Clay & Cortex Results so far

ResultsAnonymous · updated 2026-09-12

What the studies have measured, as they measure it

Every study on this site publishes its data as they come in, anonymised, whether or not they say anything flattering. The studies are designed and run by Dr. Satwant Kumar, a physician and vision neuroscientist. This page is regenerated from the study database; the numbers below are the numbers the studies hold. Sessions are labelled S01, S02, … in order of upload, and nothing else about a participant appears.

Study 1Trap occlusion

How early can you call the line?

A clay leaves the trench at a small angle left or right of straightaway, is visible for a fixed few tens of milliseconds, and is then hidden. The observer says left or right. An adaptive procedure finds, at each viewing time, the smallest launch angle the observer calls correctly three times in four. That angle is the threshold; smaller is better. 8 sessions from 8 people are shown: 4 elite or international shooters, 2 club shooters, 1 novice or non-shooter and 1 who did not say, 2026-08-05 to 2026-08-29.

2,544
calibrated trials, 7% rejected for timing
0.09°
smallest launch angle called so far
26 of 34
thresholds measurable; 8 below the task's floor
8
sessions shown, of 10 uploaded, from 8 people

The longer the target is seen, the smaller the angle that can be called

One line per session, coloured by self-reported experience. Both axes are logarithmic. Hover or tap a point for its confidence interval and trial count.

0.05°0.1°0.2°0.5°Smallest angle called correctly 75% of the time33 ms50 ms67 ms100 ms141 msVisible flight before occlusion (ms, as presented)below the smallest angle the task presents (≈ 0.1°): not measurableS02 · Elite / international · 33 ms · threshold 0.38° (95% CI 0.18–0.85), 60 trialsS02 · Elite / international · 50 ms · threshold 0.24° (95% CI 0.12–0.45), 60 trialsS02 · Elite / international · 66 ms · threshold 0.09° (95% CI 0.05–0.19), 60 trialsS02 · Elite / international · 100 ms · threshold 0.11° (95% CI 0.05–0.23), 59 trialsS02 · Elite / international · 141 ms · threshold 0.10° (95% CI 0.05–0.20), 59 trialsS04 · Elite / international · 30 ms · threshold 0.21° (95% CI 0.11–0.40), 75 trialsS04 · Elite / international · 49 ms · threshold 0.23° (95% CI 0.11–0.45), 75 trialsS04 · Elite / international · 67 ms · threshold 0.13° (95% CI 0.06–0.23), 75 trialsS04 · Elite / international · 98 ms · at the task floor: below 0.11°, the smallest angle shownS06 · Elite / international · 30 ms · threshold 0.55° (95% CI 0.26–1.10), 75 trialsS06 · Elite / international · 49 ms · at the task floor: below 0.12°, the smallest angle shownS06 · Elite / international · 67 ms · at the task floor: below 0.11°, the smallest angle shownS06 · Elite / international · 98 ms · threshold 0.16° (95% CI 0.08–0.29), 75 trialsS10 · Elite / international · 34 ms · threshold 0.18° (95% CI 0.09–0.33), 75 trialsS10 · Elite / international · 51 ms · threshold 0.11° (95% CI 0.06–0.21), 74 trialsS10 · Elite / international · 68 ms · at the task floor: below 0.11°, the smallest angle shownS10 · Elite / international · 102 ms · at the task floor: below 0.10°, the smallest angle shownS01 · Club / developing · 33 ms · threshold 0.75° (95% CI 0.21–2.06), 30 trialsS01 · Club / developing · 50 ms · threshold 0.55° (95% CI 0.19–1.41), 32 trialsS01 · Club / developing · 66 ms · threshold 0.62° (95% CI 0.19–2.48), 25 trialsS01 · Club / developing · 100 ms · threshold 0.43° (95% CI 0.16–2.33), 33 trialsS01 · Club / developing · 141 ms · threshold 0.31° (95% CI 0.07–0.80), 31 trialsS05 · Club / developing · 30 ms · threshold 0.48° (95% CI 0.26–0.97), 75 trialsS05 · Club / developing · 49 ms · threshold 0.23° (95% CI 0.12–0.45), 75 trialsS05 · Club / developing · 67 ms · threshold 0.14° (95% CI 0.07–0.26), 75 trialsS05 · Club / developing · 98 ms · at the task floor: below 0.12°, the smallest angle shownS03 · Novice / non-shooter · 34 ms · threshold 2.82° (95% CI 1.41–5.63), 74 trialsS03 · Novice / non-shooter · 51 ms · threshold 1.41° (95% CI 0.75–2.64), 73 trialsS03 · Novice / non-shooter · 68 ms · threshold 1.10° (95% CI 0.58–2.06), 70 trialsS03 · Novice / non-shooter · 102 ms · threshold 0.62° (95% CI 0.33–1.24), 72 trialsS07 · Not stated · 30 ms · threshold 0.31° (95% CI 0.17–0.55), 75 trialsS07 · Not stated · 49 ms · threshold 0.19° (95% CI 0.09–0.35), 75 trialsS07 · Not stated · 67 ms · at the task floor: below 0.12°, the smallest angle shownS07 · Not stated · 98 ms · at the task floor: below 0.11°, the smallest angle shownGroupElite / internationalClub / developingNovice / non-shooterNot statedhollow: at the floor0.05°0.1°0.2°0.5°Threshold (°)33 ms50 ms67 ms100 ms141 msVisible flight before occlusion (ms)S02 · Elite / international · 33 ms · threshold 0.38° (95% CI 0.18–0.85), 60 trialsS02 · Elite / international · 50 ms · threshold 0.24° (95% CI 0.12–0.45), 60 trialsS02 · Elite / international · 66 ms · threshold 0.09° (95% CI 0.05–0.19), 60 trialsS02 · Elite / international · 100 ms · threshold 0.11° (95% CI 0.05–0.23), 59 trialsS02 · Elite / international · 141 ms · threshold 0.10° (95% CI 0.05–0.20), 59 trialsS04 · Elite / international · 30 ms · threshold 0.21° (95% CI 0.11–0.40), 75 trialsS04 · Elite / international · 49 ms · threshold 0.23° (95% CI 0.11–0.45), 75 trialsS04 · Elite / international · 67 ms · threshold 0.13° (95% CI 0.06–0.23), 75 trialsS04 · Elite / international · 98 ms · at the task floor: below 0.11°, the smallest angle shownS06 · Elite / international · 30 ms · threshold 0.55° (95% CI 0.26–1.10), 75 trialsS06 · Elite / international · 49 ms · at the task floor: below 0.12°, the smallest angle shownS06 · Elite / international · 67 ms · at the task floor: below 0.11°, the smallest angle shownS06 · Elite / international · 98 ms · threshold 0.16° (95% CI 0.08–0.29), 75 trialsS10 · Elite / international · 34 ms · threshold 0.18° (95% CI 0.09–0.33), 75 trialsS10 · Elite / international · 51 ms · threshold 0.11° (95% CI 0.06–0.21), 74 trialsS10 · Elite / international · 68 ms · at the task floor: below 0.11°, the smallest angle shownS10 · Elite / international · 102 ms · at the task floor: below 0.10°, the smallest angle shownS01 · Club / developing · 33 ms · threshold 0.75° (95% CI 0.21–2.06), 30 trialsS01 · Club / developing · 50 ms · threshold 0.55° (95% CI 0.19–1.41), 32 trialsS01 · Club / developing · 66 ms · threshold 0.62° (95% CI 0.19–2.48), 25 trialsS01 · Club / developing · 100 ms · threshold 0.43° (95% CI 0.16–2.33), 33 trialsS01 · Club / developing · 141 ms · threshold 0.31° (95% CI 0.07–0.80), 31 trialsS05 · Club / developing · 30 ms · threshold 0.48° (95% CI 0.26–0.97), 75 trialsS05 · Club / developing · 49 ms · threshold 0.23° (95% CI 0.12–0.45), 75 trialsS05 · Club / developing · 67 ms · threshold 0.14° (95% CI 0.07–0.26), 75 trialsS05 · Club / developing · 98 ms · at the task floor: below 0.12°, the smallest angle shownS03 · Novice / non-shooter · 34 ms · threshold 2.82° (95% CI 1.41–5.63), 74 trialsS03 · Novice / non-shooter · 51 ms · threshold 1.41° (95% CI 0.75–2.64), 73 trialsS03 · Novice / non-shooter · 68 ms · threshold 1.10° (95% CI 0.58–2.06), 70 trialsS03 · Novice / non-shooter · 102 ms · threshold 0.62° (95% CI 0.33–1.24), 72 trialsS07 · Not stated · 30 ms · threshold 0.31° (95% CI 0.17–0.55), 75 trialsS07 · Not stated · 49 ms · threshold 0.19° (95% CI 0.09–0.35), 75 trialsS07 · Not stated · 67 ms · at the task floor: below 0.12°, the smallest angle shownS07 · Not stated · 98 ms · at the task floor: below 0.11°, the smallest angle shownElite / internationalClub / developingNovice / non-shooterNot statedhollow: at the floor
Every session falls with viewing time, as it should if the task measures what it claims to: more visible flight is more information about the line. Hollow points sit at the floor of what the task can present (about 0.1°), so those true values are lower still.

Experience shows in the numbers

The same thresholds grouped by experience at each viewing time. One dot per session; the bar is the group median of the measurable thresholds.

0.05°0.1°0.2°0.5°Threshold (°)33 msElite / international · 33 ms · 0.18°Elite / international · 33 ms · 0.21°Elite / international · 33 ms · 0.38°Elite / international · 33 ms · 0.55°Elite / international median of usable thresholds at 33 ms: 0.28° (n = 4)Club / developing · 33 ms · 0.48°Club / developing · 33 ms · 0.75°Club / developing median of usable thresholds at 33 ms: 0.60° (n = 2)Novice / non-shooter · 33 ms · 2.82°Not stated · 33 ms · 0.31°50 msElite / international · 50 ms · 0.11°Elite / international · 50 ms · below 0.12° (task floor)Elite / international · 50 ms · 0.23°Elite / international · 50 ms · 0.24°Elite / international median of usable thresholds at 50 ms: 0.23° (n = 3)Club / developing · 50 ms · 0.23°Club / developing · 50 ms · 0.55°Club / developing median of usable thresholds at 50 ms: 0.35° (n = 2)Novice / non-shooter · 50 ms · 1.41°Not stated · 50 ms · 0.19°67 msElite / international · 67 ms · 0.09°Elite / international · 67 ms · below 0.11° (task floor)Elite / international · 67 ms · below 0.11° (task floor)Elite / international · 67 ms · 0.13°Elite / international median of usable thresholds at 67 ms: 0.11° (n = 2)Club / developing · 67 ms · 0.14°Club / developing · 67 ms · 0.62°Club / developing median of usable thresholds at 67 ms: 0.29° (n = 2)Novice / non-shooter · 67 ms · 1.10°Not stated · 67 ms · below 0.12° (task floor)100 msElite / international · 100 ms · below 0.10° (task floor)Elite / international · 100 ms · below 0.11° (task floor)Elite / international · 100 ms · 0.11°Elite / international · 100 ms · 0.16°Elite / international median of usable thresholds at 100 ms: 0.13° (n = 2)Club / developing · 100 ms · below 0.12° (task floor)Club / developing · 100 ms · 0.43°Novice / non-shooter · 100 ms · 0.62°Not stated · 100 ms · below 0.11° (task floor)Viewing time (nominal). Within each: elite · club · novice · not stated. Bar = median of usable thresholds.0.05°0.1°0.2°0.5°Threshold (°)33 msElite / international · 33 ms · 0.18°Elite / international · 33 ms · 0.21°Elite / international · 33 ms · 0.38°Elite / international · 33 ms · 0.55°Elite / international median of usable thresholds at 33 ms: 0.28° (n = 4)Club / developing · 33 ms · 0.48°Club / developing · 33 ms · 0.75°Club / developing median of usable thresholds at 33 ms: 0.60° (n = 2)Novice / non-shooter · 33 ms · 2.82°Not stated · 33 ms · 0.31°50 msElite / international · 50 ms · 0.11°Elite / international · 50 ms · below 0.12° (task floor)Elite / international · 50 ms · 0.23°Elite / international · 50 ms · 0.24°Elite / international median of usable thresholds at 50 ms: 0.23° (n = 3)Club / developing · 50 ms · 0.23°Club / developing · 50 ms · 0.55°Club / developing median of usable thresholds at 50 ms: 0.35° (n = 2)Novice / non-shooter · 50 ms · 1.41°Not stated · 50 ms · 0.19°67 msElite / international · 67 ms · 0.09°Elite / international · 67 ms · below 0.11° (task floor)Elite / international · 67 ms · below 0.11° (task floor)Elite / international · 67 ms · 0.13°Elite / international median of usable thresholds at 67 ms: 0.11° (n = 2)Club / developing · 67 ms · 0.14°Club / developing · 67 ms · 0.62°Club / developing median of usable thresholds at 67 ms: 0.29° (n = 2)Novice / non-shooter · 67 ms · 1.10°Not stated · 67 ms · below 0.12° (task floor)100 msElite / international · 100 ms · below 0.10° (task floor)Elite / international · 100 ms · below 0.11° (task floor)Elite / international · 100 ms · 0.11°Elite / international · 100 ms · 0.16°Elite / international median of usable thresholds at 100 ms: 0.13° (n = 2)Club / developing · 100 ms · below 0.12° (task floor)Club / developing · 100 ms · 0.43°Novice / non-shooter · 100 ms · 0.62°Not stated · 100 ms · below 0.11° (task floor)Viewing time. Bar = group median.Elite / internationalClub / developingNovice / non-shooterNot statedhollow: at the floor
Group is self-reported at sign-in. For the sessions run in person the investigator has confirmed the labels. With this few people the medians are indicative, not a finding; the study's stated gate for any claim about groups is a larger sample and a repeat session per person.

Medians by group and viewing time

Threshold in degrees of launch angle, with the sideways drift it amounts to at the distance where the target disappears. A clay is 11 cm across.

Visible forDistance at occlusionElite / internationalClub / developingNovice / non-shooterNot stated
33 ms17 m0.28° ≈ 8 cm
n = 4
0.60° ≈ 18 cm
n = 2
50 ms17 m0.23° ≈ 7 cm
n = 3 (+1 at floor)
0.35° ≈ 11 cm
n = 2
67 ms18 m0.11° ≈ 3 cm
n = 2 (+2 at floor)
0.29° ≈ 9 cm
n = 2
100 ms19 m0.13° ≈ 4 cm
n = 2 (+2 at floor)

What the numbers mean on the range

Take the 50 ms condition. When the target disappears it is about 17 m from the shooter, and the median threshold of 0.23° is a sideways drift of about 7 cm from the straightaway line, less than one clay width (11 cm). That is what "calling the line" resolves to: a drift of a few centimetres, at that distance, in 50 ms.

What one session looks like underneath: S04, elite / international

The psychometric function behind each threshold at 33 ms, 50 ms, 67 ms: the proportion of correct calls against launch angle, the maximum-likelihood fit, and where it crosses the 75% criterion.

50%75%100%0.1°0.2°0.5°33 ms visiblechance0.21°0.18°: 58% correct of 19 trials (95% interval 36%–77%)0.25°: 80% correct of 45 trials (95% interval 66%–89%)0.33°: 100% correct of 3 trials (95% interval 44%–100%)0.53°: 100% correct of 3 trials (95% interval 44%–100%)0.77°: 100% correct of 1 trials (95% interval 21%–100%)1.14°: 100% correct of 1 trials (95% interval 21%–100%)1.67°: 100% correct of 2 trials (95% interval 34%–100%)2.86°: 100% correct of 1 trials (95% interval 21%–100%)0.1°0.2°0.5°50 ms visiblechance0.23°0.24°: 74% correct of 39 trials (95% interval 59%–85%)0.32°: 81% correct of 16 trials (95% interval 57%–93%)0.43°: 89% correct of 9 trials (95% interval 56%–98%)0.61°: 75% correct of 4 trials (95% interval 30%–95%)0.95°: 100% correct of 1 trials (95% interval 21%–100%)1.09°: 100% correct of 2 trials (95% interval 34%–100%)1.60°: 100% correct of 3 trials (95% interval 44%–100%)2.61°: 100% correct of 1 trials (95% interval 21%–100%)0.1°0.2°0.5°67 ms visiblechance0.13°0.15°: 79% correct of 29 trials (95% interval 62%–90%)0.23°: 84% correct of 19 trials (95% interval 62%–94%)0.31°: 80% correct of 15 trials (95% interval 55%–93%)0.44°: 100% correct of 5 trials (95% interval 57%–100%)0.68°: 100% correct of 2 trials (95% interval 34%–100%)1.03°: 100% correct of 2 trials (95% interval 34%–100%)1.47°: 100% correct of 1 trials (95% interval 21%–100%)2.63°: 100% correct of 2 trials (95% interval 34%–100%)Launch angle from straightaway (°, log scale). Point area ∝ trials; whiskers 95% intervals; dashed line = 75% criterion.50%75%100%0.1°0.2°0.5°33 ms visiblechance0.21°0.18°: 58% correct of 19 trials (95% interval 36%–77%)0.25°: 80% correct of 45 trials (95% interval 66%–89%)0.33°: 100% correct of 3 trials (95% interval 44%–100%)0.53°: 100% correct of 3 trials (95% interval 44%–100%)0.77°: 100% correct of 1 trials (95% interval 21%–100%)1.14°: 100% correct of 1 trials (95% interval 21%–100%)1.67°: 100% correct of 2 trials (95% interval 34%–100%)2.86°: 100% correct of 1 trials (95% interval 21%–100%)50%75%100%0.1°0.2°0.5°50 ms visiblechance0.23°0.24°: 74% correct of 39 trials (95% interval 59%–85%)0.32°: 81% correct of 16 trials (95% interval 57%–93%)0.43°: 89% correct of 9 trials (95% interval 56%–98%)0.61°: 75% correct of 4 trials (95% interval 30%–95%)0.95°: 100% correct of 1 trials (95% interval 21%–100%)1.09°: 100% correct of 2 trials (95% interval 34%–100%)1.60°: 100% correct of 3 trials (95% interval 44%–100%)2.61°: 100% correct of 1 trials (95% interval 21%–100%)50%75%100%0.1°0.2°0.5°67 ms visiblechance0.13°0.15°: 79% correct of 29 trials (95% interval 62%–90%)0.23°: 84% correct of 19 trials (95% interval 62%–94%)0.31°: 80% correct of 15 trials (95% interval 55%–93%)0.44°: 100% correct of 5 trials (95% interval 57%–100%)0.68°: 100% correct of 2 trials (95% interval 34%–100%)1.03°: 100% correct of 2 trials (95% interval 34%–100%)1.47°: 100% correct of 1 trials (95% interval 21%–100%)2.63°: 100% correct of 2 trials (95% interval 34%–100%)Launch angle (°). Dashed line: 75% criterion.
The adaptive procedure places most trials where the answer is least certain, which is why the large points cluster around the threshold and the far ends are sparse. Whiskers are 95% intervals on each bin. A dashed curve means the fit landed below the smallest angle shown and is reported as "at the floor".

Why the measurement can be trusted, and where it cannot yet

  • The screen is calibrated, not assumed. Scale from a standard plastic card (driving-licence size), viewing distance by the blind-spot method, refresh rate measured before the first trial. Every angle is in degrees at the eye.
  • Every stimulus is a whole number of frames, and a trial in which a frame arrived late is rejected rather than analysed with the wrong duration: 171 of 2,544 main trials so far (7%). One session (S01) lost 155 of its 318 trials to frames delivered late by a display running slower than it had measured; those trials are excluded and its thresholds rest on the rest, which is why its intervals are wide. The study now stops a session early when that starts to happen.
  • Attention is checked. Easy probe trials are interleaved throughout; a lapse there means the observer was not looking. Across every session shown, 0 of 144 probes were missed.
  • A number the task cannot measure is not reported as a number. When the fit lands below the smallest angle presented, the result is "below that angle", shown hollow. 8 of 34 fitted thresholds are in that state; they are the best shooters at the longer viewing times.
  • A display that cannot present the durations is refused. 2 sessions ran on a display that measured 30 Hz, below the 60 Hz the durations need: there the 50 ms condition was presented as 67 ms, so two conditions collapsed into one. They are left out of everything on this page, and the study now refuses such a display before the first trial.
  • What this is not. A handful of people, self-reported experience, one session each, and no peer review. It is an interim look at a running study, not a finding, and nothing here is a claim that any training or equipment improves anything.

What the first sessions changed

The study runs on a stated protocol and the protocol is versioned. The sessions above led to protocol 4.0.0: the 100 ms viewing time was dropped, because for experienced shooters it mostly sat below the task's floor and taught nothing; the three remaining durations are exact multiples of a 60 Hz frame; a display under 60 Hz is now refused outright rather than warned about; and a session that starts losing trials to late frames is stopped early rather than run to the end. Session length is unchanged.

Add your session About the studies

Study 2Lens tint and clay contrast

Does the model predict which lens helps whose eyes?

Each observer's contrast sensitivity is measured on three cone-contrast axes and on a clay-sized moving disc; then, for six lens classes presented blind as faint moving discs, the study finds the fraction of each lens's real clay–background contrast at which the observer can just tell the direction of motion. The physical model predicts that fraction from the observer's own thresholds, and the comparison is the point of the study. 1 session under the current protocol from 2 participants, and 1 earlier session shown but not pooled.

Across the 1 pooled session, the measured multiplier was on median 3.3× the model's prediction from the observer's own thresholds, and the model ordered the lenses with a rank agreement of τ = +0.33 against the study's gate of 0.6. The model is being tested on its absolute scale as well as its order, and a moving clay-sized target is harder than the model's static thresholds imply; with this little data that is a first reading, not a verdict.

2
sessions shown, 1 under the current protocol
2
participants
834
main trials, 1% rejected for timing
+0.33
mean rank agreement τ, current protocol (gate ≥ 0.6)

Lenses: what the eyes measured against what the model predicted

For each lens class, the multiplier of the lens's real clay–background contrast at which the observer could just tell the direction of motion (filled), and the model's prediction from that observer's own thresholds (diamond). Lower is better; the gap between the two symbols is the model's error.

0.020.050.10.20.51Threshold multiplier (log; lower is better)clearS01 · No tint (clear) · predicted from own thresholds: 0.174S01 · Clay shooter · No tint (clear) · measured 0.21 (95% CI 0.0804–0.576), 32 trials; preference 4/7 · protocol 0.1.0S02 · No tint (clear) · predicted from own thresholds: 0.0542S02 · Clay shooter · No tint (clear) · measured 0.163 (95% CI 0.0984–0.284), 40 trials; preference 5/7yellowS01 · Yellow (cut below ~480 nm) · predicted from own thresholds: 0.187S01 · Clay shooter · Yellow (cut below ~480 nm) · measured 0.236 (95% CI 0.0947–0.795), 32 trials; preference 3/7 · protocol 0.1.0light orangeS01 · Light orange (cut ~520 nm) · predicted from own thresholds: 0.258S01 · Clay shooter · Light orange (cut ~520 nm) · measured 0.205 (95% CI 0.0779–0.767), 32 trials; preference 3/7 · protocol 0.1.0S02 · Light orange (cut ~520 nm) · predicted from own thresholds: 0.0511S02 · Clay shooter · Light orange (cut ~520 nm) · measured 0.264 (95% CI 0.129–0.693), 40 trials; preference 4/7orangeS01 · Orange (cut ~550 nm) · predicted from own thresholds: 0.203S01 · Clay shooter · Orange (cut ~550 nm) · measured 0.247 (95% CI 0.0853–0.752), 32 trials; preference 2/7 · protocol 0.1.0S02 · Orange (cut ~550 nm) · predicted from own thresholds: 0.0474S02 · Clay shooter · Orange (cut ~550 nm) · measured 0.182 (95% CI 0.0944–0.352), 40 trials; preference 1/7vermilionS01 · Vermilion (cut ~580 nm) · predicted from own thresholds: 0.0686S01 · Clay shooter · Vermilion (cut ~580 nm) · measured 0.0771 (95% CI 0.0272–0.189), 31 trials; preference 3/7 · protocol 0.1.0S02 · Vermilion (cut ~580 nm) · predicted from own thresholds: 0.0475S02 · Clay shooter · Vermilion (cut ~580 nm) · measured 0.0734 (95% CI 0.0404–0.155), 40 trials; preference 2/7purpleS01 · Purple / background neutraliser · predicted from own thresholds: 0.151S01 · Clay shooter · Purple / background neutraliser · measured 0.139 (95% CI 0.0473–0.37), 32 trials; preference 2/7 · protocol 0.1.0S02 · Purple / background neutraliser · predicted from own thresholds: 0.0294S02 · Clay shooter · Purple / background neutraliser · measured 0.0999 (95% CI 0.0519–0.175), 40 trials; preference 3/7bronzeS01 · Bronze / copper · predicted from own thresholds: 0.226S01 · Clay shooter · Bronze / copper · measured 0.232 (95% CI 0.0845–0.74), 32 trials; preference 3/7 · protocol 0.1.0S02 · Bronze / copper · predicted from own thresholds: 0.0502S02 · Clay shooter · Bronze / copper · measured 0.163 (95% CI 0.0889–0.347), 40 trials; preference 3/7measured, coloured by group (clay shooter)predicted from the observer's thresholdsLens class. Distance between the two symbols is the model's error for that observer and lens.0.020.050.10.20.51Threshold multiplierclearS01 · No tint (clear) · predicted from own thresholds: 0.174S01 · Clay shooter · No tint (clear) · measured 0.21 (95% CI 0.0804–0.576), 32 trials; preference 4/7 · protocol 0.1.0S02 · No tint (clear) · predicted from own thresholds: 0.0542S02 · Clay shooter · No tint (clear) · measured 0.163 (95% CI 0.0984–0.284), 40 trials; preference 5/7yellowS01 · Yellow (cut below ~480 nm) · predicted from own thresholds: 0.187S01 · Clay shooter · Yellow (cut below ~480 nm) · measured 0.236 (95% CI 0.0947–0.795), 32 trials; preference 3/7 · protocol 0.1.0light orangeS01 · Light orange (cut ~520 nm) · predicted from own thresholds: 0.258S01 · Clay shooter · Light orange (cut ~520 nm) · measured 0.205 (95% CI 0.0779–0.767), 32 trials; preference 3/7 · protocol 0.1.0S02 · Light orange (cut ~520 nm) · predicted from own thresholds: 0.0511S02 · Clay shooter · Light orange (cut ~520 nm) · measured 0.264 (95% CI 0.129–0.693), 40 trials; preference 4/7orangeS01 · Orange (cut ~550 nm) · predicted from own thresholds: 0.203S01 · Clay shooter · Orange (cut ~550 nm) · measured 0.247 (95% CI 0.0853–0.752), 32 trials; preference 2/7 · protocol 0.1.0S02 · Orange (cut ~550 nm) · predicted from own thresholds: 0.0474S02 · Clay shooter · Orange (cut ~550 nm) · measured 0.182 (95% CI 0.0944–0.352), 40 trials; preference 1/7vermilionS01 · Vermilion (cut ~580 nm) · predicted from own thresholds: 0.0686S01 · Clay shooter · Vermilion (cut ~580 nm) · measured 0.0771 (95% CI 0.0272–0.189), 31 trials; preference 3/7 · protocol 0.1.0S02 · Vermilion (cut ~580 nm) · predicted from own thresholds: 0.0475S02 · Clay shooter · Vermilion (cut ~580 nm) · measured 0.0734 (95% CI 0.0404–0.155), 40 trials; preference 2/7purpleS01 · Purple / background neutraliser · predicted from own thresholds: 0.151S01 · Clay shooter · Purple / background neutraliser · measured 0.139 (95% CI 0.0473–0.37), 32 trials; preference 2/7 · protocol 0.1.0S02 · Purple / background neutraliser · predicted from own thresholds: 0.0294S02 · Clay shooter · Purple / background neutraliser · measured 0.0999 (95% CI 0.0519–0.175), 40 trials; preference 3/7bronzeS01 · Bronze / copper · predicted from own thresholds: 0.226S01 · Clay shooter · Bronze / copper · measured 0.232 (95% CI 0.0845–0.74), 32 trials; preference 3/7 · protocol 0.1.0S02 · Bronze / copper · predicted from own thresholds: 0.0502S02 · Clay shooter · Bronze / copper · measured 0.163 (95% CI 0.0889–0.347), 40 trials; preference 3/7Clay shooterhollow: at the floorpredicted from own thresholds
Every lens condition is a faint grey-field disc carrying that lens's cone-contrast vector, so the observer cannot tell which lens a trial belongs to and expectation cannot enter. Dashed rings are sessions under protocol 0.1.0.

Predicted against measured, with each session's rank agreement

Every usable lens condition. On the dashed line the model was exactly right. Kendall's τ per session: +1 means the model ordered the lenses exactly as the observer's eyes did, 0 means no relation.

0.050.050.10.10.20.2Predicted threshold multiplier (log)Measured (log)S01 · Vermilion (cut ~580 nm) · predicted 0.0686, measured 0.0771vermilionS01 · No tint (clear) · predicted 0.174, measured 0.21clearS01 · Yellow (cut below ~480 nm) · predicted 0.187, measured 0.236yellowS01 · Purple / background neutraliser · predicted 0.151, measured 0.139purpleS01 · Orange (cut ~550 nm) · predicted 0.203, measured 0.247orangeS01 · Bronze / copper · predicted 0.226, measured 0.232bronzeS01 · Light orange (cut ~520 nm) · predicted 0.258, measured 0.205light-orangeS02 · Vermilion (cut ~580 nm) · predicted 0.0475, measured 0.0734vermilionS02 · No tint (clear) · predicted 0.0542, measured 0.163clearS02 · Purple / background neutraliser · predicted 0.0294, measured 0.0999purpleS02 · Orange (cut ~550 nm) · predicted 0.0474, measured 0.182orangeS02 · Bronze / copper · predicted 0.0502, measured 0.163bronzeS02 · Light orange (cut ~520 nm) · predicted 0.0511, measured 0.264light-orangeRank agreement τS01: +0.43 (0.1.0)S02: +0.33gate: mean τ ≥ 0.60.050.050.10.10.20.2Predicted threshold multiplier (log)Measured (log)S01 · Vermilion (cut ~580 nm) · predicted 0.0686, measured 0.0771vermilionS01 · No tint (clear) · predicted 0.174, measured 0.21clearS01 · Yellow (cut below ~480 nm) · predicted 0.187, measured 0.236yellowS01 · Purple / background neutraliser · predicted 0.151, measured 0.139purpleS01 · Orange (cut ~550 nm) · predicted 0.203, measured 0.247orangeS01 · Bronze / copper · predicted 0.226, measured 0.232bronzeS01 · Light orange (cut ~520 nm) · predicted 0.258, measured 0.205light-orangeS02 · Vermilion (cut ~580 nm) · predicted 0.0475, measured 0.0734vermilionS02 · No tint (clear) · predicted 0.0542, measured 0.163clearS02 · Purple / background neutraliser · predicted 0.0294, measured 0.0999purpleS02 · Orange (cut ~550 nm) · predicted 0.0474, measured 0.182orangeS02 · Bronze / copper · predicted 0.0502, measured 0.163bronzeS02 · Light orange (cut ~520 nm) · predicted 0.0511, measured 0.264light-orangeτ per session: S01 +0.43; S02 +0.33dashed line: prediction equals measurement · gate: mean τ ≥ 0.6
The study's stated gate for a personal lens recommendation is a mean τ of at least 0.6 across observers, against at most 0.3 for a prediction that ignores the observer. Until then the recommender stays a physics estimate.

Every observer's sensitivity profile

Threshold contrast on the four measures, one dot per session; lower is more sensitive. Bars are medians of pooled thresholds once there are two or more.

0.0050.010.020.050.10.20.5Threshold contrast (log; lower is more sensitive)Luminance, 1° discS02 · Clay shooter · Luminance, 1° disc · 0.0219 (95% CI 0.0107–0.0448), 35 trialsRed–green (L−M)S02 · Clay shooter · Red–green (L−M) · 0.00665 (95% CI 0.00375–0.0123), 36 trialsBlue–yellow (S)S02 · Clay shooter · Blue–yellow (S) · 0.0742 (95% CI 0.0356–0.155), 35 trialsLuminanceclay-sized moving discS01 · Clay shooter · Luminance, clay-sized moving disc · 0.0583 (95% CI 0.0221–0.243), 36 trials · protocol 0.1.0, not pooledS02 · Clay shooter · Luminance, clay-sized moving disc · 0.0776 (95% CI 0.0414–0.154), 48 trialsClay shooterhollow: at the floordashed: protocol 0.1.0, not pooled0.0050.010.020.050.10.20.5Threshold contrastluminance 1°S02 · Clay shooter · Luminance, 1° disc · 0.0219 (95% CI 0.0107–0.0448), 35 trialsred–greenS02 · Clay shooter · Red–green (L−M) · 0.00665 (95% CI 0.00375–0.0123), 36 trialsblue–yellowS02 · Clay shooter · Blue–yellow (S) · 0.0742 (95% CI 0.0356–0.155), 35 trialsclay-sizedS01 · Clay shooter · Luminance, clay-sized moving disc · 0.0583 (95% CI 0.0221–0.243), 36 trials · protocol 0.1.0, not pooledS02 · Clay shooter · Luminance, clay-sized moving disc · 0.0776 (95% CI 0.0414–0.154), 48 trialsClay shooterhollow: at the floordashed: protocol 0.1.0, not pooled
A threshold above the screening bound is reported to the observer as a flag to see an optometrist, never as a diagnosis: the display's colour is assumed, not measured.

What one session looks like underneath: S02, clay shooter

The psychometric function behind each threshold: proportion correct against contrast or multiplier, the maximum-likelihood fit, and where it crosses the criterion.

25%62%100%0.0050.010.020.050.10.20.5Luminance, 1° discchance0.02190.0189: 14% correct of 7 trials (95% interval 3%–51%)0.0212: 71% correct of 7 trials (95% interval 36%–92%)0.0237: 64% correct of 11 trials (95% interval 35%–85%)0.0262: 80% correct of 5 trials (95% interval 38%–96%)0.0284: 100% correct of 1 trials (95% interval 21%–100%)0.0363: 100% correct of 3 trials (95% interval 44%–100%)0.0434: 100% correct of 1 trials (95% interval 21%–100%)0.0050.010.020.050.10.20.5Red–green (L−M)chance0.006650.00379: 0% correct of 2 trials (95% interval 0%–66%)0.00481: 50% correct of 4 trials (95% interval 15%–85%)0.00567: 40% correct of 10 trials (95% interval 17%–69%)0.00689: 73% correct of 15 trials (95% interval 48%–89%)0.00793: 100% correct of 1 trials (95% interval 21%–100%)0.0104: 100% correct of 3 trials (95% interval 44%–100%)0.0162: 100% correct of 1 trials (95% interval 21%–100%)0.0050.010.020.050.10.20.5Blue–yellow (S)chance0.07420.0374: 0% correct of 1 trials (95% interval 0%–79%)0.0573: 33% correct of 3 trials (95% interval 6%–79%)0.0663: 50% correct of 4 trials (95% interval 15%–85%)0.0758: 57% correct of 14 trials (95% interval 33%–79%)0.0882: 78% correct of 9 trials (95% interval 45%–94%)0.0987: 100% correct of 4 trials (95% interval 51%–100%)25%62%100%0.0050.010.020.050.10.20.5Luminance, clay-sized moving discchance0.07760.0347: 0% correct of 1 trials (95% interval 0%–79%)0.0437: 40% correct of 5 trials (95% interval 12%–77%)0.0525: 50% correct of 6 trials (95% interval 19%–81%)0.0617: 60% correct of 10 trials (95% interval 31%–83%)0.0708: 50% correct of 12 trials (95% interval 25%–75%)0.0842: 75% correct of 12 trials (95% interval 47%–91%)0.0962: 100% correct of 1 trials (95% interval 21%–100%)0.127: 100% correct of 1 trials (95% interval 21%–100%)0.0050.010.020.050.10.20.5Vermilion (cut ~580 nm)chance0.07340.0379: 0% correct of 4 trials (95% interval 0%–49%)0.0465: 60% correct of 5 trials (95% interval 23%–88%)0.0565: 67% correct of 9 trials (95% interval 35%–88%)0.0685: 36% correct of 11 trials (95% interval 15%–65%)0.0811: 89% correct of 9 trials (95% interval 56%–98%)0.112: 100% correct of 1 trials (95% interval 21%–100%)0.162: 100% correct of 1 trials (95% interval 21%–100%)0.0050.010.020.050.10.20.5No tint (clear)chance0.1630.121: 0% correct of 1 trials (95% interval 0%–79%)0.136: 0% correct of 3 trials (95% interval 0%–56%)0.154: 33% correct of 12 trials (95% interval 14%–61%)0.165: 79% correct of 14 trials (95% interval 52%–92%)0.181: 100% correct of 2 trials (95% interval 34%–100%)0.2: 100% correct of 3 trials (95% interval 44%–100%)0.218: 100% correct of 4 trials (95% interval 51%–100%)0.25: 100% correct of 1 trials (95% interval 21%–100%)25%62%100%0.0050.010.020.050.10.20.5Purple / background neutraliserchance0.09990.0655: 0% correct of 1 trials (95% interval 0%–79%)0.0777: 0% correct of 1 trials (95% interval 0%–79%)0.095: 50% correct of 4 trials (95% interval 15%–85%)0.106: 57% correct of 14 trials (95% interval 33%–79%)0.123: 83% correct of 6 trials (95% interval 44%–97%)0.135: 70% correct of 10 trials (95% interval 40%–89%)0.158: 100% correct of 3 trials (95% interval 44%–100%)0.192: 100% correct of 1 trials (95% interval 21%–100%)0.0050.010.020.050.10.20.5Orange (cut ~550 nm)chance0.1820.156: 0% correct of 3 trials (95% interval 0%–56%)0.177: 80% correct of 5 trials (95% interval 38%–96%)0.187: 50% correct of 6 trials (95% interval 19%–81%)0.205: 44% correct of 9 trials (95% interval 19%–73%)0.222: 71% correct of 7 trials (95% interval 36%–92%)0.249: 100% correct of 6 trials (95% interval 61%–100%)0.27: 100% correct of 2 trials (95% interval 34%–100%)0.304: 100% correct of 2 trials (95% interval 34%–100%)0.0050.010.020.050.10.20.5Bronze / copperchance0.1630.0784: 0% correct of 2 trials (95% interval 0%–66%)0.0983: 43% correct of 7 trials (95% interval 16%–75%)0.114: 43% correct of 7 trials (95% interval 16%–75%)0.135: 62% correct of 8 trials (95% interval 31%–86%)0.158: 40% correct of 5 trials (95% interval 12%–77%)0.179: 75% correct of 4 trials (95% interval 30%–95%)0.212: 100% correct of 6 trials (95% interval 61%–100%)0.263: 100% correct of 1 trials (95% interval 21%–100%)25%62%100%0.0050.010.020.050.10.20.5Light orange (cut ~520 nm)chance0.2640.0605: 0% correct of 1 trials (95% interval 0%–79%)0.088: 100% correct of 1 trials (95% interval 21%–100%)0.112: 0% correct of 1 trials (95% interval 0%–79%)0.139: 50% correct of 2 trials (95% interval 9%–91%)0.176: 14% correct of 7 trials (95% interval 3%–51%)0.214: 62% correct of 16 trials (95% interval 39%–82%)0.259: 75% correct of 12 trials (95% interval 47%–91%)Contrast or multiplier (log scale). Point area ∝ trials; whiskers 95% intervals; dashed line = criterion.25%62%100%0.0050.010.020.050.10.20.5Luminance, 1° discchance0.02190.0189: 14% correct of 7 trials (95% interval 3%–51%)0.0212: 71% correct of 7 trials (95% interval 36%–92%)0.0237: 64% correct of 11 trials (95% interval 35%–85%)0.0262: 80% correct of 5 trials (95% interval 38%–96%)0.0284: 100% correct of 1 trials (95% interval 21%–100%)0.0363: 100% correct of 3 trials (95% interval 44%–100%)0.0434: 100% correct of 1 trials (95% interval 21%–100%)25%62%100%0.0050.010.020.050.10.20.5Red–green (L−M)chance0.006650.00379: 0% correct of 2 trials (95% interval 0%–66%)0.00481: 50% correct of 4 trials (95% interval 15%–85%)0.00567: 40% correct of 10 trials (95% interval 17%–69%)0.00689: 73% correct of 15 trials (95% interval 48%–89%)0.00793: 100% correct of 1 trials (95% interval 21%–100%)0.0104: 100% correct of 3 trials (95% interval 44%–100%)0.0162: 100% correct of 1 trials (95% interval 21%–100%)25%62%100%0.0050.010.020.050.10.20.5Blue–yellow (S)chance0.07420.0374: 0% correct of 1 trials (95% interval 0%–79%)0.0573: 33% correct of 3 trials (95% interval 6%–79%)0.0663: 50% correct of 4 trials (95% interval 15%–85%)0.0758: 57% correct of 14 trials (95% interval 33%–79%)0.0882: 78% correct of 9 trials (95% interval 45%–94%)0.0987: 100% correct of 4 trials (95% interval 51%–100%)25%62%100%0.0050.010.020.050.10.20.5Luminance, clay-sized moving discchance0.07760.0347: 0% correct of 1 trials (95% interval 0%–79%)0.0437: 40% correct of 5 trials (95% interval 12%–77%)0.0525: 50% correct of 6 trials (95% interval 19%–81%)0.0617: 60% correct of 10 trials (95% interval 31%–83%)0.0708: 50% correct of 12 trials (95% interval 25%–75%)0.0842: 75% correct of 12 trials (95% interval 47%–91%)0.0962: 100% correct of 1 trials (95% interval 21%–100%)0.127: 100% correct of 1 trials (95% interval 21%–100%)25%62%100%0.0050.010.020.050.10.20.5Vermilion (cut ~580 nm)chance0.07340.0379: 0% correct of 4 trials (95% interval 0%–49%)0.0465: 60% correct of 5 trials (95% interval 23%–88%)0.0565: 67% correct of 9 trials (95% interval 35%–88%)0.0685: 36% correct of 11 trials (95% interval 15%–65%)0.0811: 89% correct of 9 trials (95% interval 56%–98%)0.112: 100% correct of 1 trials (95% interval 21%–100%)0.162: 100% correct of 1 trials (95% interval 21%–100%)25%62%100%0.0050.010.020.050.10.20.5No tint (clear)chance0.1630.121: 0% correct of 1 trials (95% interval 0%–79%)0.136: 0% correct of 3 trials (95% interval 0%–56%)0.154: 33% correct of 12 trials (95% interval 14%–61%)0.165: 79% correct of 14 trials (95% interval 52%–92%)0.181: 100% correct of 2 trials (95% interval 34%–100%)0.2: 100% correct of 3 trials (95% interval 44%–100%)0.218: 100% correct of 4 trials (95% interval 51%–100%)0.25: 100% correct of 1 trials (95% interval 21%–100%)25%62%100%0.0050.010.020.050.10.20.5Purple / background neutraliserchance0.09990.0655: 0% correct of 1 trials (95% interval 0%–79%)0.0777: 0% correct of 1 trials (95% interval 0%–79%)0.095: 50% correct of 4 trials (95% interval 15%–85%)0.106: 57% correct of 14 trials (95% interval 33%–79%)0.123: 83% correct of 6 trials (95% interval 44%–97%)0.135: 70% correct of 10 trials (95% interval 40%–89%)0.158: 100% correct of 3 trials (95% interval 44%–100%)0.192: 100% correct of 1 trials (95% interval 21%–100%)25%62%100%0.0050.010.020.050.10.20.5Orange (cut ~550 nm)chance0.1820.156: 0% correct of 3 trials (95% interval 0%–56%)0.177: 80% correct of 5 trials (95% interval 38%–96%)0.187: 50% correct of 6 trials (95% interval 19%–81%)0.205: 44% correct of 9 trials (95% interval 19%–73%)0.222: 71% correct of 7 trials (95% interval 36%–92%)0.249: 100% correct of 6 trials (95% interval 61%–100%)0.27: 100% correct of 2 trials (95% interval 34%–100%)0.304: 100% correct of 2 trials (95% interval 34%–100%)25%62%100%0.0050.010.020.050.10.20.5Bronze / copperchance0.1630.0784: 0% correct of 2 trials (95% interval 0%–66%)0.0983: 43% correct of 7 trials (95% interval 16%–75%)0.114: 43% correct of 7 trials (95% interval 16%–75%)0.135: 62% correct of 8 trials (95% interval 31%–86%)0.158: 40% correct of 5 trials (95% interval 12%–77%)0.179: 75% correct of 4 trials (95% interval 30%–95%)0.212: 100% correct of 6 trials (95% interval 61%–100%)0.263: 100% correct of 1 trials (95% interval 21%–100%)25%62%100%0.0050.010.020.050.10.20.5Light orange (cut ~520 nm)chance0.2640.0605: 0% correct of 1 trials (95% interval 0%–79%)0.088: 100% correct of 1 trials (95% interval 21%–100%)0.112: 0% correct of 1 trials (95% interval 0%–79%)0.139: 50% correct of 2 trials (95% interval 9%–91%)0.176: 14% correct of 7 trials (95% interval 3%–51%)0.214: 62% correct of 16 trials (95% interval 39%–82%)0.259: 75% correct of 12 trials (95% interval 47%–91%)Contrast or multiplier (log). Dashed line: criterion.
Point area scales with the trials in each bin; whiskers are 95% intervals. The adaptive procedure puts most trials near the threshold, so the ends of each curve are sparse by design.

Run the study Method and references