Last updated: 1 September 2026 · By Spencer Li, CFTe

The law of large numbers says that the average of many repeated trials drifts closer to the true average as the number of trials grows. In trading, it means your results only start to show a strategy’s real edge after a lot of trades. Before that, luck is louder than skill.

How many is a lot? Our rule of thumb at Synapse Trading is 100 to 200 trades before you judge a system. The reason is arithmetic. With 20 trades, a strategy that truly wins half the time can easily show a win rate anywhere from about 28% to 72%. With 200 trades, that band narrows to roughly 43% to 57%.

And the smaller your edge, the more trades it takes. I’ll show you both with exact numbers below.

What does the law of large numbers actually say?

Flip a fair coin 10 times and getting 7 heads is unremarkable. Flip it 1,000 times and getting 700 heads would be astonishing. The coin did not change. The sample did.

A casino runs on exactly this. Its edge on a single spin is small, and on any one evening a lucky player can walk out ahead. Over millions of spins the house result lands very close to its built-in edge, which is why the casino does not care who wins tonight, and why it happily sends the lucky player home with a free dinner. A trader with an edge is in the casino’s seat, but with far fewer spins, so what matters is how many spins it takes before the edge shows through.

How wrong can a small sample be?

Quite wrong. Say your strategy truly wins 50% of the time. Here is the range your measured win rate will land in about 95% of the time:

After 20 trades, the same strategy could look brilliant or broken purely by chance, and the trader looking at it would have no way of telling which of the 2 he was seeing. After 200, the band is still about 14 points wide. This is why one good month proves very little, and why one bad month should not send you shopping for a new system.

The Central Limit Theorem explains the shape of this. Add up enough independent trades and the total behaves like a bell curve. Its middle grows in step with the number of trades, while its spread only grows with the square root. So 4 times as many trades makes the noise half as large relative to the edge, which is a slow and fairly expensive way to buy certainty.

Can a losing strategy look like a winner?

Yes, and for longer than most people expect. Here are 2 hypothetical strategies with the same payoff, where winners make 2R and losers cost 1R, with R being the amount risked per trade.

• The good one wins 40% of the time, so it makes 0.2R per trade on average.
• The bad one wins 30% of the time, so it loses 0.1R per trade on average.

I worked out the exact odds of each one fooling you:

Look at the 20-trade row. The losing strategy is ahead almost 4 times in 10, and the winning one is still behind 1 time in 4. A trader who judges at 20 trades will dump good systems and fall in love with bad ones, and be sure of himself both times.

If you want a daily routine that keeps you taking the valid trades through a slow patch, the free 15-Minute Swing Trader’s Checklist is at the end of this post.

How many trades do you really need?

It depends on the size of your edge. The bigger the edge per trade, the sooner it stands out from the noise. Here is roughly how many trades it takes before the average result sits clearly above zero, at 2 standard errors:

Most real strategies sit in the middle rows, which is where the 100 to 200 rule comes from. It is a floor. A thin edge needs far more.

A trader on r/Daytrading ran into the bottom row in August 2026. He had 500 trades on gold futures, half backtested and half traded forward, and asked a simple question: “is this an edge or variance?”

At a 1-to-1 payoff his result was “+0.032R/trade”, which, as he wrote himself, “could easily disappear once costs are included.” He was right to be cautious. By the table, an edge that thin needs thousands of trades to confirm. He also tested several profit targets on the same 500 trades and found one that looked best, and he flagged that too as possibly “variance / overfitting”. Testing many versions on one sample and keeping the winner is the fastest way to fool yourself with a small sample, so his caution is the useful part.

What do you do while the sample builds?

3 things, none of them exciting.

1. Trade small. Size each trade so that the losing streaks a normal sample throws up cannot hurt you. The 2% money management rule for position sizing is the place to start, and smaller is fine while you learn.
2. Log every trade. Without a record, there is no sample to judge. A trading journal turns your trades into data you can count.
3. Judge the process before the results. Did you take the trades the rules said to take, at the size they said? That you can answer after 10 trades. Whether the rules work takes the 100 to 200.

The pull to judge early is very human. Our minds read patterns into short runs, which is the representativeness bias, the danger of a small sample size. Knowing it exists does not switch it off, so the rule has to be written down before the streak arrives.

Personally, I think the most useful number to know is your expectancy, the average R per trade, because it tells you which row of that table you are in. That is the next read, how to calculate a strategy’s expectancy, and its companion on win rate versus reward-to-risk. The wider map is in the practical guide to money and risk management, and why surviving the sample matters at all is in why risk management is important in trading.

Back in March 2026, another trader on r/Daytrading posted 2 months of results and asked: “Am I finding an edge or just getting lucky?” After 2 months, the honest answer is almost always that nobody can tell yet, him included. The answer arrives somewhere past trade 100, for whoever is still trading small enough to get there.

FAQ

What is the law of large numbers in trading?

It is the idea that your average result moves closer to your strategy’s true edge as you take more trades. Over a few trades luck dominates. Over hundreds the edge shows.

How many trades do I need to backtest a strategy?

At least 100 to 200, and more if the edge is thin. A strategy that makes only a few hundredths of an R per trade can need thousands of trades before it is clearly real.

Is 20 trades enough to judge a strategy?

No. After 20 trades a strategy that wins half the time can plausibly show a win rate between about 28% and 72%, so the record cannot separate a good system from a bad one.

What is the Central Limit Theorem in trading?

It says the total of many independent trades behaves like a bell curve. The edge grows with the number of trades while the noise grows only with its square root, so more trades make the edge easier to see.

Should I change my strategy after a losing streak?

A streak on its own is too little to go on. Check that you followed the rules and that the sample is large enough, because losing streaks of 5 or 6 trades are normal even in a strategy that works.

Go deeper

The free 15-Minute Swing Trader’s Checklist has the daily routine, the questions to ask before every trade, and the five rules that keep you in the game.

About the author. Spencer Li is The 15-Minute Trader and the founder of Synapse Trading. He is a Certified Financial Technician (CFTe) with 15+ years of trading, run from 70+ countries. He holds a B.Acc and B.BM from SMU. Every trade he takes is public, dated, losses left in. He teaches low-risk swing trading in 15 minutes a day, one system for any market.

Educational content only, not personalised financial advice. Trading carries risk, including loss of capital. Past performance is not indicative of future results. Synapse Trading is not licensed or regulated by MAS.

Two risk-adjusted return ratios can rank the same 2 strategies in opposite order. Here is why, worked through on 12 hypothetical months.

Published: 16 October 2026 · Last updated: 16 September 2026 · By Spencer Li, CFTe

Strategy A made money in 11 months out of 12. Strategy B lost money in 6 of them.

Ask the Sharpe ratio which one is better, and it picks A. Ask the Sortino ratio, and it picks B by almost 3 times.

The Sharpe ratio divides your average return above a safe rate by the standard deviation of all your returns, so every swing counts as risk, whether it went up or went down. The Sortino ratio divides the same excess return by the downside deviation, which counts only the returns that fall below a target you choose.

When your returns are lopsided, the two will rank strategies differently. Read them together. The gap between them tells you the shape of your risk, and the shape is what you actually sit through.

Below are both formulas, the 2 strategies worked out line by line, a quick rule for reading the gap, and the 2 things neither ratio can see.

What is the Sharpe ratio, in plain words?

William Sharpe introduced it in 1966 to compare mutual funds. He called it the “reward-to-variability ratio”. As he wrote in 1994, “the measure has gained considerable popularity, the name has not.”

The formula:

Sharpe ratio = (average return − risk-free rate) ÷ standard deviation of returns

The top line is the reward: what you earned above a safe alternative like cash. The bottom line is the variability: how far your returns wander from their own average.

Do note that it measures the wander in both directions. A month 5% better than your average raises the standard deviation exactly as much as a month 5% worse. To the Sharpe ratio, a pleasant surprise is risk too.

In the examples below I set the risk-free rate to 0 to keep the arithmetic clean. When you compare your own numbers, use the same rate for everything you compare.

What is the Sortino ratio, and what does it change?

The Sortino ratio keeps the top line and swaps the bottom one. Instead of the standard deviation, it divides by the downside deviation: how far your returns fall short of a target you pick, often 0.

Sortino ratio = (average return − target return) ÷ target downside deviation

The idea comes from Frank Sortino’s work in the early 1980s. The clearest public walkthrough I know is a short paper by Thomas Rollinger and Scott Hoffman, “Sortino: A ‘Sharper’ Ratio”. It defines the downside deviation as the root-mean-square of each month’s shortfall below the target, “where all returns above the target return are treated as underperformance of 0.”

That last part trips people up. The good months are set to 0, but they stay in the count. The authors underline it: “we do not ‘throw away’ the 0% values.” Taking the standard deviation of the losing months alone is a common shortcut, and their paper shows why it gives the wrong number.

In practice, this means a big up month costs a strategy nothing on the Sortino ratio. Only shortfall counts as risk.

What happens when Sharpe and Sortino disagree?

Here are 2 hypothetical strategies over the same 12 months. The returns are invented to show the effect, and kept to round numbers.

Sharpe ranks A first, narrowly. Sortino ranks B first, at 2.7 times A’s figure.

The reason sits in the bottom line of each formula. B’s standard deviation is high because of its 3 big up months of 4%, 5% and 6%, and Sharpe counts those swings as risk even though they are the best thing that happened to the account all year. Sortino ignores them and sees only B’s small losses, none worse than 1.5%.

A looks calm to Sharpe because 11 of its 12 months are almost identical. Sortino sees the one month that hurt: a 6% drop that wiped out 4 months of gains.

Which one would you rather hold? Asked honestly, most traders pick B. Its worst month was 1.5%, and A’s was 4 times that. A’s pattern, small steady gains with a rare large loss, is the pattern of selling insurance, and it looks safest on paper right up to the month the big claim comes in.

Good Wobble, Bad Wobble: how do you read the two together?

I call this Good Wobble, Bad Wobble. Every strategy wobbles. Good wobble is the swing above your target, and bad wobble is the swing below it. Sharpe counts both. Sortino counts only the bad.

That makes the gap between the 2 ratios a reading on the shape of your returns. There is a simple benchmark for it.

If your monthly returns are spread evenly on both sides of 0, the Sortino ratio comes out at about 1.4 times the Sharpe ratio. That 1.4 is the square root of 2, and I checked it with 200,000 simulated months. With a positive average, the multiple climbs higher still.

A ratio below 1.4 is your cue to go and look at the worst month before you trust the smooth line.

Both ratios only describe how a strategy has behaved, and what makes a strategy behave well in the first place is the routine behind every trade: a stop fixed before entry and a position sized to it.

Our free 15-Minute Swing Trader’s Checklist walks through that routine before every trade. Get the free checklist →

Why can 12 months of returns not settle the question?

Sharpe gave the test himself. In his 1994 paper he wrote: “The t-statistic will equal the Sharpe Ratio times the square root of T (the number of returns used for the calculation).”

Apply that to Strategy A. A monthly Sharpe of 0.40 times the square root of 12 gives a t-statistic of 1.40. The usual rough bar for a result being more than luck is about 2, and 1.40 does not clear it.

To reach 2 at a monthly Sharpe of 0.40, you would need about 25 months of returns. At a monthly Sharpe of 0.20, you would need 100 months, which is more than 8 years.

It is the same lesson as trade counts, where we give a system 100–200 trades before judging it. A ratio worked out from a short sample is a guess with 2 decimal places. The full argument is in How Many Trades Do You Need? The Law of Large Numbers and Sample Size.

Do note the √12 step too. Multiplying a monthly ratio by √12 assumes each month has nothing to do with the last. Sharpe flagged that returns “may be serially correlated”, and when they are, the annual figure overstates or understates the truth.

What can neither ratio see?

Both ratios are built from an average and a spread. Sharpe was open about the limit. Comparisons built only on those 2 numbers “do not take into account possible differences among portfolios in other moments”, which in plain words means the size and shape of the tails.

Put 3 things beside either ratio before you trust it.

The worst month and the max drawdown. A’s −6% month is the single number that explains the whole table above. Drawdown has its own section in The Performance Numbers That Matter.

The order of the months. Take Strategy B and move its 6 losing months together so they land in a row. Both ratios stay exactly the same, because neither cares about order. But the max drawdown goes from 1.5% to 5.4%, and a 6-month losing run is a very different thing to sit through than 6 small losses scattered across the year between your winning months.

How many trades sit behind each month. A month built on 2 trades and a month built on 30 trades count the same in both formulas. Your journal knows the difference, so keep the trading journal next to the ratios.

How do you work out both ratios from your own returns?

You need monthly returns as percentages, which a decent journal already gives you. Then:

1. Pick a target and keep it. Use 0, or the cash rate. Whatever you pick, use the same one for everything you compare.
2. Work out the Sharpe ratio. Take the average monthly return, subtract the target, then divide by the standard deviation. Sharpe’s own paper gives the spreadsheet version for 60 months of excess returns: AVERAGE(C1:C60)/STDEV(C1:C60).
3. Work out the downside deviation. For each month, take the shortfall below the target, or 0 if the month beat it. Square each one, average them over every month including the zeros, then take the square root.
4. Work out the Sortino ratio. Divide the same top line as step 2 by the downside deviation.
5. Annualise both the same way. Multiply each monthly ratio by √12, and remember the independence assumption.
6. Write the worst month and the max drawdown next to them. Then work out Sortino ÷ Sharpe and read it against 1.4.

Step 6 is the one most people skip. It is also the one that would have caught Strategy A.

A ratio is a summary of a shape. Before you trust the summary, look at the shape.

Sharpe and Sortino ratio FAQ

What is a good Sharpe ratio?

There is no cut-off that holds across every market, period and method. A ratio only means something next to another ratio worked out the same way: same period length, same risk-free rate and a similar number of months.

Is a higher Sortino ratio always better?

No. A high Sortino ratio built on very few losing months rests on very few data points. Strategy A’s entire downside deviation comes from a single month.

Can a Sharpe ratio be negative?

Yes. If your average return is below the risk-free rate, the top line of the formula is negative, and so is the ratio.

Why does my Sortino ratio differ from an online calculator’s?

Check 2 things: the target return, and whether the tool drops the above-target months from the count. Dropping them is the shortcut the Red Rock paper shows to be incorrect.

Should I use daily, weekly or monthly returns?

Monthly is the common choice for a trader’s own account. Sharpe’s paper recommends fairly short periods such as monthly, then annualising for comparison. Whatever you choose, use the same period for every strategy you compare.

Go deeper

This post sits under our guide to money and risk management. If you would like the routine that fixes your stop and size before every trade, the free 15-Minute Swing Trader’s Checklist is the place to start.

About the author. Spencer Li is The 15-Minute Trader and the founder of Synapse Trading. He is a Certified Financial Technician (CFTe) with 15+ years of trading, run from 70+ countries. He holds a B.Acc and B.BM from SMU. Every trade he takes is public, dated, losses left in. He teaches low-risk swing trading in 15 minutes a day, one system for any market.

Educational content only, not personalised financial advice. Trading carries risk, including loss of capital. Past performance is not indicative of future results. Synapse Trading is not licensed or regulated by MAS.