Weight Estimation Game

About Weight

Weight is a quiz about the stuff around you. Each round shows one object as a big emoji with its name, such as a tennis ball, a loaf of bread, a grand piano or an airliner, and asks one question: how much does it weigh? You answer on a single slider that runs from 1 gram to 100,000 kilograms, which is a hundred-million-fold range, so the same control covers a paper clip and a diesel locomotive.

The game draws from a pool of more than 75 objects, all with typical, well-documented masses: a chicken egg is 60 grams, a Labrador retriever 30 kilograms, an upright piano around 250 kilograms, an African elephant about 5.5 tonnes. Early rounds stick to things you have probably held, like fruit, phones and shoes. Later rounds bring in things few people ever lift, such as a violin, an emperor penguin or a fire truck, and that is where gut feeling has to do real work.

How to play

1. Look at the object and its name. If the name is ambiguous, the pool uses the common version: an AA battery, a packed suitcase, a city bus with no passengers.
2. Drag the slider, or use the minus and plus buttons for fine steps. Hold a button to scroll faster. The big number above the slider shows your current guess in grams, kilograms or tonnes.
3. Think in steps of ten rather than in exact numbers. Decide first whether the object is a gram-sized thing, a kilogram-sized thing or a tonne-sized thing, then refine.
4. Press Lock in (or Enter on a keyboard) before the timer runs out. The true value appears as a green marker on the slider, along with your score for the round.

You see an object. Slide the scale to its typical weight, anywhere from a paper clip to a locomotive. The slider is logarithmic: each tick is the same percentage step.

How scoring works

Weight is scored on a ratio scale, not by subtracting numbers. Being twice too high costs exactly as much as being half the true weight, and a guess of 600 grams for a 60 gram egg is as wrong as 6 grams. The score is 100 minus a penalty proportional to the base-2 logarithm of guess divided by truth. At the easiest setting a score of zero needs a miss of about a factor of 4.6; at the hardest setting the zero point shrinks to about a factor of 2.6.

In practice this means a guess within 25 percent of the truth scores about 85 on level 1 and 77 on level 10, and a miss by a factor of 1.5 still earns roughly 73 on level 1 and 58 on level 10. Only a near-exact guess gets into the high 90s. Each round also has a timer, 16 seconds at the start and 12 seconds at the top difficulty. If it runs out, whatever is on the slider is submitted, but a late answer counts for half.

What it trains

This game exercises magnitude estimation: placing an unfamiliar quantity on a mental scale by comparing it with things you know well. People who do this fast tend to anchor on reference masses, like a 1 liter bottle of water at 1 kilogram, an adult at 70 kilograms and a small car at about 1.4 tonnes, and then ask whether the object is a bit more or a lot more than the anchor.

The skill turns up whenever you pack a bag for a flight, decide whether a shelf can take a box, guess whether you can carry a delivery up the stairs alone, or sanity-check a number in a news article. It also protects against the quiet errors that come from unfamiliar units, for example reading a tonne as a kilogram.

Tips for a higher score

• Memorize a ladder of anchors: paper clip 1 g, coin 5 g, egg 60 g, apple 180 g, liter of water 1 kg, laptop 1.6 kg, bowling ball 6 kg, adult 70 kg, small car 1.4 t. Everything else sits between two rungs.
• Compare to water. Most solid fruit and most animals are about as dense as water, so volume in liters is nearly the same number as mass in kilograms: if you could pour it into a bucket of 10 liters, it is around 10 kilograms.
• Metal and stone are heavy for their size, so a brick, a barbell or a pool ball weighs more than the same shape made of wood or foam. Hollow things such as a basketball, a guitar or a bicycle are much lighter than they look.
• When you are stuck, move the slider to the middle of your uncertainty on a log scale. A guess that is off by a factor of 2 in either direction still scores decently, while a hopeful guess that is wrong by a factor of 10 scores close to nothing.
• Watch your bias in the stats screen. Many players underestimate very large masses such as vehicles and whales, so nudging big guesses upward is often a free gain.

The idea behind it

Our sense of magnitude is roughly logarithmic. The Weber-Fechner law, formulated in the 19th century, says that the smallest change we can notice in a stimulus is proportional to its size: you can feel the difference between 100 and 110 grams in your hand about as well as between 1 and 1.1 kilograms, but not between 1,000 and 1,010 grams. That is why this game uses a logarithmic slider and a ratio score.

Judging weight by sight is harder than it looks. In the size-weight illusion, first described by Augustin Charpentier in 1891, the smaller of two objects of identical mass feels heavier when lifted. Expectation, not only muscle feedback, shapes the sense of heaviness, which is one reason a practiced eye for what things are made of is worth more than a strong arm.

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