Where does difficulty collide?

In item response theory, difficulty is a property of a test item placed on the same scale as the person's ability: a harder item requires more of the latent trait to be answered correctly, and in the Rasch model the difficulty parameter is exactly the trait level at which a person has a fifty-fifty chance of a correct response. Rasch's Probabilistic models for some intelligence and attainment tests defined this parameter so that item difficulty and person ability are expressed in the same units and compared directly. The referent is a location parameter of an item on a latent scale, estimated from response patterns, not the felt effort of a task or the tuning of a game.[1]

Unit

The trait level (in logits) at which an item is solved with probability one-half

Recovery means

Not applicable

Measured by

Estimated as the item's location parameter (or the proportion answering correctly) within a response model

In the psychology of motivation, difficulty is a feature of a goal or task that governs how much effort it mobilises: within the person's ability, harder goals reliably produce higher performance than easy or vague ones because they direct attention and sustain effort. Locke's Toward a theory of task motivation and incentives established this near-linear link between goal difficulty and output that became goal-setting theory. The referent is the demandingness of an assigned goal as it drives behaviour, a motivational variable rather than a scaling parameter of a test item or a design setting in a game.[2]

Unit

The level of challenge set by a goal, relative to a person's capacity

Recovery means

Not applicable

Measured by

Manipulated by assigned goal level and indexed by its effect on effort and task performance

In game design, difficulty is the level of challenge a game poses to a player, the gap between what the game demands and what the player can currently do, and keeping it in a productive band is central to engagement. Hunicke's The case for dynamic difficulty adjustment in games argued for tuning this challenge in real time to a player's performance so that a game stays neither trivial nor overwhelming. The referent is a design property of a game experience, adjusted and sensed through play, distinct from an item's scaling parameter or the demandingness of a motivational goal.[3]

Unit

The level of challenge a game presents, often tuned to player skill

Recovery means

Not applicable

Measured by

Gauged by player success and failure rates, completion times, and responses to difficulty adjustment