Two-Outcome Arithmetic Matrix

Risk/Reward Win Rate Matrix Calculator

Compare many entered win-rate and average reward-to-risk combinations in one expected-value matrix. Every cell assumes a full 1R average loss, the displayed average win multiple and one equal cost per outcome in R; it does not estimate a strategy’s win rate, forecast future profitability or grade any combination.

Entered scenariosEqual cost in RNo edge claimModel 1.0.0

Enter the matrix rows and columns

Provide comma-separated win rates and average win multiples. Use one cost in R per outcome, where 1R is the assumed average loss magnitude before that cost.

Entered

One to 20 comma-, space- or semicolon-separated values from 0 through 100.

One to 20 positive average winning outcomes, each relative to a 1R average loss.

Model boundary: The matrix is a sensitivity table, not evidence of a trading edge. Real outcomes can include partial wins, partial losses, breakeven exits, variable size, changing costs, dependence, regime shifts and estimation error that the two-outcome cells do not represent.

Enter at least one row and one columnThe result will show expected value in R for every combination, plus positive, zero and negative arithmetic counts.

How each win-rate and reward-risk cell is calculated

Win probability = entered win rate ÷ 100Average winning outcome = entered reward multiple × 1RAverage losing outcome = −1RExpected value in R = win probability × reward multiple − loss probability × 1 − cost per outcome RArithmetic breakeven win rate = (1 + cost R) ÷ (1 + reward multiple) × 100

Each cell is a two-outcome weighted average. The winning branch receives the entered average win multiple and the losing branch receives minus one risk unit. The entered cost is then subtracted from every outcome. No random sequence is generated and no trade count is needed for the per-outcome arithmetic.

The win-rate rows are scenarios, not estimates. Entering 40%, 50% or 60% does not assert that a strategy can achieve those rates. A defensible observed rate requires a representative sample with clear handling of partial outcomes, costs, exclusions, dates and strategy changes.

The reward columns are average winning outcomes in units of one average loss. They are not planned target distances unless actual winners and losses consistently realize those values. A 2R target does not create a 2R average win when trades are closed early, scaled out, slipped or missed.

Cost is expressed in the same R basis and is applied equally to every outcome. If cost is 0.10R, the zero-cost equation is reduced by 0.10R in every cell. Real spread, commission, slippage, financing and conversion can vary by symbol, session, direction, holding time and order size.

Positive, zero and negative colors classify the entered equation only. A positive cell means that weighted average is above zero under the assumptions. It does not establish statistical significance, persistence, independence, stationarity, capacity or executable future profit.

The matrix complements rather than replaces the scalar Breakeven Win Rate and Expectancy calculators. It is useful when the question is sensitivity across several combinations at once; the scalar tools are better for one entered scenario or a recorded outcome sample.

Worked example from the audited fixture

Reproduce it with “Load audited example”

The audited fixture enters win-rate rows of 30%, 40%, 50% and 60%; average-win columns of 1R, 1.5R, 2R and 3R; and an equal 0.10R cost per outcome.

At 40% win rate and a 2R average win, expected value is 0.40 × 2 − 0.60 × 1 − 0.10 = +0.10R per outcome. Arithmetic breakeven for the same column is 1.10 ÷ 3 = 36.6667%.

At 50% and 1R, the cell is −0.10R because equal gross wins and losses are reduced by cost. At 60% and 3R, the cell is +1.30R. Neither cell is a forecast because both rates and average outcomes are entered assumptions.

How to interpret the result

  1. Read across a row to see how the equation changes when average winning outcome changes while win rate and cost stay fixed. This is a sensitivity comparison, not evidence that the different targets preserve the same win rate.
  2. Read down a column to see how the equation changes when win rate changes while average win, average loss and cost stay fixed. The cells do not include uncertainty around an estimated win rate.
  3. A zero cell is mathematical breakeven under the two-outcome assumptions. Real breakeven can differ when outcomes include zeros, partial exits, asymmetric costs, missed trades, changing size or nonstationary behavior.
  4. A positive cell can coexist with severe drawdown, long losing streaks and high uncertainty. Expected value alone does not describe path risk, capital requirements or the probability of a specific sample result.
  5. Use cost in R only after normalizing comparable recorded costs against the same initial-risk basis. Mixing dollars, pips, percentages and R units inside one matrix invalidates the interpretation.
  6. Validate any promising observed scenario with the trade journal, expectancy, confidence-interval, drawdown and losing-streak tools. The matrix should remain the first arithmetic map, not the final performance conclusion.

Choose the exit-planning view that matches the question

These three pages share governance and presentation, but they do not answer the same job. Keeping the jobs separate prevents a fixed-level calculation from being mistaken for trailing-platform behavior or a performance sensitivity table.

Comparison of the three entered exit-planning tools
ToolPrimary inputsOutputHard boundary
Stop Loss & Take ProfitPosition, money limits and entered costReverse-solved fixed exit pricesNo placement recommendation
Trailing StopEntered favorable reference and explicit ruleOne stepped applied-stop scenarioNo live terminal behavior
Win Rate MatrixEntered win rates, average wins and cost in RTwo-outcome EV sensitivity gridNo estimated edge

Assumptions and limitations

  • No trades, dates, instruments, strategy labels, account history, broker statement or market data are connected.
  • Only two outcomes are represented: one average win and one 1R average loss. Breakeven, partial and variable outcomes are excluded.
  • The same cost in R is subtracted from every outcome. Real costs can be asymmetric and can change with symbol, size, time and execution.
  • Sample size, confidence intervals, dependence, autocorrelation, stationarity, regime change, selection bias and data quality are not assessed.
  • The matrix calculates an arithmetic mean per outcome, not compounded account growth, drawdown, risk of ruin, profit probability or future return.
  • No win rate, reward multiple, cost, setup, strategy, risk amount, position size, signal or trade is recommended.

Sources and methodology

The arithmetic is independently fixture-tested. The external references define platform fields, execution boundaries or statistical concepts; they do not verify any entered price, broker specification, cost, win rate or future outcome.

Frequently asked questions

  • It shows expected value in R for every entered win-rate row and average-win column under a full 1R average loss and one equal cost per outcome.
  • Expected value equals win probability multiplied by average win R, minus loss probability multiplied by 1R, minus the entered cost per outcome in R.
  • It means the entered two-outcome weighted average is above zero. It does not prove a strategy has an edge or that the assumptions will persist.
  • It is arithmetic breakeven under the entered win rate, average win, 1R average loss and equal cost. Real breakeven can differ when outcomes and costs vary.
  • No. Every win rate is entered as a scenario. The page receives no trade sample and calculates no confidence interval or future probability.
  • The matrix uses one common unit so the same equation can compare combinations. Normalize comparable costs to the same initial-risk basis before entering them.
  • Only as a hypothetical scenario. Planned targets do not establish realized average wins because exits, fills, partial closes and losing-trade behavior can differ.
  • This route compares many row-and-column combinations at once. The Breakeven Win Rate Calculator examines one entered average-win, average-loss and cost scenario in greater detail.

Verify symbol, cost and execution terms

Before translating an entered scenario into an order, check the exact symbol contract, tick and volume settings, Stop Loss and Take Profit rules, spread, commission, financing and execution policy for the broker entity and account available in your jurisdiction.

XM

Verify the applicable symbol specification, stop rules and execution terms.

Check XM terms

FBS

Check contract, volume, cost and stop-order conditions for the account.

Check FBS terms

FXOpen

Confirm symbol settings and execution conditions before placing a trade.

Check FXOpen terms

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Disclaimer: The results from this tool are estimates for educational and informational purposes only and may differ from your broker's figures. This is not financial or investment advice. Trading forex and CFDs carries a high level of risk and can result in the loss of all your capital. Always verify calculations with your broker and trade within your risk tolerance.