Lengths

What you see

One trial is a set of pairs, from 8 at level 1 to 18 at level 10. Each pair runs the same way:

1. A small fixation cross appears at the centre of a dashed reference line for 300 milliseconds.
2. Two bars appear, one left of centre and one right. Each is a rounded bar of the same width, standing roughly upright.
3. You choose the longer bar by clicking its half of the field, clicking Left or Right below it, or pressing the left or right arrow key.
4. The pair leaves as soon as you answer. If you do not answer before the deadline, it leaves anyway and that pair is recorded as unanswered.

There is no feedback on individual pairs while the set runs. A line under the buttons shows which pair you are on, for example "Pair 3 of 12". After you check your answer, a row of cells marks each pair green if you were right, red if you were wrong, and with a red dashed outline if it timed out. Exactly half of the pairs in every set have the longer bar on the left, so a habit of favouring one side can only cost you.

What changes with level

The shorter bar in each pair is between 18 and 36 field units long (the field is 75 units tall). The longer bar is the shorter one multiplied by a ratio drawn from the level's range. On top of that, four kinds of noise are added: each bar is tilted by up to a set number of degrees, shifted up or down off the reference line, surrounded by thin distractor strokes at the top levels, and cut off by a tighter deadline.

Tilt and shift are chosen separately for each bar, so the two bars in a pair usually lean differently and sit at different heights. The distractor strokes are thin grey lines, not bars, scattered above and below the pair. By design none of them is within 10% of the length of either bar, so they can never be a plausible match for either one.

What it measures

Lengths feeds the Perceptual precision facet of the Attention dimension, alongside Timing Tasks. Its main scoring weight is on quantitative comparison, with a smaller weight on processing speed. In plain terms: how finely can you tell two magnitudes apart, and can you keep doing it quickly while irrelevant features pull at your eye?

Weber's law

The central idea comes from nineteenth-century psychophysics. Weber's law says that the smallest difference you can reliably detect between two magnitudes is a roughly constant proportion of their size. If I is the size of the stimulus and ΔI the difference you can just detect, then ΔI = k × I. The constant k is the Weber fraction.

Weber fraction

The smallest proportional difference between two stimuli that an observer can reliably detect. For visual length, the commonly cited estimate is about 3%.

For visual length the agreed estimate, as Ganel and colleagues put it, is about 3%, a figure that traces back to Teghtsoonian's classic analysis. That is why the game describes difficulty in percentages, not units. A 2-unit difference is easy between bars of 20 and 22 units (10%), and much harder between bars of 40 and 42 (5%).

The drill below uses clouds of dots rather than lines, but it shows the same law at work: your accuracy falls as the ratio between the two sides moves toward 1.

Practice drillSign in to try it

Why tilt and shift make it harder

If the difference at level 10 (4 to 8%) is above the 3% Weber fraction, why is it hard? Because a textbook threshold is measured under ideal conditions: two clean, aligned lines and unlimited time. This game strips away the helpful cues one by one.

• Shift removes the shared baseline. Cleveland and McGill's graphical perception experiments ranked the accuracy of basic visual judgements. Judging position along a common scale came out on top, above judging length. When both bars stand on the same line, you can compare their tops as positions. Once each bar is shifted up or down by a different amount, the tops no longer line up with the lengths, and you are forced back onto the less accurate length judgement.
• Tilt distorts the height. A tilted bar's vertical extent is shorter than its true length. At 24° a bar's height is only about 91% of its length, a 9% loss that is as large as many of the 7 to 13% differences you judge at level 8. Orientation also biases perception directly: in the vertical–horizontal illusion, a vertical line looks longer than a horizontal line of the same length, with reported biases of roughly 3 to 10% for lines drawn on a flat surface.
• Clutter competes for the eye. The distractor strokes are never close in length to either bar, but they still take a glance you cannot spare when the deadline is 1.3 seconds.

How it is scored here

Scoring is simple and strict.

• A pair is correct if you chose the longer side before its deadline.
• An unanswered pair is simply not correct. There is no separate penalty, but it earns nothing.
• Your set score is the share of pairs you got right.
• Responses faster than 150 milliseconds are flagged as anticipations in your session review, because that is too fast to have been a genuine judgement.

Speed itself adds nothing to the score. Your time per pair is reported, but the only speed demand is the deadline. A correct answer at 1,200 milliseconds counts exactly as much as one at 400.

Difficulty is adaptive. A perfect set (every pair correct) moves you up one level. A set with some correct answers keeps you at your level. A set with no correct answers moves you down. Your 0 to 100 score compares your accuracy with what the level you work at predicts; 50 means you are doing what that level predicts.

The session report includes a headline that is worth understanding: Smallest difference you can call. It groups your pairs by how different the bars were (in 5% steps) and finds the smallest step at which you were right at least 75% of the time, with at least three pairs at that step. The 75% point is the standard threshold used in two-choice psychophysics, halfway between guessing (50%) and perfect.

Where you will meet it

The best-known cousin is the Lengths game in the pymetrics battery. pymetrics' patent describes a Reward Learning Task in which subjects see digital faces with either a short or a long mouth, where the difference is minimal but perceptible, and press an arrow key to classify each one, earning money for correct answers under a differential reward schedule. Candidate guides describe the pymetrics game in the same terms: faces, and a judgement of longer or shorter mouths.

That task descends from the Probabilistic Reward Task of Pizzagalli and colleagues. In the research version, a short mouth (11.5 mm) or long mouth (13 mm) appears on a cartoon face for just 100 milliseconds. Correct answers for one of the two lengths are rewarded three times as often as for the other, which lets researchers measure how strongly rewards bias your choices.

So the family resemblance is real, but the tasks differ in important ways:

The practical lesson for a pymetrics-style version: the perceptual skill you build here helps, but in the reward version you should expect to be uncertain often, and you should notice that rewards are not a reliable signal of whether you were right.

The method

1. Settle your gaze on the fixation cross

   The cross appears exactly where the gap between the bars will be. Look at it, not at either side, so both bars land in view at the same moment.

2. Take in both bars whole, as lengths

   Look at each bar from end to end rather than at its top. At levels 1 to 2 the tops line up and a glance at them works. From level 3 onwards each bar is shifted off the line, so the tops tell you about position, not length.

3. Correct for tilt

   If one bar leans noticeably more than the other, its height understates its length. Judge along the bar, not up the screen. When a pair feels like a tie, the more tilted bar is the one being short-changed by a height pair.

4. Ignore the thin strokes

   Distractor strokes are thin grey lines and are never within 10% of either bar's length. You never need to compare anything to them. Treat them as background.

5. Commit to your first clear impression

   Once you have one clear impression, answer. A second or third look at a 5% difference rarely resolves it and risks the deadline. An unanswered pair earns nothing, while even a guess earns half on average.

Worked example 1: the tops disagree

You are at level 4. The right bar's top sits clearly higher on the screen than the left bar's top. Which bar is longer, and by how much?

Show the solution

The left bar is longer. It is 30 units long; the right bar is 25 units. The ratio is 30 ÷ 25 = 1.20, so the left bar is 20% longer, inside level 4's 16–26% range.

The trap is the tops. The left bar was shifted 3 units down and the right bar 3 units up, so the right bar's top ends up 3.5 units higher even though it is 5 units shorter. If you compared tops, you got this wrong. If you compared each bar from end to end, the left bar's extra length is obvious: its bottom reaches far below the right bar's bottom.

A quick check that works at any tilt: compare how far each bar extends both above and below the reference line. The right bar sits mostly above the line; the left bar reaches well past it at both ends.

Worked example 2: the tall-looking loser

You are at level 8, with a 1.7-second deadline. The right bar looks at least as tall as the left one, and a long grey stroke cuts across the bottom of the field. Which bar is longer?

Show the solution

The left bar is longer. It is 34.5 units long against the right bar's 32 units, a difference of about 7.8%, inside level 8's 7–13% range.

Height fools you here. Leaning at 24°, the left bar's vertical extent is 34.5 × cos 24° ≈ 31.5 units. The nearly upright right bar has a vertical extent of about 31.9 units. So by height the right bar looks slightly taller, even though the left bar is the longer one by 2.5 units.

The grey strokes are 19.2 and 24 units long. Neither is within 10% of either bar (the generator forbids that), so neither tells you anything. The long stroke near the bottom is simply a distraction.

The method handles this: judge along each bar, and when a pair feels like a tie, remember that the more tilted bar is the one a height pair short-changes.

Tips and traps

Levelling up

A perfect set is needed to move up, and set sizes grow as you climb: 12 pairs at level 4, 16 at level 8 and 18 at level 10. At level 10 you need 18 out of 18 at 4 to 8% differences, with tilt up to 30°, shift up to 8 units and a 1.3-second deadline. Expect to spend most of your time holding at your level, with occasional promotions. That is normal and still counts: your 0 to 100 score rewards accuracy relative to the level you work at, not promotions.

Three things change as you climb, and each needs its own adjustment.

• Levels 3 to 5: tilt and shift arrive. Retrain your eyes from tops to whole lengths.
• Levels 6 to 7: differences fall to around 10%, and tilt reaches 20 to 24°. Tilt correction becomes decisive, because a tilted bar can lose more height than the difference you are judging.
• Levels 8 to 10: distractor strokes appear and deadlines fall under 1.7 seconds. Your gaze routine matters more than extra effort: fixation cross, both bars, one impression, answer.

Be honest with yourself about what practice does. Perceptual learning research finds that improvements from practising a specific discrimination are often specific to the trained task and stimuli, as Fahle's review of the field emphasises. Practice here will sharpen this kind of judgement and your routine for it. It will not upgrade your eyesight in general.

1. Week 1: whole-length habit
   • Three sessions of about 10 minutes at your natural level
   • After each set, note whether your misses were pairs where the tops disagreed
   • Say to yourself end to end as each pair appears, until it is automatic
2. Week 2: tilt and speed
   • Three sessions; on close pairs, consciously ask which bar leans more
   • Check your Smallest difference you can call figure after each session
   • Add one Timing Tasks session to train the other half of the Perceptual precision facet
3. Week 3: pressure routine
   • Three sessions at your highest stable level
   • Aim for zero unanswered pairs, even if it means more guesses
   • Compare your accuracy and time per pair across the three weeks

Check yourself

5 practice questions

1. By Weber's law, which pair is hardest to tell apart?
2. From level 3 upwards, why is comparing the tops of the bars unreliable?
3. A bar 34.5 units long leans at 24°. Roughly how tall does it stand on screen?

and 2 more

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Sources

1. Weber's law and Fechner's law (course handout). New York University, Center for Neural Science. cns.nyu.edu
2. Ganel, T., Freud, E., Chajut, E., & Algom, D. (2012). Accurate visuomotor control below the perceptual threshold of size discrimination. PLoS ONE, 7(4), e36253. doi:10.1371/journal.pone.0036253
3. Teghtsoonian, R. (1971). On the exponents in Stevens' law and the constant in Ekman's law. Psychological Review, 78(1), 71–80. doi:10.1037/h0030300
4. Cleveland, W. S., & McGill, R. (1984). Graphical perception: Theory, experimentation, and application to the development of graphical methods. Journal of the American Statistical Association, 79(387), 531–554. doi:10.1080/01621459.1984.10478080
5. Durgin, F. H., Kwok, C. S., Becker, K. M., & Phyu, Y. M. (2025). Large bias in matching small horizontal and vertical extents separated in depth in the real world is similar for upright and supine observers. Vision, 9(1), 11. doi:10.3390/vision9010011
6. Pizzagalli, D. A., Jahn, A. L., & O'Shea, J. P. (2005). Toward an objective characterization of an anhedonic phenotype: A signal-detection approach. Biological Psychiatry, 57(4), 319–327. doi:10.1016/j.biopsych.2004.11.026
7. Cheng, Z., et al. (2025). Reinforcement learning and decision making in depression in adolescents and young adults: Insights from a new model of the Probabilistic Reward Task. Computational Psychiatry, 9(1), 268–283. doi:10.5334/cpsy.147
8. Polli, F., & Yoo, J. (Pymetrics Inc.). Systems and methods for data-driven identification of talent. US Patent 9,842,314. Google Patents
9. GraduatesFirst. Pymetrics games: practice and guide (candidate-reported game descriptions). graduatesfirst.com
10. Fahle, M. (2005). Perceptual learning: specificity versus generalization. Current Opinion in Neurobiology, 15(2), 154–160. doi:10.1016/j.conb.2005.03.010

Put it into practice: LengthsSign in to try it