A mathematical description of the speed/accuracy trade-off of aimed movement

Abstract

Target clicking having proved an indispensable building block of interface design, it is little surprise that the speed/accuracy trade-off of aimed movement has always been a keen concern of HCI research. The trade-off is described by the Fitts law. In HCI and psychology likewise, the traditional approach has focused on the time-minimisation paradigm of Fitts [5], ignoring other relevant paradigms in which the Fitts law fails, such as the spread-minimisation paradigm of Schmidt et al. [18]. This paper aims at unearthing and consolidating the foundations of the speed/accuracy trade-off problem. Taking mean movement time as our speed measure and relative spread as our accuracy measure, we show that a small set of obvious mathematical axioms predict not only the data from the Fitts and the Schmidt paradigms but also the data from the more recent dual-minimisation paradigm of Guiard et al. [7]. The new mathematical framework encourages a more complete understanding: not only is it possible to estimate an amount of resource, a quantity equivalent to the classic throughput, it is also possible to characterize the resource-allocation strategy --- the other, no less important facet of the trade-off problem which has been left aside so far. The proposed approach may help HCI practitioners obtain from their experimental data more reliable and more complete information on the comparative merits of design options.