Editing Fitts's law (section)

== Original model formulation ==
The original 1954 paper by [[Paul Fitts|Paul Morris Fitts]] proposed a metric to quantify the difficulty of a target selection task.
The metric was based on an information analogy, where the distance to the center of the target (''D'') is like a signal and the tolerance or width of the target (''W'') is like noise.
The metric is Fitts's ''index of difficulty'' (''ID'', in bits):

<math display="block">\text{ID} = \log_2 \Bigg(\frac{2D} {W}\Bigg)</math>

[[File:Fitts Task English.jpg|thumb|Fitts task from the original experiment]]

Fitts also proposed an ''index of performance'' (''IP'', in bits per second) as a measure of human performance. The metric combines a task's index of difficulty (''ID'') with the movement time (''MT'', in seconds) in selecting the target. In Fitts's words,
"The average rate of information generated by a series of movements is the average information per movement divided by the time per movement."<ref name=Fitts1954/> Thus,

<math display="block">\text{IP} = \Bigg(\frac{\text{ID}} {\text{MT}}\Bigg)</math>

Today, ''IP'' is more commonly called ''throughput'' (''TP''). It is also common to include an adjustment for accuracy in the calculation.

Researchers after Fitts began the practice of building linear regression equations and examining the correlation (''r'') for goodness of fit. The equation expresses the relationship between
''MT'' and the ''D'' and ''W'' task parameters:

<math display="block">\text{MT} = a + b \cdot \text{ID} = a + b \cdot \log_2 \Bigg(\frac{2D}{W}\Bigg)</math>

[[File:Fitts&#039; Law Evaluation English.svg|thumb|Graph of the linear relationship of Fitts's law parameters]]

where:
* ''MT'' is the average time to complete the movement.
* ''a'' and ''b'' are constants that depend on the choice of input device and are usually determined empirically by [[regression analysis]]. ''a'' defines the intersection on the ''y'' axis and is often interpreted as a delay. The ''b'' parameter is a slope and describes an acceleration. Both parameters show the linear dependency in Fitts's law.<ref name="Graham">{{cite journal |title=Physical versus virtual pointing |journal=Proceedings of the SIGCHI Conference on Human Factors in Computing Systems |date=1996 |last1=Graham |first1=E. D. |last2=MacKenzie |first2=C. L. |pages=292–299 }}</ref>
* ''ID'' is the index of difficulty.
* ''D''	is the distance from the starting point to the center of the target.
* ''W'' is the width of the target measured along the axis of motion. ''W'' can also be thought of as the allowed error tolerance in the final position, since the final point of the motion must fall within ±{{frac|''W''|2}} of the target's center.

Since shorter movement times are desirable for a given task, the value of the ''b'' parameter can be used as a metric when comparing computer pointing devices against one another. The first [[human–computer interface]] application of Fitts's law was by Card, English, and Burr,<ref name=Card1978>{{cite journal |last1=Card |first1=Stuart K. |first2=William K. |last2=English |first3=Betty J. |last3=Burr |date=1978 |title=Evaluation of mouse, rate-controlled isometric joystick, step keys, and text keys for text selection on a CRT |journal=Ergonomics |volume=21 |number=8 |pages=601–613 |doi=10.1080/00140137808931762|url=http://bitsavers.trailing-edge.com/pdf/xerox/parc/techReports/SSL-77-1_Evaluation_of_Mouse_Rate-Controlled_Isometric_Joystick_Step_Keys_and_Text_Keys_for_Text_Selection_on_a_CRT.pdf |citeseerx=10.1.1.606.2223 |s2cid=59725361 }}</ref> who used the index of performance (''IP''), interpreted as {{frac|1|''b''}}, to compare performance of different [[input device]]s, with the [[mouse (computing)|mouse]] coming out on top compared to the joystick or directional movement keys.<ref name=Card1978/> This early work, according to [[Stuart Card]]'s biography, "was a major factor leading to the mouse's commercial introduction by [[Xerox]]".<ref>{{cite web|url=http://www2.parc.com/istl/groups/uir/people/stuart/stuart.htm |title=Stuart Card |website=[[PARC (company)|PARC]] |archive-url=https://web.archive.org/web/20120711210730/http://www2.parc.com/istl/groups/uir/people/stuart/stuart.htm |archive-date=2012-07-11 |url-status=dead }}</ref>

Many experiments testing Fitts's law apply the model to a dataset in which either distance or width, but not both, are varied. The model's predictive power deteriorates when both are varied over a significant range.<ref name=Graham1996>{{cite thesis |last=Graham |first=Evan |title=Pointing on a Computer Display |type=Ph.D. |publisher=Simon Fraser University |year=1996}}</ref> Notice that because the ''ID'' term depends only on the ''ratio'' of distance to width, the model implies that a target distance and width combination can be re-scaled arbitrarily without affecting movement time, which is impossible. Despite its flaws, this form of the model does possess remarkable predictive power across a range of computer interface modalities and motor tasks, and has provided many insights into user interface design principles.