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Required expectancy and trades needed

Lesson 10 · about 10 min

The ratio tells you how hard the challenge is. Your expectancy tells you whether you can do it and how long it will take. This lesson works in R, the amount you risk per trade, because it makes the arithmetic the same for any account size and any product. If R and expectancy are new to you, the Risk Management course, Module 3, covers them.

Express the challenge in R

Choose a risk per trade. Module 3, lesson 4 will argue for one-fifth to one-tenth of the daily limit; for now take a "$50,000" account with a $3,000 target, a $2,000 drawdown and a $1,000 daily limit, and risk $200 per trade.

  • Target = $3,000 / $200 = 15R
  • Drawdown = $2,000 / $200 = 10R
  • Daily limit = $1,000 / $200 = 5R

Everything that follows is in those units.

Expectancy and trades needed

Expectancy is your average result per trade in R. If your log shows a 50% win rate with average winner 1.4R and average loser 1.0R:

E = 0.5 x 1.4 - 0.5 x 1.0 = 0.20R per trade

Expected trades to reach the target = target / E = 15 / 0.2 = 75 trades.

Expectancy per trade Trades to reach 15R (expected) At 2 trades/day At 4 trades/day
0.05R 300 150 days 75 days
0.10R 150 75 days 38 days
0.20R 75 38 days 19 days
0.30R 50 25 days 13 days
0.50R 30 15 days 8 days

Two things follow. A 0.05R edge, which is real and would make money over a career, takes 300 trades to pass at this size. And expectancies above 0.3R per trade are rare over any sample large enough to trust. Most retail traders who pass do so with a 0.1R to 0.3R edge, patience, and a few hundred trades of history behind the number.

Required expectancy from a time limit

Run the table backwards. If the evaluation has a 30-day limit and you take 2 trades per day, you have 60 trades. Required expectancy = 15R / 60 = 0.25R per trade, and that is only the expectation; half the time you will be behind schedule.

Time limit Trades/day Trades available Required E for 15R
30 days 2 60 0.25R
30 days 4 120 0.125R
60 days 2 120 0.125R
None 2 Unlimited Any positive E

Time limits force a higher expectancy or more trades per day. More trades per day usually means lower-quality trades, which lowers expectancy. This is why an evaluation with no time limit is worth paying more for.

Key idea: Trades needed = target in R / expectancy in R. Know your expectancy from a log of at least 100 trades before you buy; if you do not have that log, the evaluation is a $150 way of finding out, and you should expect the answer to be "not yet".

Variance: why the expected path is not the likely path

Expectancy is an average. The sum of 75 trades with a standard deviation of about 1.2R each has a standard deviation of roughly 1.2 x sqrt(75) = 10.4R. Your expected finish is +15R, but one standard deviation below that is +4.6R and two below is -5.8R. Your drawdown allowance is 10R, and the trailing rule means it is often less.

In plain terms: with a genuine 0.2R edge and 10R of room, a perfectly ordinary bad stretch can end the evaluation. The next lesson puts a number on that. The cure is not a bigger edge, which you cannot conjure. It is smaller R, which converts the same dollar allowance into more R of room, and more trades, over which variance matters less relative to expectancy.

Halve the risk to $100:

  • Target = 30R, drawdown = 20R, trades needed at 0.2R = 150.
  • Standard deviation of the sum = 1.2 x sqrt(150) = 14.7R against 20R of room, a better ratio than 10.4R against 10R.
  • It takes twice as long.

That trade-off, time against safety, is the central decision of the evaluation. The firm's fee structure pushes you toward speed. The maths pushes you toward patience. Only one of those is on your side.

A realism check on your expectancy

Before trusting a number from your log, ask:

  1. Is it from at least 100 trades? Fewer, and the true value could be half or double.
  2. Is it net of commissions and realistic slippage?
  3. Is it from the same product, session and setup you will use in the challenge?
  4. Did it include the losing streaks, or did you stop logging during them?

If the honest answer to any of these is no, use half the number you computed for planning purposes.

Try it: From your own trade log, compute win rate, average win in R, average loss in R and expectancy. Then compute trades needed for your target at two risk sizes: one-fifth and one-tenth of the daily limit. Write both numbers on your rules sheet. Try the calculator at /tools/prop-firm-challenge to check your arithmetic.

Recap

  • Convert target, drawdown and daily limit to R; then trades needed = target in R / expectancy in R.
  • Realistic retail expectancies of 0.1R to 0.3R need 50 to 150 trades to pass a 15R target; time limits raise the required expectancy.
  • Variance over the required number of trades is comparable to the drawdown allowance, so ordinary bad stretches can fail a trader with a real edge.
  • Smaller R buys more room and more trades, at the cost of time; the maths favours patience, the fee structure favours speed.

See it drawn

Original diagrams for the ideas on this page. Illustrative, not real market data.

The spread of outcomes behind an expectancyA histogram of forty trades: a tall block of small losses on the left, a low spread of larger wins on the right, and a line marking the average outcome.NUMBER OF TRADES051024 LOSSES, AVG −$20016 WINS, AVG +$600EXPECTANCY +$120−$400−$200$0+$200+$400+$600+$800PROFIT OR LOSS PER TRADEexpectancy = (40% × $600) − (60% × $200) = +$120 per trade
Expectancy: the average trade. Forty trades sorted by outcome: 24 small losses and 16 larger wins. Weighting each side by how often it happens gives the average result per trade, marked here by the dashed line at +$120.
Risk and reward on one tradeA price scale showing an entry with a stop two points below and a target six points above, so the reward band is three times the risk band.PRICETARGET 106.00ENTRY 100.00STOP 98.00REWARDRISK6.00 pointsthree times the risk2.00 pointsthe most you loserisk : reward = 1 : 3
Risk and reward on one trade. One trade on a price scale: the entry sits 2.00 points above the stop and 6.00 points below the target, so the shaded reward band is three times the risk band. The ratio compares what is lost if the stop is hit with what is gained if the target is reached.
An equity curve and its drawdownAn account balance rising over a year, falling from a peak to a trough, then climbing back to the old peak.ACCOUNT EQUITY$20k$12k$8k024681012TIME (MONTHS)PEAK $16,000TROUGH $12,000DRAWDOWN−25%RECOVERY
Equity curve and drawdown. An account balance plotted month by month. The fall from the $16,000 peak to the $12,000 trough is a 25% drawdown, and the shaded area lasts until the balance climbs back to the old peak.