Beware of Second-Order Effects

Games are basically glorified math problems with metaphors partially covering the numbers and fancy symbols. The best games are usually interesting and engaging metaphors plastered over difficult math problems.

Unfortunately, game designers are a bit less apt at math than programmers. Being both a programmer and a wannabe designer, I approach game design from equal parts design and math. I’m no mathematician, but I have a toolbox of mathematical concepts that I use to better understand game design.

Many games fail to accomplish a semblance of balance because designers add mechanics and reward systems without a view of the broader math those mechanics will force their will upon. One such concept often missed: Second-order effects. Whereas a player’s superior skill has an additive impact on their effectiveness (a first-order effect), complex and over-rambunctious reward systems can multiply that bonus of skill into an insurmountable obstacle for less-skilled players.

The “Slippery Slope” of Success in Strategy Games

Imagine two players of measurably uneven skill at a certain strategy game. If they were to play against one another in this game, let’s say it’s a competitive turn-based strategy game whose result is based entirely on skill, the more skillful player would increase his advantage every turn. Every single turn the less skillful player would be losing by a wider margin than the turn before. The less skillful player can never win such a game and will lose the game each time by a predictably wide margin that has compounded each turn into a massive deficit. This is the nature of skill: this process of compounding advantage/disadvantage cannot be altered but by adding elements of chance and asymmetry to the game.

In reality, a player’s pure skill doesn’t directly map to a higher advantage turn-over-turn. The dynamics of a strategy game usually mitigate skill differences in the early-game (the first four moves in chess, for example) because there are fewer possible moves and those moves are usually somewhat obvious to even an advanced beginner. In most western strategy games, the number of possible moves explodes as the game progresses, peaking at some point in the mid-game, then tapering off due to fewer pieces being on the board, or the board position becoming more and more determinate as more pieces are places and static positions grow. A noticeable exception to this pattern is Go, which moves from a completely empty to a mostly full board throughout the game—leading to a continual restriction of possible moves and possible good moves.

As the game progresses and the strategy space widens, the player who can better distinguish successful strategies from unsuccessful ones will win. This discrimination between strategies is the essence of skill—players who are more skillful are better at discriminating between strategies that might, to a lesser player, seem to have the same utility.

At each point of decision, the more skillful player will choose a better strategy. The more viable strategies to discriminate between, the more of an effect skill will have. At each decision point, the better player compounds his advantage, while the less player sees the game slowly slipping away. The worse player can never make up ground.

(Humans do not behave uniformly, though, and skill is not static. We need to play against others in order to determine there skill, and players behave with different skill at different times. Playing a strategy game doesn’t degenerate as quickly or regularly as a describe here, because I’m describing ideal conditions—human flaws add much appeal to strategy games where otherwise such games would be repeated drubbings of less-skilled players.)

Skill => Success => Reward => Less Skill Required?

Designers love to reward displays of skill with game mechanical perks. Kill enough goblins and you’ll level up! You played well, so now the game is going to become easier. This kind of design is surprisingly dangerous if you want to design a game of skill and not a timesink or casual game. But it’s so intuitive—it rewards you for doing something well, which will make you want to continue to play. Using positive feedback to reinforce the actions in games that you want players to keep doing—this seems like a completely reasonable thought process.

Here we see a second-order effect. Certain mechanics multiply the player’s effectiveness beyond the normal turn-over-turn addition caused by outplaying an opponent.

Rewards can cause second-order effects that ruin the balance in games of skill; A second-order effect that quickly make matches unwinnable for the less skilled side by multiplying the effectiveness of the more skilled player, increasing his advantage by leaps and bounds as the match progresses. In lopsided and poorly-designed reward systems, actions at the beginning of the game are multiplied and lead to surprisingly enormous benefits later in the game, instead of actions at the beginning of the game leading intuitively to equally important actions later in the game.

I approach games of skill that involve vertical character advancement and gear collection with intense suspicion because I’m aware of how easily second-order effects can skew the players’ apparent skill levels and sap the fun out of what could otherwise be a strategically interesting game. Most of the time, game designers appear oblivious to what they are doing when they add rewards. They tack on external reward structures to make their games more addictive, but in the process they’re punishing new players who are necessarily less-skilled by giving a multiplicative bonus to the effectiveness of veteran, higher-skill players.

When designing a competitive skill-based games, reward structures need to be looked at with the utmost suspicion. They have a tendency to compound in broken ways—ways that quickly transform a game that would otherwise have numerous viable strategies into a one-dimensional, strategically uninteresting race for the first imbalanced reward.