Speed-Accuracy Tradeoff: A Formal Information-Theoretic Transmission Scheme (FITTS)

The rationale for Fitts’ law is that pointing tasks have the information-theoretic analogy of sending a signal over a noisy channel, thereby matching Shannon’s capacity formula. Yet, the currently received analysis is incomplete and unsatisfactory: There is no explicit communication model for pointing; there is a confusion between central concepts of capacity (a mathematical limit), throughput (an average performance measure), and bandwidth (a physical quantity); and there is also a confusion between source and channel coding so that Shannon’s Theorem 17 can be misinterpreted. We develop an information-theoretic model for pointing tasks where the index of difficulty (ID) is the expression of both a source entropy and a zero-error channel capacity. Then, we extend the model to include misses at rate e and prove that ID should be adjusted to (1−e)ID. Finally, we reflect on Shannon’s channel coding theorem and argue that only minimum movement times, not performance averages, should be considered.