path through the medium rooms, avoiding the central conflict area.

By doing so, we have created two different strategies for players; they can use the middle room as a Steiner node or use the outer rooms as a spanning tree solution (Figure 39). These strategic options play to a player's sense of accomplishment. The player feels a sense of pride, as they feel they are outwitting the rest by taking a shortcut to the proper room. Level assets used to populate the various rooms also served to reduce the total amount of possible Steiner points, creating higher intrinsic value for finding one of the limited solutions.

Figure 39

The final published map went through eight major revisions, resulting in updates to either the grey box or the molecules themselves to achieve the final product. Underpinning each revision was a revised molecule concept that would then be converted into a grey box. As such, each revision had clear objectives and goals and the final product benefited greatly from this, as time was extremely limited.

Conclusion

People like Dan Cook and Chris Crawford look at how people's motivation to play games stems from our need to learn and prove these new gained skills. Raph Koster takes this notion further by being even more specific; people are pattern-finding machines and we take pleasure from games when we identify patterns and pre-empt them. It therefore stands to reason that using the pattern-based approach of molecule design to define play spaces immediately plays to this desire.

There is one main consideration to keep in mind; the player doesn't perceive the game as a planar map; they sense it from their own camera frustum. As such, the scale and "identifiability" of the molecules you want to implement is very much limited by how much of the game world the player can perceive at any one point in the game.

Too often designers create labyrinth type maps, which -- although being easily understand from a planar perspective -- are absolutely impossible to traverse when viewed through the limited perspective of the player. As such, molecules and the patterns that they create need not necessarily be complex in order for them to be "fun" for the player.

Instead, well designed game spaces tend to have a number of nested molecules, rather than a molecule that defines the space as a whole. The practical example created by Nassib Azar is relatively simple from a graphing perspective, however the amount of molecule permutations created by the dynamic game elements create a diverse, yet manageable set of strategies for the players to explore.

It is important to point out the use of graphing theory to conceptualize and analyze game spaces is not a new idea, but rather one that has been discussed in various forms by different authors. The original inspiration for this research came from Raph Koster and his Games are Math presentation, and I would recommend Koster's work to anyone interested in rational approaches to design. Joris Dormans also has a few informative articles that deal with how graphing theory can be a powerful tool for level designers. Dormans' Adventures in Level Design and Level Design as Model Transformation [pdf links] are excellent and display the malleability of this toolset.