Catching what you cannot see
Think of a ball passing behind a football player, a train entering a tunnel, or a cyclist disappearing behind a lorry for a moment. When something goes out of sight we do not lose touch with it: we keep predicting where it will be. Catching a ball, crossing a road and timing a tennis shot all rely on that prediction.
In this experiment a ball moves at a steady speed from left to right towards a yellow line. Near the end of its path it goes behind a screen and disappears. Your job is to tap the screen at the moment the ball touches the line. As soon as you tap, the screen turns see-through and you see where the ball really was.
Time to collision
In 1976 David Lee put forward an influential idea: to know how long it will be before an approaching object hits us, we do not need to work out its distance and speed separately. The ratio of the size of its image to the rate at which that image is growing gives the time directly. Lee showed that this information could be enough for drivers to control when and how hard to brake.
This game is different: the ball is not coming towards us but passing sideways, and for the last part of its journey it cannot be seen at all. There is no information to read from the image; to predict the moment of contact you have to grasp the ball's speed while it is visible and keep that motion running in your head while it is hidden. Researchers call tasks like this 'prediction-motion' tasks.
Time is what matters
In 1991 Christopher Peterken, Brian Brown and Kenneth Bowman used a task very much like this one: a target moving horizontally across a screen disappeared partway, and participants pressed a key when they thought it would pass a point on the far side. Following the target with the eyes was not necessary for success.
Their main finding was that performance depended not on how long the target was visible, how far the prediction had to reach, or how fast the target moved, but on the time over which the prediction was made. Earlier literature had assumed distance was what mattered; they found that temporal factors were the main determinant. In this game each round also has one short, one medium and one long hidden time, while speed varies separately, so the two effects can be seen apart.
A speed controller in the mind
In 2018 Alexis Makin reviewed the prediction-motion literature. In most tasks both the average estimate and the spread of estimates grow linearly with the time the object is hidden. Someone who predicts a short occlusion almost perfectly gives much more scattered answers when the occlusion is long.
Makin argues that this internal simulation is paced by a 'common rate controller': the same mechanism operates when predicting the position of a hidden object, the value a hidden counter has reached, or the colour a slowly changing surface has arrived at. Participants trained with false feedback to respond early on one of these tasks started responding early on the other too. Makin also notes that people sometimes use shortcuts, such as 'tap straight away if the screen is small' or 'tap early if the ball is fast'.
Early or late?
The direction of the timing error varies from study to study; there is no single 'right' direction. But the growth of the error as the hidden time increases is a fairly consistent finding. So on the results screen we look at two things: your average error for short, medium and long occlusions, and the slope of the line that best fits all your errors. The slope shows how many milliseconds your error changes when the hidden time gets one second longer.
We also split the balls into faster and slower halves and compare your average error for each. Going by Peterken and colleagues' finding, speed on its own should not make a big difference for the same hidden time; if there is a clear difference, you may be using speed as a separate cue.
What your score does and does not tell you
Each ball's score depends on how large your timing error is relative to the hidden time: 10 / (1 + (|error| / (hidden time + 300 ms) / 0.1)^1.6). An error of the same size is penalised less after a long occlusion, because the task is harder. With a one-second hidden time, a 130 ms error earns 5 points and a 65 ms error about 7.5. Balls you do not tap for count as zero. A round's score is the average of its three balls; the maximum total is 50.
Screen and touch delays can shift all your errors towards 'late' by the same amount, so look at how your error changes as the hidden time grows rather than at its exact value. Seeing the ball's real position after every trial may let you correct yourself as you go; your first game is the one kept in the scientific data. As crowd data comes in, we will show how errors are distributed by hidden time.