How to Think in Probabilities, Not Absolutes

Five years ago at a two-day trading conference I led in Chicago, I met Mark, a PhD aerospace engineer with an impressive 62% win rate on his options trades. His account was down 43% over six months.

The problem wasn't his analysis. It was that he thought trading was about being right.

Mark sized positions based on conviction: 20% of his account when really confident, 10% when moderately confident. When he lost, which happened 38% of the time with normal frequency, he lost catastrophically. Three consecutive losses at 15 to 20% each, and he was down 45% overall.

Six months later, same 62% win rate, up 38% on the year. The only change? He learned to think in probabilities instead of predictions.

Why Being Right Doesn't Matter as Much as You Think

Research by Brad Barber (UC Davis) and Terrance Odean (UC Berkeley) examined 66,465 retail brokerage accounts. They found that the investors who traded the most, a behavioral sign of overconfidence, earned significantly lower returns than both the market and less active investors. In other words, it wasn’t superior insight that drove their activity, but overconfidence, and that overconfidence translated into worse performance.

The problem wasn't accuracy, it was certainty. Confident traders size on conviction, hold losers too long, and make emotional decisions when predictions fail.

I've had thousands of trades where I was "wrong" about direction and still made money. I've had hundreds where I was "right" and still lost money. Directional accuracy and trading profitability are surprisingly weakly correlated.

The Tale of Two Mindsets

Consider Apple trading at $180, with $175 puts at $1.50 expiring in 30 days.

The absolute thinker: "Apple is heading to $195. iPhone cycle is strong, services revenue accelerating. I'm buying $185 calls with maximum conviction." Risks $4,200 (8.4% of account). Needs Apple to rally significantly. Every downtick creates anxiety. If Apple goes to $177 instead, holds through time decay because "the thesis hasn't changed." Watches position expire worthless.

The probability thinker: "I lean bullish, but I'll structure this probabilistically. The $175 put has 20-delta, implying 80% success probability. Expected value: (0.80 × $150) + (0.20 × -$300) = $60 per contract. Over 100 trades, I expect $6,000 profit despite losing roughly 20 trades. I'll risk 2% of account, selling 2 contracts for $1,000 total risk." Doesn't need Apple to reach $195, just needs it not to fall below $175. If assigned, sells covered calls. Records as expected loss in quarterly tracking.

Same bullish thesis. Completely different implementation. Dramatically different outcomes.

The Mathematics of Survival

Here's the arithmetic that destroys conviction-based traders.

Setup: $50,000 account, 65% win rate strategy.

Conviction-based sizing:

• Trade 1: Risk $7,500 (15%). Loss. Account: $42,500

• Trade 2: Risk $6,375 (15%). Loss. Account: $36,125

• Trade 3: Risk $7,225 (20%). Loss. Account: $28,900

Three losses in a row, which happens 4.3% of the time with 65% win rate, leaves you down 42.2%. You need 73% returns to recover. Psychology destroyed.

Probability-based sizing:

• Trade 1: Risk $1,000 (2%). Loss. Account: $49,000

• Trade 2: Risk $980 (2%). Loss. Account: $48,020

• Trade 3: Risk $960 (2%). Loss. Account: $47,060

Same losses, down 5.9%. Need 6.2% returns to recover, easily achievable over next 10 to 15 trades. Psychology intact. System continues.

This is the entire secret: surviving inevitable streaks long enough to let probability work in your favor.

The Expected Value Framework

Before every trade, I run a simple calculation that separates systematic trading from sophisticated gambling.

Real trade: Microsoft at $380, evaluating $370 puts (20-delta), 35 days, $3.20 premium

Expected value calculation:

Success probability: 80%
Win scenario (80%): Keep $320
Loss scenario (20%): $800 unrealized loss

(0.80 × $320) + (0.20 × -$800) = $256 - $160 = $96 per contract

Over 100 trades (one contract per trade): $9,600 expected profiit

Notice what's absent? Any prediction about Microsoft reaching specific price targets. Any certainty about market direction. I'm not betting on Microsoft rallying to $420. I'm betting it probably won't fall below $370, and if it does, my risk is defined.

This is what Barber and Odean found: traders who survive think in expected value, not predictions.

Why You Need 30 Trades Minimum

Most traders quit before the math can work. They make five trades, lose three, conclude it doesn't work.

Behavioral finance research shows humans are terrible at recognizing randomness in small samples. With a genuine 70% win rate strategy, you have a 10% chance of winning only 5 out of 10 trades, pure variance, not system failure.

Research in the Journal of Financial Economics by Campbell Harvey found even professional fund managers need 16 quarters of data to distinguish skill from luck. For individual traders, that's 30 to 50 trades minimum.

Track these metrics after 30 trades:

• Win rate vs. expected (based on delta)

• Average winner vs. average loser

• Expectancy: (Win rate × Avg winner) - (Loss rate × Avg loser)

If your expectancy is positive after 30 trades, continue. If negative, something needs fixing. But after 5 to 10 trades? You know almost nothing except that variance exists.

Delta: Your Built-In Probability Guide

Delta measures price sensitivity, but it's also a probability estimate:

• 30-delta put: ~30% chance stock finishes below strike, 70% probability of success

• 20-delta put: ~20% chance below strike, 80% probability of success

• 10-delta put: ~10% chance below strike, 90% probability of success

None is inherently "better", they're different risk-reward profiles:

Over 100 trades:

• 10-delta: 90 wins × $60 minus 10 losses × $300 = $2,400 net

• 20-delta: 80 wins × $120 minus 20 losses × $350 = $2,600 net

• 30-delta: 70 wins × $200 minus 30 losses × $400 = $2,000 net

The question isn't "which delta is best?" It's "which probability profile fits my psychology and capital?"

When Perfect Decisions Produce Losing Trades

March 2023: I sold puts on a regional bank with strong fundamentals at $45 strike, stock at $52. 18-delta, 82% probability of success. Everything textbook.

Three days later, Silicon Valley Bank failed. Regional banks collapsed indiscriminately. My stock dropped to $38. I was assigned at $45.

Was this a bad trade? Absolutely not.

The decision was sound. The process was correct. The probability was favorable. An unpredictable contagion event doesn't invalidate the decision.

I sold covered calls at $42, collected $1.10, stock recovered to $43, got called away. Roughly break-even overall.

But more importantly: I didn't change my system. I recognized this as one of the 18% expected losses.

Research by Nobel laureate Daniel Kahneman shows humans judge decision quality by outcomes rather than process. Professional traders break this pattern, they judge decisions by process adherence, not individual results.

When Probabilities Break Down

March 2020 taught several options traders I know that delta-based probabilities are estimates that sometimes fail due to sequence risk.

Expected with 20-delta puts: 8 wins, 2 losses across 10 positions Actual result: 3 wins, 7 losses, down 18% for the month.

The probability model broke when volatility exploded and correlations hit 1.0.

Protection strategies:

• Cut position size 50% when VIX exceeds 30

• Track actual vs. expected monthly; if divergence exceeds 15% for two months, pause

• Build 10% probability margins into targets

• Diversify across time and sectors

My probability-based sizing meant 18% drawdown while conviction-based traders were down 40 to 60%. By summer 2020, I'd recovered and finished up 23%. The others were gone.

The Three-Month Transformation

Month 1 (Trades 1-10): Risk 1% per trade, 20-30 delta options only. Focus: process adherence, not profit.

Month 2 (Trades 11-30): Risk 2% per trade. Calculate cumulative statistics. Compare actual vs. expected win rate.

Month 3 (Trades 31-50): Maintain 2% risk. Calculate final expectancy. If positive, continue. If negative, analyze and adjust.

Most traders never reach 50 trades. They think of quitting after 5 to 10 trades due to variance, modify their strategy due to impatience, rinse and repeat. Don't be most traders.

The Bottom Line

After 24 years trading options professionally, I've watched hundreds come and go. The ones who disappear never made the mental shift from prediction to probability.

The ones who last figured out this principle: You don't need to predict where stocks are going. You need to identify trades with positive expected value, size them to survive losing streaks, execute enough times for the math to work, and track results to verify your edge.

Mark told me the most useful thing I taught him: "Stop trying to predict where stocks are going. Start trying to be profitable over 100 trades." Basically he was stating, allow the law of large numbers to work in your favor.

Same intelligence. Same analytical ability. Completely different results.

Your trading career follows one of two paths: Continue thinking in absolutes, sizing on conviction, quitting after variance, and eventually stopping, or start thinking in probabilities, sizing for survival, committing to 30+ trade samples, and still trading in 20 years.

The only difference is the mental framework you choose today.

Stop asking where stocks are going. Start asking what your expected value is over 100 trades.

Stop judging trades by directional accuracy. Start judging by process quality.

Stop sizing on conviction. Start sizing for survival.

The math is simple. The psychology is hard. But once you make this shift, everything else in options trading finally makes sense.

This is the difference between gambling and trading. Between guessing and knowing. Between disappearing and lasting.

Probabilities over predictions,

Andy Crowder

📩 Start trading smarter and more confidently, join thousands of readers who get The Option Premium every week.

📺 Want more education and community?
🎥 Subscribe on YouTube for in-depth tutorials and live trade breakdowns.
📘 Join the conversation on Facebook for exclusive insights, discussions, and real-time updates.

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