ITR Atlas
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Eye-Tracking Keyboard, dwell (Majaranta et al., 2009)

Measured by Majaranta, Ahola & Špakov · ACM CHI 2009 (2009)

Eye Gaze 2009

Inputs

The measured or assumed values behind the calculations, each with its source.

rate = 19.9 wpm
Best (session 10) entry rate in a 10-session longitudinal study; first session was 6.9 wpm. Adjustable dwell fell from 876 ms to 282 ms.
P = 0.9964
1 − 0.36% error rate at session 10 (1.28% at session 1)
H = 1.0 bits/char
English-text entropy (Shannon).
N = 30
On-screen keys, for the raw-key Wolpaw ceiling (uniform prior over the alphabet). The headline Shannon figure uses English entropy instead.
T_key = 0.603 s/key
Gross dwell-selection interval for the Wolpaw ceiling: 60 / (19.9 wpm × 5) = 0.603 s. The bare gaze-pointing Fitts channel is a separate entry (Eye-Gaze Pointing), not duplicated here.

Strictest ITR

Each scoring method is an upper bound on the channel, so the headline is the strictest (smallest) one for this entry. Use the score selector on the home page to view any single method across entries.

Strictest Shannon (text) Recomputed
Character-entropy throughput
Net of English redundancy and dwell errors
1.65 bits/s

  1. Net words per minute

    19.9 wpm × (1 − 0.0036) = 19.83 net wpm

  2. Characters per minute

    19.83 × 5 chars/word = 99.1 chars/min

  3. Information transfer rate

    99.1 char/min × 1.0 bit/char ÷ 60 s/min = 1.65 bits/s

What counts as a bit depends on the action space. The number of distinguishable actions and how likely each one is are design choices of the task, not the sensing hardware. The same modality can present a fixed set of targets, a set pruned per step by a grammar or language model, or a continuous control space. Each of these changes how many actions are live and how the probability mass is spread, and therefore the information per selection. Read the action space below before comparing headline numbers across entries.

Action space

What the user can produce at each step, and how those options are distributed.

Structure
Fixed set of targets
Size
30 distinguishable actions
Prior
Context-conditioned: likelihoods depend on prior actions
Notes
An on-screen keyboard selected by gaze dwell. The reference counts the English character stream at Shannon entropy (consistent with the other typing entries); a predictive layout that reorders keys by likelihood would change the per-selection information. The bare eye-gaze pointing channel underneath (Fitts throughput) is a separate entry (Eye-Gaze Pointing); this entry is its realized text output, the same channel-vs-application split as the BrainGate2 cursor BCI.

Comparability The strictest bound here is the Shannon entropy of the output text, under one predictor held constant across the whole atlas (≈1 bit per character). That shared predictor makes it directly comparable to every other text entry (keyboards, spellers, silent speech and speech BCIs) regardless of prior or vocabulary size. For most text interfaces it comes out tighter than the raw-selection bounds, but not always. Where a small vocabulary makes Wolpaw tighter, that wins instead. Any Fitts, Wolpaw or log₂(N) figure shown below is another bound on the same channel. Switch the home-page score selector to compare one across entries.

Other bounds considered for the headline

Also valid upper bounds for this entry and eligible to be the headline. They just came out looser than the strictest above. Pick any of these in the home-page score selector.

Wolpaw Recomputed
Wolpaw bitrate over the raw key set
Uniform-prior ceiling on the dwell-key channel, before English redundancy
8.05 bits/s

  1. Bits per selection (Wolpaw formula)

    B = log2(N) + P*log2(P) + (1-P)*log2((1-P)/(N-1))
  = log2(30) + 0.9964*log2(0.9964) + 0.0036*log2(0.0036/29)
  = 4.855 bits / selection

    Term 1 is the information if every choice were correct; terms 2-3 subtract the bits lost to the error rate, assumed spread evenly over the other N-1 targets.

  2. Selections per second

    T = 0.603 s/selection  ->  1 / 0.603 = 1.658 selections/s

  3. Information transfer rate

    ITR = B * selections/s = 4.855 * 1.658 = 8.051 bits/s

Other score types

Bounds the atlas keeps out of the default strictest headline: as-reported figures, alternate task conditions, or raw-channel ceilings that shouldn't win the headline by default. Each still carries a score type, so the home-page selector ranks this entry on it when you choose that type. Read its derivation before comparing across entries.

Nuyujukian Recomputed
Nuyujukian achieved bitrate over the raw key set
Achieved-bitrate view of the dwell-key channel, shown for comparison
8 bits/s

  1. Achieved-bitrate credit per net-correct key

    N = 30 keys → log2(N − 1) = log2(29) = 4.86 bits per net-correct selection (field-standard achieved bitrate, e.g. Webgrid; Nuyujukian 2015, which introduced the metric, used log2(N)).

  2. Net-correct key rate

    net-correct = 2P − 1 = 2(0.9964) − 1 = 0.993 of keys. At 0.603 s/key → 0.993 / 0.603 = 1.65 correct/s.

    A dwell error commits the wrong key rather than timing out, so incorrect = 1 − P. Same N (30 keys), accuracy (99.64%) and key interval (0.603 s) as the entry's raw-key Wolpaw ceiling, and lands on the same ~8 bits/s. Both are the uniform-prior key channel before English redundancy, far above the 1.65 bits/s Shannon headline that holds this entry to the realized text.

  3. Achieved bitrate

    4.86 bits × 1.65 correct/s = 8.0 bits/s.

Source

Authors
Majaranta, Ahola & Špakov
Publication
ACM CHI 2009, 2009
Paper
10.1145/1518701.1518758