How Probability Is Shaped by Frequency

Author: Zhang Suhang

The previous article states: frequency comes first; probability follows.

This article goes one layer deeper, explaining how probability is brought into being.

No formulas, no jargon, only the underlying mechanism.

I. Coin tosses and video likes: fluctuating at first, settling on a value

Take coin tossing first.

Toss ten times. Heads may appear seven times, or three times.

Toss one hundred times. The proportion of heads drifts toward one half.

Toss ten thousand times. The proportion of heads stays near one half.

This proportion is not stable from the start.

The more we toss, the steadier it becomes, until it settles on a value.

The same applies to video likes.

When only dozens of people have viewed a video, its like ratio swings wildly.

From this perspective, views and clicks are essentially the frequency of behavioural occurrences.

When viewership reaches several thousand, the like ratio begins to stabilize. At tens of thousands of views, the ratio barely changes and remains around a fixed value.

Both examples follow the same pattern:

Few trials, volatile data; many trials, stable data; eventually converging to an average value.

This average value is not pre-set somewhere.

It emerges little by little as trials accumulate.

Without trials, there is no such average.

Only when enough trials occur does the average take shape.

II. Theft: the more offences committed, the greater the chance of arrest

Now consider theft.

After a first theft, the chance of being caught is low.

With the second and third offences, more traces are left, and the risk of being noticed rises.

The more thefts are committed, the higher the chance of being witnessed, identified, and linked to prior crimes.

Once offences accumulate to a certain point, arrest becomes almost inevitable.

This differs from coin tossing and video likes.

Coin tossing and likes move from volatility toward a fixed value.

The risk of theft starts low and keeps rising.

It does not converge to a steady average.

As offences increase, the risk is pushed upward unidirectionally, drawing closer to certainty.

If no theft is committed, the risk does not grow.

Each theft adds to the risk.

More offences mean higher risk.

The act of theft itself pushes the probability of arrest higher step by step.

III. Probability follows different evolutionary paths, yet all are driven by frequency

Coin tosses and video likes: fluctuating, finally converging to an average.

Theft: higher frequency brings a unidirectional rise in risk, moving toward certainty.

Probability evolves along entirely different paths in these cases.

Still, they share the same core mechanism.

Whether converging to stability or climbing continuously, the underlying rule holds:

Probability only takes form after events actually occur.

When trials are too few, probability cannot develop or stabilise.

No coin toss, no proportion of heads.

No views, no like ratio.

No theft, no probability of arrest.

Probability is never predetermined.

It is progressively driven and shaped by repeated actions and their frequency.

IV. What probability really is

Probability does not exist inherently.

It does not hang in waiting to be discovered.

Probability is a product of behaviour.

When actions are few, probability either fluctuates sharply or stays unchanged.

As actions accumulate, probability either stabilises or keeps rising.

In some cases, sufficient trials make probability converge to an average.

In others, higher frequency pushes probability continuously upward.

Whichever form it takes, the principle remains:

Events come first, then probability.

Frequency comes first, then patterns.

This is the full process through which frequency shapes probability.