🧩 How Close Are We to the Human Limit of Solving a Rubik's Cube?

Can machine learning estimate the fastest time a human will ever achieve?

For over two decades, speedcubers have continued to push the boundaries of what's possible. Every new world record raises the same question:

🤔 Is there a human limit to solving a Rubik's Cube?

I decided to explore this question by analyzing 23 years of World Cube Association (WCA) world records, spanning from 2003 to 2026, and using machine learning and statistical modeling to estimate the theoretical limits across all official speedcubing events.

📊 The Dataset

The analysis is based on the historical progression of world records from the 17 official WCA events, including:

3x3 Cube
2x2, 4x4, 5x5, 6x6, and 7x7
One-Handed
Blindfolded events
Fewest Moves
Pyraminx
Skewb
Megaminx
Square-1
Clock

Each event has followed a unique trajectory, making it fascinating to compare how quickly different disciplines are approaching their performance limits.

🤖 Modeling Human Performance

Instead of fitting a simple trend line, I combined two complementary statistical techniques.

Gaussian Processes

Gaussian Processes are well suited for modeling nonlinear trends while also providing uncertainty estimates.

They allow the model to capture how world records improve over time without assuming a fixed mathematical curve.

Extreme Value Theory (EVT)

Since world records represent extreme observations, I used Extreme Value Theory (EVT) to model the behavior of these exceptional performances rather than the average competitor.

Combining EVT with Gaussian Processes results in more realistic projections for the long-term performance ceiling.

🚀 What Does the Model Predict?

One of the most interesting results comes from the classic 3x3 Rubik's Cube.

The model estimates that the human limit could approach approximately 2.37 seconds, with performance gradually converging around 2036.

Of course, this doesn't mean someone will suddenly achieve exactly 2.37 seconds in 2036. Instead, it suggests that future improvements will become increasingly difficult as performances approach this estimated limit.

🌐 Explore the Interactive Dashboard

To make the results easier to explore, I built an interactive dashboard where you can visualize:

📈 Historical world record progression
🤖 Machine learning projections
🎯 Estimated performance limits
📉 Confidence intervals
🔄 Comparisons across all 17 WCA events

👉 Try it here:
https://nkmelndz.github.io/speedcubing-limits/

💭 Final Thoughts

Predicting human performance is inherently uncertain, especially in a sport influenced by training methods, hardware improvements, and innovation in solving techniques.

Still, combining Gaussian Processes with Extreme Value Theory provides an interesting way to explore how close we might be to the physical limits of speedcubing.

I'm curious to hear what the speedcubing community thinks.