CHAPTER 25

Statistics: The Maths That Proves An Edge

Only statistics can tell you whether you are profitable or merely lucky. These are the numbers that tell you when to stop and when to scale.

25.1Expectancy

Expectancy = (win% x average win) - (loss% x average loss). Example: 45 percent wins, average win 2.5R, average loss 1R gives (0.45 x 2.5) - (0.55 x 1) = +0.57R per trade.

Metric	Formula	Good value
Expectancy	(W x AvgW) - (L x AvgL)	Above +0.2R
Profit factor	Gross profit divided by gross loss	1.5+
Average R	Total R divided by trades	+0.2
Break-even win rate	1 divided by (1 + payoff)	33 percent at 1:2

Payoff	Break-even win rate	Your actual win rate
1:1	50%	Profitable above 55 percent
1:1.5	40%	Comfortable above 45 percent
1:2	33%	Excellent above 40 percent
1:3	25%	Outstanding above 35 percent
1:4	20%	Rare above 30 percent

25.2Results Are A Distribution

**Fig. 25.1** The distribution of R multiples

Notice: most trades lose 1R and the profit comes from a few big winners. That is why you can be profitable even after three losses - and why patience is maths, not emotion.

**Fig. 25.2** Win rate times payoff equals expectancy

25.3How Many Trades You Need

Sample	Standard error (50% win)	Decision
20	±11%	It tells you nothing
50	±7%	A first hint
100	±5%	Direction is visible
300	±3%	Trustworthy
1,000	±1.6%	Edge established

25.4Risk Of Ruin

**Fig. 25.3** Same strategy, different risk, wildly different ruin probability

Same strategy, 45 percent wins at 1:3. At 0.5 percent risk the chance of losing half the account is under 1 percent; at 10 percent it is 64 percent. Risk is your biggest controllable variable.

25.5Monte Carlo And Walk-Forward

Shuffle your 100 R values a thousand times to see the worst realistic drawdown.
If the simulation shows a 20 percent drawdown, be ready for it in reality.
Walk-forward: test on six months, validate on the next two with unchanged rules.
A backtest without out-of-sample data is decoration.

25.6Statistical Traps

Trap	What happens
Curve fitting	Tweaking rules until the backtest looks good - useless live
Survivorship	Only saving screenshots of winners
Cherry picking	Showing the best month as the year
Small sample	Deciding on ten trades
Outliers	One 10R trade distorts everything

"Luck can give you a good month. Without statistics you cannot tell which was which."

Educational material only · not financial advice.