Options 101: The Law of Large Numbers, and Why It Matters in Trading

If you have a real edge and you stick to it, your results will get closer and closer to that edge the more trades you make.

That's it.

It won't be smooth. You'll still have bad days and bad weeks. But if you keep doing the same thing with discipline, the math eventually takes over.

• Small number of trades = mostly luck, good or bad.

• Large number of trades = your actual edge shows up.

Your job isn't to win the next trade. Your job is to create a system you can run 100, 200, or 300 times so your edge has room to work.

Three Myths to Kill Right Now

Myth #1: "I'm due for a winner"

No, you're not.

If a coin lands on heads five times in a row, it doesn't "owe" you tails on flip six. Each flip starts fresh. The universe doesn't keep score. It doesn't remember. It doesn't owe you anything.

This is called the gambler's fallacy, and it destroys traders.

Myth #2: "The Law of Large Numbers eliminates bad stretches"

It doesn't.

You'll still have losing streaks. You'll still have drawdowns that make you question everything. What changes is that these bad stretches become predictable. They're not proof your system is broken. They're just math doing what math does.

Myth #3: "Any 100 trades will work"

Not if they're all the same trade.

If you put on five positions in the same stock, on the same day, in the same direction, you don't have five trades. You have one trade you counted five times.

Spread your trades across different stocks and different weeks. Make them actually independent.

The Only Formula that Matters: Expectancy

Most traders obsess over win rate. "I win 70% of the time!" they brag.

But win rate alone tells you nothing. What matters is expectancy, how much you make on average per trade.

Here's the formula:

E = (Win Rate × Avg Win) − (Loss Rate × Avg Loss)

Let's say you win 65% of the time. When you win, you make $1. When you lose, you lose $1.20.

E = (0.65 × $1) - (0.35 × $1.20)
E = $0.65 - $0.42
E = $0.23

You make 23 cents per trade on average.

Not exciting. Not impressive. But here's what matters: If you can do this same trade 200 times without changing anything, your average profit per trade should land near 23 cents.

That's the Law of Large Numbers at work.

The question isn't whether trade #47 wins or loses. Nobody cares about trade #47. The question is whether you can repeat this trade 200 times without getting bored, scared, or "creative."

Why you need hundreds of trades to know anything

Here's a truth most traders ignore: 25 trades tells you almost nothing.

If you win 60% of your first 25 trades, your "true" win rate could easily be anywhere from 50% to 70%. That's a huge range. You're basically guessing.

Run that same strategy over 400 trades? Now you actually know something. The noise shrinks. The picture clears up.

Rule of thumb: You need about 370 trades to nail down your win rate within 5% accuracy.

That's why serious traders think in terms of 100 to 400 trades to evaluate a strategy. Anything less and you're reading tea leaves.

Most traders quit after 20 or 30 trades and say "it doesn't work." They never gave it a chance to work.

Losing Streaks are Normal, Plan for Them

Even great strategies have brutal losing streaks.

Let's say you win 60% of the time. Pretty good, right? Over 200 trades, expect to lose 5 to 7 times in a row at some point.

Even if you win 70% of the time, which is fantastic, expect 3 to 5 losses in a row.

Read that again. You can be right 70% of the time and still be wrong five straight times. That's not bad luck. That's normal.

These streaks aren't warning signs. They're not proof you've lost your touch. They're just part of the deal.

The key question: Can your account survive a normal losing streak?

If five losses in a row would blow up your account, you don't have an edge problem. You have a position sizing problem.

Position Sizing: The Thing Nobody Wants to Talk About

This is where most traders mess up. They get the strategy right but size their positions wrong. And position sizing always wins that fight.

Rule #1: Risk 1% to 5% per trade

If you have a $10,000 account, risk $100 to $500 per trade. Not $1,000. Not $5,000.

I know it feels too small. I know you want to make money faster. But small sizing is the price you pay to stay alive long enough for the Law of Large Numbers to work.

Rule #2: Don't put everything on Friday

Don't bunch five positions into the same Friday expiration in the same sector. One news headline and they all blow up together.

Spread your trades across different weeks and different stocks.

Rule #3: Take profits at 50 to 75%

When you're selling premium and you've captured 50 to 75% of the max profit, close it.

I know you want that last 25%. But you're trading a tiny bit more profit for the risk of a total disaster. Take the win and move on.

Rule #4: Be even more conservative than you think

Your estimates are wrong. My estimates are wrong. Everyone's estimates are wrong.

Size your positions assuming you're a little wrong about everything. Because you are.

Real Example: Short Premium Done Right

Let's use actual numbers.

The Strategy:

• Sell credit spreads or iron condors on SPY, QQQ, DIA, or IWM

• Use 15 to 25 delta (far out of the money)

• Enter when IV Rank is elevated (you're getting paid well)

• Exit when you've captured 50 to 75% of the profit

• If things go wrong, roll out to a later date first, then adjust strikes if you must

Hypothetical Results:

• Win rate: 68%

• Average win: $1 per spread

• Average loss: $1.40 per spread

Expectancy = (0.68 × $1) - (0.32 × $1.40) = $0.23 per trade

What this means:

Over 20 trades, anything can happen. You might be up or down. The sample is too small to tell you anything.

Over 200 trades, if you stick to the plan, your average should hover around 23 cents per trade.

That's your edge showing up. Not through luck. Through repetition.

The Trap: Chasing Win Rate

A lot of traders fall for "70% win rate!" marketing. It sounds great. But watch what happens:

Scenario A:

• Win 70% of the time

• Make $1 when you win

• Lose $1.80 when you lose

Expectancy = (0.70 × $1) - (0.30 × $1.80) = $0.16

Still positive, but barely. Slippage and commissions might erase it completely.

Scenario B (same win rate, worse losses):

• Win 70% of the time

• Make $1 when you win

• Lose $2.40 when you lose

Expectancy = (0.70 × $1) - (0.30 × $2.40) = -$0.02

You're losing money. And the more trades you make, the more certain that loss becomes.

The lesson: Win rate is marketing. Expectancy is what pays the bills.

How Many Trades Before You Can Trust Your Edge?

Use this guide:

30 to 50 trades: You're still learning. Expect lots of noise. Focus on executing the strategy cleanly and tracking your costs.

100 to 150 trades: You're starting to see if this might work. If your actual results are wilder than expected, shrink your position size.

300 to 500 trades: Decision time. If your expectancy is still positive after all costs, and your worst losing streak didn't kill you, you can carefully scale up.

Don't skip ahead. Don't get impatient. The market punishes impatience.

Sequence Risk: Same Strategy, Different Year

Here's something strange: Two traders can run the exact same strategy and have totally different results in the same year.

Same entries. Same exits. Same position sizes. Different outcomes.

Why? Because of when the wins and losses hit.

If all your losses cluster at the start of the year, you might not have enough money left to capture the wins later. If your wins come first, you build a cushion.

The Law of Large Numbers says the average will work out eventually. But sequence risk determines whether you survive to see "eventually."

The fix: Small position sizes. Lots of trades spread out over time. Take profits quickly when you have them.

We're not trying to be clever. We're trying to still be here when the math works.

Your Weekly Checklist

Before you enter any trade:

• Is IV Rank high enough that you're getting paid well?

• Do you already have two other positions that would move the same way as this one?

• Are you risking 5% or less of your account?

While the trade is open:

• Do you have profit-taking orders set at 50 to 75% of max profit?

• If the trade moves against you, are you rolling out to a later date for a credit first?

• If the loss is getting bigger than planned, are you willing to exit?

After you close the trade:

• Did you log everything? Win or loss, P&L, IV Rank when you entered, days you were in the trade, why you exited?

• Every 10 trades, are you checking for patterns? Are your losses bigger than expected? Are costs eating your edge?

The log is the only way to know if you're actually doing what you think you're doing.

Mistakes the Law of Large Numbers Can't Fix

Changing your rules: If you keep adjusting your strategy, tighter stops here, bigger positions there, you're not giving any single approach time to prove itself.

Oversizing "special" trades: Every trader thinks their current trade is different. It's not. It never is.

Bunching your risk: Five trades on Fed announcement day aren't five independent trades. They're one trade you made five times. When it goes wrong, everything goes wrong together.

Judging too fast: A month is noise. Hundreds of trades is signal. Be patient.

Quick Answers to Common Questions

Q: Can the Law of Large Numbers save a bad strategy?
A: No. If your expectancy is negative, more trades just means losing more money more reliably. Fix the math first.

Q: Should I stop after a losing streak?
A: Only if you broke your rules or something major changed (like volatility collapsed). Otherwise, maybe shrink your size a bit, but keep going. If you stop every time you hit a rough patch, you'll never accumulate enough trades for the math to work.

Q: Is a higher win rate always better?
A: Only if your losses stay small. A 90% win rate with terrible risk/reward can lose money. A 40% win rate with great risk/reward can make a fortune. Do the math.

The Bottom Line

The Law of Large Numbers gives you permission to be boring.

Find trades where you're getting paid fairly. Risk tiny amounts. Take profits at 50 to 75%. Run the same process over and over and over.

Some months will hurt. Some trades won't make sense. That's normal. That's not a problem to solve, it's the cost of doing business.

What shouldn't change is your process. Make it so boring, so mechanical, so predictable that the only question is whether you can stand to keep doing it long enough.

Most traders can't stand it. They get bored. They get creative. They blow up.

Don't be most traders.

Probabilities over predictions,

Andy Crowder

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Disclaimer: This is educational content only. Not investment, tax, or legal advice. Options involve risk and aren't suitable for all investors. Examples are illustrative. Real results will vary. Talk to professionals before you risk real money