Methodology

What ITR measures

Information transfer rate (ITR) is the rate, in bits per second, at which a user gets information through an interface. For a discrete selection task, papers usually start with the Wolpaw formula for bits per selection:

B = log2(N) + P*log2(P) + (1-P)*log2((1-P)/(N-1))

Then they multiply by selections per second. Here N is the number of targets and P is the selection accuracy.

Why one number can mislead

The Wolpaw formula describes an idealized discrete channel. Every target is equally likely, errors are spread evenly over the other targets, selection time is fixed, and mistakes cost no correction time. Under those assumptions, the formula above is exact. Real interfaces rarely satisfy all of them, so the number is better read as an upper bound. The overestimate grows with accuracy and with the number of symbols (Speier, Arnold & Pouratian 2013, Yuan et al. 2013).

Different estimators relax different assumptions. Confusion-matrix mutual information removes the symmetric-error assumption (Nykopp 2001, Kronegg et al. 2005). A language model removes the uniform-prior assumption (Speier and colleagues, above). A continuous control channel needs a throughput model instead of a discrete-selection count. Most entries in the atlas come down to that choice: which assumption fails, and which replacement measure the source data can support.

The predictor is part of the measurement

A bits figure depends on the predictor assumed at the receiving end, not just on the physical or neural channel. If a language model can recover redundancy from context, that redundancy did not have to cross the interface. A stronger predictor gives a lower information rate. For comparisons to mean anything, the predictor has to stay constant across entries. We use a conservative full-context bound of about 1 bit per character for English text. Shannon's prediction experiments first bracketed printed English between 0.6 and 1.3 bits/char (Shannon 1951). Modern estimates land just above our working value: about 1.12 bits/char by extrapolating neural language models to unlimited data (Takahira et al. 2016) and about 1.22 bits/char in a large-scale replication of Shannon's guessing game (Ren et al. 2020). So 1 bit/char is a deliberate, slightly conservative floor. The per-word figure is not a separate measurement. Text-entry rates define one word as five characters (Soukoreff & MacKenzie 2003), the same convention behind the words-per-minute figures in this atlas, so the bound is equivalently 5 bits per word.

Speech makes the predictor issue easy to see. A widely cited cross-language study reports an average information rate of ~39 bits/second for spoken language (Coupé et al. 2019). That study set out to compare encoding efficiency across 17 languages, and for that purpose it uses syllable-level entropy estimated from local context. That estimator is computable and comparable across languages with very different corpus resources. It also counts redundancy that a full-context predictor would resolve, so it measures a different quantity from the channel-net information tracked here. If we used ~39 bps here, speech would be evaluated with a different predictor from QWERTY, Morse, and the BCI spellers.

Hold the predictor fixed and the speech number changes. When conversational English is measured with a large language model as the predictor, the same full-context standard we apply to text, it lands at ~13 bits/second (Bergey & DeDeo 2024), matching our text entries (≈150 wpm × 5 bits/word). Spoken and written English carry essentially the same net information under the same predictor. The 3× spread is an estimator difference, not a speech versus text difference.

What we rank on: the strictest upper bound

Every measure in the atlas is an upper bound on the information a channel delivers. Each one caps the rate under its own assumptions. Fitts' index of difficulty, the Wolpaw bits-per-selection, log₂(N), the Nuyujukian achieved bitrate, and the Shannon entropy of the realized text all bound the same quantity from different directions. Since one entry often admits several measures, the headline uses the strictest (smallest) valid bound. The score selector on the home page can still re-rank the atlas by any single method. The methods are computed as follows:

• Shannon entropy of the output text: characters/min × ~1 bit/char (or the equivalent 5 bits/word), under the full-context predictor held constant across every text entry (see above). Applies wherever the interface emits English: keyboards, Morse, eye-typing, and the BCI spellers (P300, SSVEP, c-VEP). It bounds the rate at the information the text carries, not at the raw selections the decoder happened to make.
• Fitts throughput: log₂(A/W + 1) per movement ÷ movement time, from the interface's own geometry, for continuous cursor motion (mouse, trackball, stylus, tongue drive, gaze pointing, cursor BCIs). Accuracy enters through the effective width W_e = 4.133·SD of the endpoints (ISO 9241-9), so the bound tracks the precision actually achieved. Moving fast and missing does not help. Where a source publishes no endpoint scatter (e.g. the sensorimotor-rhythm cursor), we say so and fall back to a plain completion-rate discount.
• Wolpaw / log₂(N): bits per selection over the real action set, discounted by accuracy, for a closed command set with no language model to apply. (No current speller is such a set. Every speller here types English.)
• Nuyujukian: log₂(N−1) × max(correct − incorrect, 0) ÷ time, the field-standard grid metric reported as Webgrid BPS and the like (Pandarinath 2017, Neuralink's Webgrid, Card 2026). The namesake Nuyujukian et al. 2015 (Eq. 1) used log₂(N); the atlas standardizes on the now-conventional log₂(N−1) so every entry is comparable.

The strictest-bound rule handles cases that can be scored more than one way. A speller that emits English has both a Shannon bound (~1 bit/char) and a raw-selection bound (log₂(40) per letter). The raw-selection figure is loose: enlarge the alphabet and it rises while the typing behavior is unchanged, so the headline uses the text figure. Grid cursors go the other way. Neuralink's Webgrid credits log₂(900) ≈ 9.8 bits per cell, while the Fitts bound on the same movement is ~4.1 bits/s. The tighter figure is the headline. As a check, the able-bodied ~10 BPS on Webgrid reduces by this method to ~4.1 bits/s, close to a physical mouse's independently measured ~4.5 bits/s. The rule can also favor Wolpaw: the sensorimotor-rhythm cursor's eight cued targets give a Wolpaw estimate below its Fitts estimate, and Moses et al.'s 50-word ECoG speech ranks on its Wolpaw bound (0.86 bits/s) rather than its Shannon figure (0.95). Shannon is one bound among several, not a floor.

Some raw-channel bounds are too loose to make good headlines. EEG2Code discriminates 500,000 random codes at ~100% from 2 s of EEG: log₂(500,000) ≈ 19 bits per selection, or 11.7 bits/s. The authors themselves flag a "ceiling effect" where those bits are not usable as control (Nagel & Spüler 2019). It stays in the atlas as a selectable secondary figure, not the ranked number. Speech has a similar issue: a syllable-level estimator gives ~39 bps, while a full-context predictor gives ~13 bps.

The same rule keeps the taxonomy from carrying too much weight. A cursor moving through space (Fitts), a code classifier (SSVEP, c-VEP), and covert attention with no movement (P300) can use different method labels. We do not need to decide whether covert attention obeys Fitts' law. The smallest valid bound is the headline.

How we pick the headline number

1. Compute every applicable method from the paper's inputs: the paper's own calculation where it exists and is sound, otherwise a modality-appropriate recomputation.
2. Rank the entry on the strictest (smallest) valid bound. Shannon entropy is one of those bounds, on equal footing with the rest.
3. Keep the looser figures as secondary derivations on the entry page, reachable through the score selector.

Provenance labels

• Author-reported · reproduced: we recomputed the number from the paper's stated inputs and matched it.
• Author-reported · not reproduced: the paper gives a number but doesn't expose enough to recompute it.
• Recomputed: no comparable ITR in the paper. We computed one from its inputs.