Prerequisites: Dead Reckoning (performance tracking) · Ballast Management (position sizing) · 20 min read
A captain who navigates by the stars knows his position regardless of the weather. A captain who navigates by the horizon sees only what is directly in front of him — and is easily deceived by mirages. The Astrolabe is your star chart. It tells you whether your strategy has an edge before you risk a single dollar.
THE MEASUREMENT
Expectancy is the average amount you can expect to win (or lose) per trade over a large number of iterations. It is the single most important number in trading. A positive expectancy means your strategy has an edge. A negative expectancy means you are paying tuition to the market.
Notice the distinction. The first formula gives expectancy as a multiple of your risk unit (R). The second gives it in absolute dollars. Both are useful. The first tells you if your edge is structural. The second tells you if your sizing is appropriate.
The Breakeven Win Rate
If your reward-to-risk ratio is fixed, what win rate do you need to break even?
Profit Factor
Profit Factor measures the gross efficiency of a strategy. It is the ratio of total gains to total losses.
PF > 1.5 = viable. PF > 2.0 = strong. PF < 1.0 = you are losing money. Period.
Maximum Consecutive Losses
Even a strategy with 60% win rate will experience strings of losses. The probability of n consecutive losses is:
Sharpe & Sortino (Risk-Adjusted Returns)
| Metric | Formula | What It Measures | Good Value |
|---|---|---|---|
| Sharpe Ratio | (Rp − Rf) / σp | Return per unit of total volatility | > 1.0 acceptable, > 2.0 excellent |
| Sortino Ratio | (Rp − Rf) / σd | Return per unit of downside volatility only | > 1.5 acceptable, > 3.0 excellent |
| Calmar Ratio | CAGR / Max Drawdown | Return per unit of worst peak-to-trough loss | > 1.0 acceptable, > 3.0 excellent |
THE MECHANISM
How to Backtest Without Lying to Yourself
Backtesting is where most traders commit statistical suicide. They optimize parameters on historical data, achieve spectacular results, and then watch the strategy fail in live markets. This is not bad luck. It is curve fitting.
Define the strategy before touching data
Write down entry rules, exit rules, stop rules, and position sizing before you run a single backtest. If you change rules after seeing results, you are not backtesting. You are storytelling.
Use out-of-sample data
Split your data: 70% for development (in-sample), 30% for validation (out-of-sample). Optimize on the 70%. Test the final strategy on the 30% exactly once. If it fails on out-of-sample, the strategy is invalid. Do not re-optimize and try again.
Account for transaction costs
Include commissions, slippage, and borrow fees in every backtest. A strategy that generates $50 per trade in gross profit may generate $10 after costs. That changes everything.
Require statistical significance
A strategy tested on 30 trades is not a strategy. It is a hypothesis. Minimum viable sample: 100 trades for intraday, 30 trades for swing (over multiple market regimes).
Walk-forward analysis
The gold standard. Optimize on a window (e.g., 12 months), test on the next window (3 months), then roll forward. Repeat across the entire dataset. This simulates how you would actually trade: re-optimize periodically, then trade forward.
The Four Lies of Backtesting
| Lie | How to Detect It | How to Fix It |
|---|---|---|
| Look-ahead bias | Strategy uses information not available at trade time (e.g., closing price for entry at open) | Use only data known before the signal bar closes |
| Survivorship bias | Backtest universe excludes delisted stocks, inflating returns | Include historical constituents, including bankruptcies |
| Data mining | Tested hundreds of parameter combinations, reported only the best | Penalize results by number of tests (Bonferroni correction) |
| Overfitting | Too many rules, too few trades. Strategy fits noise, not signal | Require > 10 trades per rule. Simplify. Use out-of-sample validation |
THE DECK CALCULATOR
Expectancy & Strategy Health
Backtest Results — Inputs
Star Readings — Output
False Breakout Probability Estimator
Not every breakout is genuine. This estimator combines five factors to calculate the probability that a breakout will fail within 5 bars.
Breakout Context — Inputs
Failure Probability — Output
IN PRACTICE
Scenario A: The Mutiny (E10)
A trader developed a breakout strategy on the S&P 500. His backtest showed a 62% win rate with an average win of $380 and average loss of $280. He was thrilled. He went live with $100,000 and risked 2% per trade.
| Metric | Value |
|---|---|
| Win rate | 62% |
| Average win | $380 |
| Average loss | $280 |
| Reward:Risk | 1.36:1 |
| Expectancy | +$129.20 / trade |
| Profit Factor | 1.58 |
| Verdict | Positive edge |
The math looked good. But the trader had committed three sins:
- He did not account for slippage. Breakout entries on S&P 500 futures often slip 2–3 ticks. At $12.50 per tick, that is $25–$37.50 per trade. Over 150 trades, that erases $5,625 in gross profit.
- He optimized on all his data. No out-of-sample test. The 62% win rate was curve-fitted to the specific 18-month period he tested.
- He traded it in the wrong regime. The strategy was developed during a trending market. When volatility spiked and whipsaws increased, the win rate collapsed to 38%. Expectancy turned negative: (0.38 × $380) − (0.62 × $280) = −$29.20 per trade.
The strategy did not fail. The trader failed to validate it properly. The Astrolabe would have flagged this: a 62% win rate with 1.36 R:R is marginal. Add slippage and it becomes borderline. Trade it in the wrong regime and it becomes a wealth destruction machine.
Scenario B: The High-Frequency Mirage
A retail trader backtested a 5-minute scalping strategy on 2 years of ES futures data. Results: 1,200 trades, 54% win rate, $85 average win, $75 average loss.
| Metric | Value |
|---|---|
| Win rate | 54% |
| Average win | $85 |
| Average loss | $75 |
| Reward:Risk | 1.13:1 |
| Expectancy (gross) | +$10.20 / trade |
| Expectancy (net, $25 costs) | −$14.80 / trade |
| Profit Factor | 1.08 → 0.72 |
What the stars tell you: A 1.13 R:R with 54% win rate is mathematically viable — barely. But with $25 round-trip costs (commission + slippage on ES), the expectancy flips from +$10.20 to −$14.80. The strategy is not an edge. It is a donation to your broker and the HFT firms front-running your market orders.
The Astrolabe reveals this in seconds. Without it, the trader would have blown up his account wondering why his backtested edge evaporated.
FROM THE LOGS
🎙️ Episode 10 — The Mutiny
When a trading strategy revolts against its creator — and how to regain command before the ship sinks. The Mutiny is what happens when expectancy turns negative and the captain keeps trading, hoping the old edge returns. It does not. The math has changed. The regime has shifted. The only correct response is to stop, recalculate, and rebuild.
🎙️ Episode 06 — The Ballast Run
Mike's disaster was not a backtesting failure — it was a position sizing failure. But the underlying lesson is the same: the math does not care about your conviction. A 20% position on a binary event has negative expectancy regardless of your research quality.
CROSS-LINKS
Dead Reckoning
Performance tracking and journaling. The qualitative companion to The Astrolabe's quantitative rigor.
Ballast Management
Position sizing and the 1% rule. How to translate expectancy into actual share count.
The Helm Response
Rolling Beta. Know your portfolio's market sensitivity before you size your positions.
The Engine Telegraph
Option Greeks. Expectancy applies to options too — but the R:R distribution is asymmetric.
The Captain's Temper
Discipline and psychology. The hardest part of negative expectancy is accepting it and stopping.
The Standard Signal Book
Bilingual glossary. Translate every nautical term to its Bloomberg and standard brokerage equivalent.
The Geometer's Proof
Statistical testing of Fibonacci retracements vs. random controls. Geometry meets evidence.
The Barometer's Proof
Wilder's RSI derived step-by-step. Bounds proof, smoothing mechanics, and the 50-level truth.