Since 500 BCE, the arts and sciences have studied and utilized the Golden Ratio in their work. Either consciously or subconsciously, the usage and recurrence of the mathematical constant 1.618 and the proportion of thirds in nature, architecture, and biology is one that has kept boffins and people who wear bow ties intrigued for years.
In Gears of War 2, guided by the Golden Ratio, the player's eye and Marcus' path are channeled between the two buildings, with the main action area staying in the bottom third of the screen.
At the risk of comparing Bayonetta's currency progression system to the works of Pythagoras and Da Vinci, the Golden Ratio is also in active use in video games, as a modern day medium where art and science collaborate.
For the purposes of simplicity, though there are many equations and diagrams that can aid the definition of the Golden Ratio, we'll consider an approximation -- the relationship between one-third and two-thirds.
This ratio creates an interesting asymmetrical balance, and is often used as a compositional device. In this guise, the Golden Ratio can be extensively seen in game interface design, camera positioning, and environment layout.
If we take a broader look at the mathematics around gameplay length, the Golden Ratio can also bear some interesting analysis there too.
Dependent on genre or platform, one statistic that remains generally constant is that a third of purchasers actually finish games, according to research we did at sony.
In today's world of "butterfly media" (where users move rapidly between different media sources), traditional games now fight for spare time with many other electronic activities, such as TV, social networking, and mobile gaming/internet browsing. It's worth considering, then, that the chances of players actually getting that final Weapon of Epicness or reaching that Ultimate Boss Battle are generally quite slim.
Therefore, one good usage of the Rule of Thirds is to keep splitting your total game length into thirds until you reach a "gameplay bite" length of around half an hour (the average time spent by players in a session).
When in cover, the camera in Splinter Cell naturally moves into position so that Sam Fisher takes up a vertical third of the screen, with his eyeline hitting the top horizontal third.
If you ensure that some new experience or gameplay change or substantial reward is synchronized with these half-hour session, you can be more confident that the player is going to keep returning to the game because to them, regular and meaningful "carrots on sticks" provide compelling gameplay rewards.
Evidence of this can be seen in some of the more memorable and successful games of the past few years, such as Resident Evil 4, Uncharted 2, Shadow Complex, and Batman: Arkham Asylum, all of which continue to throw brand new experiences at the player.
Whether that's with a new mission type, weapon, location change, story twist, character introduction, or power-up, the regularity of these incentives may keep the player involved beyond their traditional cutoff point. Subconsciously, players look forward to the next reveal, since they know they won't have to wait very long for it.
A simple interface in Mass Effect 2 allows the player to reconstruct Commander Shepard's face. This is made all the more aesthetically pleasing and user-friendly through the lens of thirds.
On Need For Speed: SHIFT we achieved this by layering multiple reward mechanisms of Cash, Badges, Stars, and Driver Levels in order to create a persistent urge of "just one more race" within the player. Where possible, these were timed to occur within half hour bites, and at a higher level, we used the concept of thirds to structure the introduction of game modes, Tier unlocking, track and car reveals, and communication of the roadmap for the player's final entry into the NFS World Championship.
We also provided sneak peeks of future events in Career in order to give the player a chance to experience our equivalents of the Weapons of Epicness ahead of time. Telemetry showed that over 55 percent of players reached the penultimate tier in the game due to these choices, significantly higher than the baseline statistic.