Trend following is rooted in basic statistical understandings. Take for example the baby boys to baby girls ratio. Consider the following example from research on statistical reasoning. There are two hospitals: in the first one, 120 babies are born every day, in the other, only 12. On average, the ratio of baby boys to baby girls born every day in each hospital is 50/50. However, one day, in one of those hospitals twice as many baby girls were born as baby boys. In which hospital was it more likely to happen? The answer is obvious for a good trader, but as research shows, not so obvious for a lay person: It is much more likely to happen in the small hospital. The reason for this is that technically speaking, the probability of a random deviation of a particular size (from the population mean), decreases with the increase in the sample size.

What does this mean in terms of trading? Take 2 traders that on average win 40% of the time with their winners being 3 times as large as their losers. One has a history of 1000 trades and the other has a history of 10 trades. Who has a better chance in the next 5 trades to have winners only be 10% of their total trades (instead of the typical 40%)? The one with the 10 trade history has the better chance. Why? The more trades in a history, the more probability to adhere closer to the average. The less trades in a history, the more probability to deviate from the average.

How does this help? Think about a friend who gets a stock tip and makes money. He tells everyone. He seems like he really knows his trading. The problem this trader has is that his population of tips is very small. He could just as easily follow the next stock tip given to him and lose it all. One tip means nothing. There is no history. You might as well be playing the lottery or sitting at a craps table.

What the Hospital Example Teaches Traders

The hospital example is one of the clearest demonstrations available of why human intuition fails at statistical reasoning. When asked which hospital is more likely to have a day where twice as many girls as boys are born, most people say it makes no difference, since the underlying probability is 50/50 at both hospitals. This answer is wrong, and the wrong answer is produced by focusing on the population probability (50/50) rather than on the sample size.

The 120-baby hospital will produce a 2:1 girl-to-boy ratio on roughly one day per year. The 12-baby hospital will produce the same deviation on roughly one day per month. Both hospitals have the same underlying probability. The small hospital produces extreme deviations more often because small samples deviate further from the population mean with higher frequency. The law of large numbers says that as sample size increases, the observed ratio converges toward the population probability. Small samples are inherently noisier.

Applied to trading track records, this is the foundation of every evaluation methodology that institutional allocators use. A trader with 10 trades has produced a sample so small that almost any observed win rate is consistent with almost any underlying probability distribution. A trader with 10 trades and a 40% win rate might have an underlying probability of 10% or 70%. There is not enough data to distinguish these possibilities. A trader with 1,000 trades and a 40% win rate has provided enough data to say with statistical confidence that the underlying win rate is close to 40%.

The stock tip example is the retail version of the same error. A friend makes money on one tip. One data point. The sample size is 1. With a sample size of 1, you cannot distinguish between a person with genuine edge and a person who got lucky once. The lottery has a positive outcome for one ticket per drawing. The winner is not demonstrating investment skill. They are demonstrating the arithmetic of large samples: give enough people one ticket each and someone will win. The winning ticket holder will tell everyone about their success. Their sample size is still 1.

Systematic trend following solves the sample size problem structurally. A trend following system that trades 200 instruments across multiple time horizons generates hundreds of trades per year. Over 10 years, the system generates thousands of trades. This sample is large enough to evaluate whether the observed win rate and payoff ratio are consistent with the theoretical values the system is designed to produce, and to distinguish genuine edge from favorable variance. The friend’s stock tip cannot be evaluated this way. It never will be. There is no system to evaluate, only outcomes to celebrate or regret.

Frequently Asked Questions

Why does the small hospital have more extreme days in the baby example?

Because small samples deviate further from the population mean with higher frequency than large samples. The underlying probability of a boy or girl birth is 50/50 at both hospitals. But with only 12 births per day, random variation produces 2:1 ratios frequently. With 120 births per day, random variation is more tightly constrained around the 50/50 mean. The law of large numbers states that larger samples produce observations closer to the population probability.

Why does a 1,000-trade history give more confidence than a 10-trade history?

Because the larger sample allows the observed win rate to converge toward the underlying probability with higher statistical confidence. A trader with 10 trades and a 40% win rate might have an underlying win rate anywhere from 10% to 70%. A trader with 1,000 trades and a 40% win rate has provided enough data to estimate the underlying win rate within a narrow confidence interval. The 1,000-trade history distinguishes edge from luck. The 10-trade history cannot.

How does systematic trend following produce a large enough sample to evaluate edge?

By trading many markets across multiple time horizons and holding positions long enough to generate hundreds of completed trades per year. Over multiple years, this produces thousands of trades across diverse market conditions. This sample is large enough to evaluate whether the system’s observed performance is consistent with its theoretical characteristics, to identify whether losing periods are normal variance or evidence of a broken system, and to distinguish the system’s genuine edge from favorable variance in any single market or period.

Trend Following Systems
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