Module 1: Trading Math: Expectancy

Building an Expectancy Spreadsheet from Scratch

5 min readLesson 10 of 10

Expectancy Really Means, Lesson 10

Building an Expectancy Spreadsheet from Scratch

Expectancy quantifies the average profit or loss per trade. A positive expectancy indicates a profitable system over a large sample size. A negative expectancy suggests a losing system. This lesson details constructing an expectancy spreadsheet.

Core Expectancy Formula

Expectancy (E) is calculated as:

E = (Probability of Win * Average Win) - (Probability of Loss * Average Loss)

This formula requires four inputs:

  1. Probability of Win (P_win): Total winning trades / Total trades
  2. Average Win (Avg_win): Sum of all winning trade profits / Total winning trades
  3. Probability of Loss (P_loss): Total losing trades / Total trades
  4. Average Loss (Avg_loss): Sum of all losing trade losses / Total losing trades

Note that P_win + P_loss = 1.

Spreadsheet Setup: Data Entry

Begin with a spreadsheet. Create columns for each trade.

Trade #DateInstrumentDirectionEntry PriceExit PriceShares/ContractsP&L (Gross)CommissionsP&L (Net)Win/Loss
1
2
...

P&L (Gross): (Exit Price - Entry Price) * Shares/Contracts for long trades. (Entry Price - Exit Price) * Shares/Contracts for short trades. Commissions: Fixed cost per trade or per share/contract. Example: $0.005 per share, $2.50 per contract. P&L (Net): P&L (Gross) - Commissions. Win/Loss: A simple indicator. "Win" for P&L (Net) > 0, "Loss" for P&L (Net) < 0.

Spreadsheet Setup: Calculation Block

Create a separate section for calculations.

MetricValueFormula
Total Trades
Total Winning Trades
Total Losing Trades
Total Net Profit/Loss
Probability of Win (P_win)
Probability of Loss (P_loss)
Sum of Winning Profits
Sum of Losing Losses
Average Win (Avg_win)
Average Loss (Avg_loss)
Expectancy (E)
Expectancy (in R-Multiples)

Step-by-Step Calculation Example

Consider a futures trader with 10 trades on ES (E-mini S&P 500 futures). Each contract has a point value of $50. Commissions are $2.50 per side per contract ($5.00 round trip).

Trade Data:

Trade #DateInstrumentDirectionEntry PriceExit PriceContractsP&L (Gross)CommissionsP&L (Net)Win/Loss
12023-10-26ESLong4300.004305.002$500.00$10.00$490.00Win
22023-10-26ESShort4302.004300.501$75.00$5.00$70.00Win
32023-10-27ESLong4310.004308.003-$300.00$15.00-$315.00Loss
42023-10-27ESShort4315.004316.501-$75.00$5.00-$80.00Loss
52023-10-28ESLong4320.004323.002$300.00$10.00$290.00Win
62023-10-28ESShort4325.004324.001$50.00$5.00$45.00Win
72023-10-30ESLong4330.004328.502-$150.00$10.00-$160.00Loss
82023-10-30ESShort4332.004330.001$100.00$5.00$95.00Win
92023-10-31ESLong4335.004337.503$375.00$15.00$360.00Win
102023-10-31ESShort4338.004339.002-$100.00$10.00-$110.00Loss

Calculations:

  1. Total Trades: Count of all entries in "Trade #" column = 10.
  2. Total Winning Trades: Count of "Win" in "Win/Loss" column = 6.
  3. Total Losing Trades: Count of "Loss" in "Win/Loss" column = 4.
  4. Total Net Profit/Loss: Sum of "P&L (Net)" column = $490 + $70 - $315 - $80 + $290 + $45 - $160 + $95 + $360 - $110 = $785.
  5. Probability of Win (P_win): Total Winning Trades / Total Trades = 6 / 10 = 0.60 (or 60%).
  6. Probability of Loss (P_loss): Total Losing Trades / Total Trades = 4 / 10 = 0.40 (or 40%).
  7. Sum of Winning Profits: Sum of positive "P&L (Net)" values = $490 + $70 + $290 + $45 + $95 + $360 = $1350.
  8. Sum of Losing Losses: Sum of absolute values of negative "P&L (Net)" values = $315 + $80 + $160 + $110 = $665.
  9. Average Win (Avg_win): Sum of Winning Profits / Total Winning Trades = $1350 / 6 = $225.00.
  10. Average Loss (Avg_loss): Sum of Losing Losses / Total Losing Trades = $665 / 4 = $166.25.
  11. Expectancy (E): (P_win * Avg_win) - (P_loss *
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