Risk of ruin: the position-sizing math day traders never run

Most day traders blow up not because their setup is bad, but because their position size is fatal. They survive a 60% win streak and then lose 40% of their account on a normal 4-trade losing streak.

This post is the math.

The thing nobody calculates

Given a strategy with win rate W, average reward/risk R, and per-trade risk r (as % of account), the probability of drawing down 50% before doubling — your risk of ruin — is non-zero for nearly every retail setup at normal sizing.

The intuition: variance is brutal. A 55% win rate with 1:1 R has a roughly 6% chance of an 8-trade losing streak. If you're risking 5% per trade, that streak takes you from $50,000 to ~$33,000. If you're risking 10% per trade, you're at ~$22,000 — and now you need a 127% return just to get back to even.

The Kelly fraction (and why we don't use full Kelly)

The Kelly fraction tells you the position size that maximizes long-term geometric growth. For binary outcomes:

f* = W − (1 − W) / R

For a strategy with W = 55%, R = 1.5:

f* = 0.55 − 0.45 / 1.5
f* = 0.55 − 0.30
f* = 0.25

Kelly says size at 25% of capital per trade. Nobody should do this.

Full Kelly assumes you've measured W and R correctly to two decimal places. Day traders haven't. Your real W is somewhere within a 10-point band of your sampled W, and the variance from misestimation will wreck a full-Kelly account.

Half-Kelly, quarter-Kelly, and the rule we actually use

The pros use fractional Kelly — typically half or quarter — to absorb measurement error.

Our rule:

risk_per_trade = 0.25 × Kelly_fraction

For the W=55%, R=1.5 strategy above: 6.25% per trade. That's still aggressive. For most retail day traders we'd cap it at 2% anyway, because:

1. Your sample size is too small to trust W and R.
2. Slippage and missed fills shave 5–10% off your real-world R.
3. Drawdowns are psychologically harder than they look on paper.

The actual position-sizing formula

For a single trade:

shares = (account_equity × risk_pct) / (entry − stop)

Walk through it. $50k account, 1% per trade risk, entry $100, stop $98:

shares = (50,000 × 0.01) / (100 − 98)
shares = 500 / 2
shares = 250 shares

You buy 250 shares. If you stop out at $98, you lose $500 — exactly 1% of the account. Your position size in dollars is $25,000 — half your account — but your risk is $500.

This is the difference experienced traders draw a line in the sand over: position size and risk are not the same number.

A simple sizing table to keep on your desk

For 1% risk-per-trade, here's what size you take based on stop distance:

Stop distance ($)	$50k account	$100k account	$250k account
$0.50	1,000 sh	2,000 sh	5,000 sh
$1.00	500 sh	1,000 sh	2,500 sh
$2.00	250 sh	500 sh	1,250 sh
$5.00	100 sh	200 sh	500 sh
$10.00	50 sh	100 sh	250 sh

Tape this to your monitor. The bigger the stop, the smaller the position — always.

Why our strategies ship with sizing baked in

Every TradingView strategy we publish takes risk_per_trade as an input in dollars or percent. The script computes the position size automatically based on the ATR-derived stop. You don't have to do the math each trade — and you don't have to remember the formula at 9:31 AM when the chart is moving fast.

That, more than any other feature, is what separates a usable strategy from a chart toy.