How is the centroid calculated?

Simple arithmetic mean of all dot x-coordinates for the horizontal component, and all y-coordinates for the vertical. Every dot contributes equally regardless of size.

What pixel error is considered excellent?

Under 20 px is excellent. Under 40 px is solid. Dense clusters with outliers are harder — 30 px on those is very good.

Is this related to center-of-mass in physics?

Only conceptually — this game assumes equal mass for every dot. In physics, center of mass weights each point by its mass, which could differ.

Can You Spot the Center of Mass?

Can you spot the center of mass of a scattered dot cloud — the single point that balances all the dots equally? A cluster of dots appears and you click where you think their visual centroid is. Your score is the pixel distance from your click to the true averaged position of all the dots. With 5 dots it's manageable; with 20 dots at varying densities, your visual averaging system starts revealing its biases.

How to Play

A random scatter of dots appears on the canvas.
Click once where you think the center of mass (average position) falls.
The true centroid is revealed and your error in pixels is shown.
Harder levels add more dots with asymmetric clustering.

Why It's Hard

Humans are decent at averaging positions across small sets (under 8 items) but our centroid estimation is systematically biased toward visually dense clusters. When dots are unevenly distributed, you over-weight the dense cluster and under-weight isolated outlier dots, pulling your estimate toward the "bulk" of the pattern rather than the true arithmetic mean.

Tips

1Scan the full extent of the dot cloud before clicking — don't anchor on the densest group.
2Find the leftmost and rightmost dots, then estimate the horizontal midpoint. Repeat vertically.
3Outlier dots that seem "alone" actually shift the centroid significantly toward them — don't ignore them.

FAQ

How is the centroid calculated?: Simple arithmetic mean of all dot x-coordinates for the horizontal component, and all y-coordinates for the vertical. Every dot contributes equally regardless of size.
What pixel error is considered excellent?: Under 20 px is excellent. Under 40 px is solid. Dense clusters with outliers are harder — 30 px on those is very good.
Is this related to center-of-mass in physics?: Only conceptually — this game assumes equal mass for every dot. In physics, center of mass weights each point by its mass, which could differ.

Built by

Ethan R. Caldwell

Game Developer · Wilmington, DE

Designed Can You Spot the Center of Mass? and 46 other browser puzzles. Game developer based in Wilmington, Delaware. Hardcore puzzle gamer at heart — obsessed with logic puzzles, sokoban-style mechanics, and physics-based brain teasers. Off the clock, unwinds with ARPGs, RPGs and JRPGs.

[email protected]