Core Concepts

Position sizing, R-multiples, expectancy, and the math behind risk management.

These are the concepts Testudo is built on. Each one is simple on its own. Together, they form a complete framework for managing risk.

Position Sizing

What it is: Calculating how large a position to take based on how much you’re willing to lose if the trade hits your stop-loss.

Why it matters: Position sizing is the single most important variable in trading. Two traders can take the exact same entries and exits, but if one risks 1% per trade and the other risks 15%, they’ll have completely different outcomes.

The formula:

$\text{position size} = \frac{\text{account balance} \times \text{risk percent}}{\text{stop distance}}$

Where stop distance is the difference between your entry price and stop-loss price:

$\text{stop distance} = |\text{entry price} - \text{stop loss price}|$

Example: You have a $10,000 account and risk 2% per trade. You want to long BTC at $50,000 with a stop-loss at $49,000.

Risk amount = $10,000 x 2% = $200
Stop distance = $50,000 - $49,000 = $1,000
Position size = $200 / $1,000 = 0.2 BTC

If BTC hits your stop, you lose exactly $200 — 2% of your account. If it goes to your target, the reward depends on how far that target is.

Conservative Wins

Testudo doesn’t just calculate one number. It computes four constraints and takes the smallest:

$\text{final size} = \min\left(\text{size}_{\text{risk\%}},\; \text{size}_{\text{max risk}},\; \text{size}_{\text{max position}},\; \text{size}_{\text{margin}}\right)$

Constraint	What it limits
Account % risk	Size from your configured risk percentage
Max risk amount	Hard dollar cap on risk per trade (e.g., never risk more than $150)
Max position size	Hard cap on position size in base currency
Margin capacity	Ensures you have enough margin at your leverage level

The most conservative constraint always wins. This prevents oversizing even when individual limits seem fine.

R-Multiples

What it is: A way to measure every trade in units of risk — regardless of position size.

Why it matters: R-multiples normalize your results. A $500 win on a $250 risk is the same quality trade as a $50 win on a $25 risk. Both are +2R.

The formula:

$R = \frac{\text{net P\&L}}{\text{risk amount}}$

Examples:

Risk Amount	Net P&L	R-Multiple	Meaning
$100	+$250	+2.5R	Won 2.5x what you risked
$100	-$100	-1.0R	Full stop-loss hit
$100	-$50	-0.5R	Partial loss (moved stop)
$200	+$600	+3.0R	Big winner, 3x risk

When you review trades in R-multiples, you’re looking at the quality of the trade — not the dollar amount. A +0.3R trade is mediocre regardless of whether it made $30 or $3,000.

Expectancy

What it is: Your average R per trade across your entire history. The single number that tells you whether your trading system makes money.

Why it matters: Positive expectancy means you’re profitable over a large sample. Negative expectancy means you’re losing — even if you’re “winning” most trades.

The formula:

$E = (W \times \bar{R}_w) - (L \times \bar{R}_l)$

Where:

$W$ = win rate (as a decimal)
$\bar{R}_w$ = average R on winning trades
$L$ = loss rate ( $1 - W$ )
$\bar{R}_l$ = average R on losing trades (absolute value)

Example: You win 40% of the time at an average of +2.0R, and lose 60% of the time at an average of -1.0R.

$E = (0.40 \times 2.0) - (0.60 \times 1.0) = 0.80 - 0.60 = +0.20R$

This means on average, every trade you take earns +0.2R. Over 100 trades risking $100 each, that’s $2,000 in profit — despite losing more than half.

Profit Factor

What it is: The ratio of total gross profit to total gross loss.

The formula:

$PF = \frac{\text{gross profit}}{\text{gross loss}}$

Profit Factor	Interpretation
< 1.0	Losing money
1.0 - 1.5	Marginally profitable
1.5 - 2.0	Solid edge
> 2.0	Strong edge

A profit factor of 1.5 means for every dollar you lose, you make $1.50 back. Simple and intuitive.

Maximum Drawdown

What it is: The largest peak-to-trough decline in your account equity.

Why it matters: Drawdown tells you how much pain your system delivers. A 50% drawdown means you need a 100% gain just to get back to even. Knowing your max drawdown helps you decide if you can psychologically survive your system’s losing streaks.

$\text{drawdown} = \frac{\text{peak equity} - \text{current equity}}{\text{peak equity}} \times 100$

If your equity peaked at $12,000 and dropped to $10,200, your drawdown is:

$\frac{12{,}000 - 10{,}200}{12{,}000} \times 100 = 15\%$

Testudo tracks this automatically and can block new trades if you exceed a daily drawdown limit (configurable — default is 5%).

Win Rate vs. Edge

The counterintuitive truth: Win rate alone means nothing.

A system that wins 70% of the time can lose money. A system that wins 30% of the time can be highly profitable. What matters is the relationship between win rate and average win/loss size.

Win Rate	Avg Win (R)	Avg Loss (R)	Expectancy
70%	+0.3R	-1.0R	-0.09R (losing!)
50%	+1.5R	-1.0R	+0.25R
40%	+2.0R	-1.0R	+0.20R
30%	+3.0R	-1.0R	+0.20R
20%	+5.0R	-1.0R	+0.20R

The 70% win rate system is the only loser in this table — because the average win is too small relative to the average loss. This is why Testudo tracks R-multiples, not just win/loss counts.

High win rate feels good. Positive expectancy is good.