The game
What is Scale of Things?
Scale of Things is a size comparison game: two outlines side by side, one labelled with its real size, and your job is to make the other one the right size.
Each round pairs a reference you can picture with a target you have to judge: a blue whale beside a school bus, a country beside a lake, a planet beside a moon. The reference's size is written beside it. You drag the target's corner, or slide the ruler under it, until it looks the right size next to the reference, then lock it in, and the real outline grows or shrinks out of your guess to show how far off you were.
The things come from a catalog of animals and prehistoric creatures, countries, states and lakes, vehicles, buildings and landmarks, everyday objects and the bodies of the solar system, each with a documented size. A run is 5 rounds, and every guess is scored by proportion, so a whale is marked exactly as a beetle is.
- rounds in a run, each weighted more than the last
- 5
- points for a perfect run
- 1,000
- too big or too small, and a guess scores nothing
- 4×
The name
What does Scale of Things mean?
Scale is size seen in proportion, and proportion is the only kind of size the game judges.
Scale comes from the Latin scala, a ladder or a flight of steps, and by way of the marked rule it came to mean the ratio between a drawing and the thing it draws: a model at one to a hundred, a map at one to a million. To grasp the scale of something is to see it in proportion to something else, which is exactly the move the game asks for. You are never asked how many metres long an aardvark is, only how long it is beside a thing you know.
The scoring keeps to the same idea. A guess twice the real size and a guess half the real size are one mistake, a factor of two, and they cost the same.
A short history
Where judging size by eye has been studied
Map makers, statisticians and psychologists have each found a way in which people get size wrong.
1569
The map that stretches the poles
Gerardus Mercator publishes the projection that still hangs on classroom walls. It keeps compass bearings straight and pays for it in area: Greenland looks as big as Africa and is about a fourteenth of its size.
1907
A crowd guesses a weight
Francis Galton collects 787 guesses at the weight of an ox from a fair in Plymouth. The middle guess lands within one percent of the truth, the first measured case of a crowd estimating well.
1910
The pull toward the middle
Harry Hollingworth shows that people judging a quantity drift toward the middle of the range they have seen: small things are judged too big and large things too small. He calls it the central tendency of judgement.
1957
Perceived size has a law
S. S. Stevens proposes that sensation grows as a power of the stimulus. For area the exponent is below one, so a shape twice as large looks less than twice as large, a finding Robert Teghtsoonian confirms for drawn figures in 1965.
1974
The anchor
Amos Tversky and Daniel Kahneman describe anchoring: a number you have just seen drags your estimate toward it, even when it has nothing to do with the question.
Now
Scored as a factor
Scale of Things puts those findings to work: a known reference as the anchor, a target to judge against it, and a score that measures the factor you were off by rather than the metres.
Why it works
Why do people misjudge size the same way?
Most lost rounds are not wild guesses. They are sensible guesses pulled the same direction by the same habits.
Judgements drift to the middle
Hollingworth's central tendency means a guess at anything big tends to come in small, and a guess at anything small comes in big. When the target dwarfs the reference, your first instinct is almost always too timid.
Area fools the eye
Stevens' power law says perceived area grows more slowly than real area. A shape with twice the area does not look twice as big, so when you size a wide, flat thing, a lake or a country, you tend to leave it short.
The reference anchors you
The labelled outline is there to help, and it also drags your guess toward its own size. That is anchoring, and it is why guesses crowd the reference rather than spreading out to where the targets actually are.
Maps lie about size
Anyone who learned geography from a Mercator map carries its distortions: Canada and Russia oversized, Africa and South America undersized. A country round asks for the real area, and the wall map is the wrong memory to consult.
The method
How to judge size by eye in Scale of Things
Four habits that turn a hunch into a measured guess.
01
Count copies, not metres
Ask how many of the reference would fit along the target. Three buses end to end is a judgement your eye can make; thirty-six metres is a number it cannot.
02
Judge one axis at a time
Settle the length first, then check the height against the reference separately. Two one-dimensional comparisons are more reliable than one impression of the whole shape.
03
Lean toward the extreme
Big things get guessed too small and small things too big. When the target is clearly much bigger or much smaller than the reference, push your guess a little further than feels right.
04
Learn the yardsticks
After each reveal the game puts the answer in familiar terms. Those comparisons come from a short list of everyday objects, and knowing their sizes turns every reveal into practice for the next round.
| Within 5% | 100 points, spot on |
|---|---|
| 15% too big or too small | 90 points |
| 50% too big or too small | 63 points |
| Twice or half the real size | 37 points |
| Three times or a third | 10 points |
| 4× or more, either way | 0 points |
In this game
How Scale of Things turns a guess into a score
A factor, not a difference; a ladder of multipliers; and pairs that drift further apart as a run goes on.
A guess is marked by the factor it is off by, in either direction: within 5% is a perfect 100, and 4 times too big or too small is nothing, with a curve between that keeps a near miss worth having. Each round's score is then multiplied by its place in the run, ×1, ×1, ×2, ×3 and ×3, for a perfect run of 1,000. The later rounds pair things further apart in size, and more often very far apart, 3 to 6.5 times, which is where the zoom keys come in.
Nothing is timed, nothing is dealt twice in a row, and there is no daily limit: a new run of 5 rounds is one press away.
Vocabulary
Size and estimation terms, defined
The words for judging how big something is, and for the ways the eye gets it wrong.
- Scale
- Size in proportion to something else: the ratio between a drawing and the real thing, or between two things set side by side.
- Reference and target
- The two outlines in a round of Scale of Things: the reference comes labelled with its real size, and the target is the one you resize.
- Factor
- How many times too big or too small a guess is. Twice the real size and half the real size are both a factor of two, and score the same.
- Central tendency of judgement
- Hollingworth's 1910 finding that estimates drift toward the middle of the range a person has seen: big things judged small, small things judged big.
- Power law
- Stevens' rule that perceived intensity grows as a power of the real one. For area the power is below one, so doubling a shape's area makes it look less than twice as big.
- Anchoring
- Letting a number you have just seen pull your estimate toward it. In the game, the reference's label is the anchor.
- Mercator projection
- The 1569 world map that keeps compass bearings straight and inflates everything near the poles, the source of most people's wrong ideas about how big countries are.
- Silhouette
- A shape filled in flat, with no detail inside its outline. Every thing in the game is drawn as one, so only its size and outline can be judged.