GOMS

"None of the techniques address user unpredictability - such as user behaviour being affected by fatigue, social surroundings, or organizational factors. The techniques are very explicit about basic movement operations, but are generally less rigid with basic cognitive actions. It is a fact that slips cannot be prevented, but none of the GOMS models allow for any type of error. Further, all of the techniques work under the assumption that a user will know what to do at any given point - only applicable to expert users, novices are not considered."

"Functionality of the system is not considered, only the usability. If functionality were considered, the evaluation could make recommendations as to which functions should be performed by the system (i.e. mouse snap). User personalities and habits are not accounted for in any of the GOMS models. All users are assumed to be exactly the same."
Wikipedia

CMN-GOMS
@ARTICLE{Card1980,
author = {Stuart K. Card and Thomas P. Moran and Allen Newell},
title = {The keystroke-level model for user performance time with interactive
systems},
journal = {Commun. ACM},
year = {1980},
volume = {23},
pages = {396--410},
doi = {http://doi.acm.org/10.1145/358886.358895},
number = {7},
address = {New York, NY, USA},
issn = {0001-0782},
publisher = {ACM},
}

"... there are many different dimensions to the performance of a user-computer system"
p.396

Time
Errors
Learning
Functionallity
Recall
Concentration
Fatigue
Acceptability

"there is no single kind of user. Users vary along many dimensions"
Knowledge of the different tasks
Knowledge of other systems
Motor skills
Technical Ability
Experience with the system

"there is no single kind of task"

"the model to be presented is specific to one aspect of the total user-computer system: how long it takes expert users to perform routine tasks"
"The central idea behind the model is that the time for an expert to do a task on an interactive system is determind by the time it takes to do the keystrokes."
"We havve formulated the prediction problem to predict only the execution time of unit tasks, not the acquisition time."
p.397

"Task acquisition times are highly variable, except in special situations (such as the manuscript interpretation situation): and we can say little yet about predicting them."
pp. 397-398

"Two important assumptions underlie our treatment of execution time. First, execution time is the same no matter how a task is acquired. Second, acquisition time and execution time are independent"
"A method is a sequence of system commands for executing a unit task that forms a well-integrated ("compiled") segment of a user's behavior".
"We are simply ignoring the tasks containing errors and only predicting the error-free tasks, for we do not know how to predict where and how often errors occur. But if the method for correcting an error is given, the model can be used to predict how long it will take to make the correction."

"The Keystroke-Level Model asserts thatthe execution part of a task can be described in terms of four different phyical-motor operators: K (keystroking), P (pointing), H (homing), and D (drawing), and one mental operator, M, by the user, plus a response operator, R, by the system."
"K refers to keys, not characters (e.g., hitting the SHIFT key counts as a separate K). The average time for K, tK, will be taken to be the standard typing rate, as determined by standard one-minute typing tests."
"Users can differ in their typing rates by as much as a factor of 15."
"If a user population has users with large tK differences, then the population should be partitioned and analyzed separately, since the different classes of users will be likely to use different methods."
p. 398

What about with Wii games, are all K the same? What about twisting, balancing pitch / yaw? How about Wii Fit balance games - it's all about error between the brain (which understands the goal and how to achieve it) and body (physically learnt motor response).

"Thus, in making predictions we can use the model to compute the times for the alternative methods and predict that the fastest method will be used ..."
"The optimality assumption holds, of course, only if the users are familiar with the alternatives, which is usually true of experts ... This assumption is helped by the tendency of optimal methods to be the simplest."
p. 400

True for competition gameplay but not for creative, fun, exploration.

"... the basic design of the experiment was to have ten versions of each task on each system done by four different users, giving 40 observed instances per task-system. No user was observed on more than one system to avoid transfer effects. Four tasks were observed for each of the text-editing systems, five tasks for each of the graphics systems, and one task for the executive subsystems."
"There were in all 28 different users (some technical, some secretarial): 12 for the editing systems, 12 for the graphics systems, and 4 for the executive subsystems. All were experts in that they had used the systems for months in their regular work and had used them recently."
"Each experimental session, lasting approximately 40 minutes, was videotaped and the user's keystrokes recorded automatically."
p. 402

What constitutes and expert gameplayer? One who's played through the whole game and is only replaying parts they've already played through and have learnt the correct responses to? What about deathmatch where the game, level, etc are well know, but the competitors' responses are the unknown factors, and for which there's no clearly defined best method?

"Acquisition time began when the user first looked over to the manuscript to get instructions for the next task and ended when the user started to perform the first operator of the method. Execution time began at that point and ended when the user looked over to the notebook for the next task."
pp. 402 - 403

"Those tasks on which there were significant errors (i.e., other than typing errors) or in which the user did not use the prescribed method were excluded from further consideration. After this exclusion, 855 (69 percent) of the task instances remained as observations to be matched against the predictions."

"... prediction error appears to be rougly proportional to duration. The roo-mean-square (RMS) error is 21 percent of the average predicted exeuction time."
"Prediction accuracy is related to the duration of the attempted prediction."
"Since unit tasks are essentially independent, prediction of the time to do a sequence of tasks will tend to be more accurate."
"The accuracy of the model is somewhat inflated by the determination of one of its parameters from the data itself. The substantial variability of tM indicates that this inflation is probably not too serious, which is to say that small changes in the value of tM do not make much difference."
"it should be noted that the tM estimated from this experiment is now available as an independent estimate for use by others."
p. 403

"The RMS error of these predictions is 21 percent, which is just as accurate as predicting the execution times alone."
p. 404

"Given the method used, the time required for experts to perform a unit task can be predicted to within about 20 percent by a linear function of a small set of operators. This result is poweful in permitting prediction without having to do any measurements of the actual situation and in expressing the prediction as a simple algebraic expression. Its limitation lies in requiring that the method be completely specified at the level of keystrokes and in being limited to error-free expert behavior."

Error-free behavior is the exception in gameplay regardless of the users level. If it weren't then the game would probably not be challenging enough. See also Flow.
Also, how can we be sure that the techniqued used is the best one for each situation? Especially complicated with embodied games like Wii Fit where the challenge is not cognitive but rather control of one's own body, or Wii Sports boxing where there's no clear tutorial or feedback on how to do each punch.

"... simplifications substantially degrade accuracy. However, they provide useful approximation where the lowered accuracy can be tolerated."
p. 407

"We view this model as a system design tool."
"Any new proposal must do better than the Keystroke-Level Model (improve on its accuracy or lessen its restrictions) to merit serious consideration."
"The Keystroke-Level Model has several restrictions: The user must be an expert; the task must be a routine unit task; the method must be specified in detail; and the performance must be error-free."
"... there are many other important aspects of performance, there are nonexpert users, and there are nonroutine tasks. ... Desiging for expert, error-free performance time on routine tasks will not satisfy these other aspects."
p. 409

We could take the attitude that many tasks are acquired and mastered early by users (WASD movement, reticule targeting, etc), and that it's more about the specific instance (Fitts' law to predict accuracy of targeting, etc) that matters. Perhaps psychological state is more important than merely keystroke level?


CMN-KLM
Card, S.K.; T.P. Thomas & A. Newell (1983), written at London, The Psychology of Human-Computer Interaction, Lawrence Erbaum Associates, ISBN 0-89859-243-7

NGOMSL
"NGOMSL inherits the ability to not only give estimations for execution times but it can also estimate the time taken to learn how to use the system"
Kieras, David (1988). "Towards a practical GOMS model methodology for user interface design", in Martin Helander: Handbook of Human-Computer Interaction. Amsterdam, The Netherlands: Elsevier Science Publishers, p135-157. ISBN 0-444-88673-7.

CPM-GOMS
"CPM-GOMS stands for two things: Cognitive, Perceptual, and Motor and the project planning technique Critical Path Method"
"CPM-GOMS does not assume that the user's interaction is a serial process, and hence can model multitasking behavior that can be exhibited by experienced users."
"This is the most difficult GOMS technique to implement."
Gray, Wayne D.; John,Bonnie E. & Atwood, Michael E. (1992). "The Precis of Project Ernestine or an overview of a validation of GOMS". Proceedings of the SIGCHI conference on Human factors in computing systems. doi:10.1145/142750.142821. ISBN 0897915135.

Cognitive Complexity Theory
" * the number of mental structures we use, how abstract they are, and how elaborately they interact to shape our perceptions.
* the level of a person's social perception skill [1]."
Burleson, B.R., & Caplan, S.E. (1998). Cognitive complexity. In J.C. McCroskey, J.A. Daly, M.M. Martin, & M.J. Beatty (Eds.), Communication and personality: Trait perspectives (233-286). Creskill, NJ: Hampton Press. - Cited according to: The impact ofcognitive complexity and self-monitoring on leadership emergence, Melissa Ann Dobosh, thesis submitted to the Faculty of the University of Delaware in partial fulfillment of the requirements for the degree of Master of Arts in Communication Summer 2005