The core principles and applications of the trader's equation

The trader's equation is an important mathematical framework in the trading field, helping traders assess the rationality of trading opportunities from the perspective of probability and expected value. Here is a detailed analysis of the trader's equation:

1. The mathematical foundation of the trader's equation

The core formula of the trader's equation can be expressed as:

Win Rate × Expected Profit > Loss Probability × Risk

  • Win Rate: The probability of a successful trade

    Expected Profit: The average profit amount when the trade is successful

    Loss Probability: 1 - Win Rate

    Risk: The average loss amount when the trade fails

This inequality indicates that a trade is mathematically reasonable only when the expected return on the left side is greater than the expected loss on the right side.

II. Trade-off of the three elements of trading


Successful trading requires balancing three key elements:

  1. Win rate: the probability of successful trading


    • High win rates usually require stricter entry conditions and more significant stop-loss space


      Low win rate strategies often come with a higher risk-reward ratio


    Risk: maximum loss of a single trade

    • Risk control is key to long-term survival

      Too small a stop-loss may lead to frequent stop-outs

    Return: potential profit space

    • High return opportunities usually have a lower win rate
      Need to form a reasonable proportion with risk (e.g., 2:1 or 3:1)

Key principle: high win rate, high return, and low risk cannot all be achieved, at most only two can be chosen.

III. Practical application of the trader's formula

1. Application in breakout trading

In breakout trading, the trader's formula can be applied like this

  • In a strong breakout environment, the win rate can be estimated to be around 60%

    In a choppy range, the raw win rate may only be 40%

    By widening stop-loss and incrementally increasing positions, the win rate can be appropriately improved

2. Z-score for assessing system reliability

The Z-score is an important indicator for assessing the stability of trading systems:

  • Calculation formula: average profit and loss distance / profit and loss standard deviation

    The Z-score of top scalpers can reach 5

    Ordinary system Z-scores between 2-3 are already quite good

    High Z-score systems can withstand higher risk ratios (1-2%)

    Low Z-score systems need to reduce positions to prevent consecutive losses from destroying the account

3. Comparison of different types of strategies

Differences in performance of different strategies in the trader's formula:

  • High Z strategy: such as High 2 or Low 2 flag rapid scalping, one-time risk take profit, high win rate, low volatility

    Low Z strategy: such as simple breakout of the recent ten candlestick highs/lows, low win rate, relying on a few large profitable trades

IV. Differences between professional traders and amateur traders

Professional traders and amateur traders have essential differences in applying the trader's formula:

1. Differences in psychological mechanisms

  • Amateur trader:
    Fear when profitable, prematurely closing profits

    Hope when losing, stubbornly holding losing positions

    Forming a 'small win big loss' fatal pattern

    Professional Trader:

    Fear of losses, timely stop-loss

    Forming a profit model of 'cutting losses short and letting profits run'

    Expected profits, let profits run

2. Differences in execution systems

Professional traders have established two major pillar systems:

  1. Mechanical defense:

    • Use non-negotiable stop-loss

      View stop-loss as 'the ultimate tool for capital preservation'

    Disciplinary offense:
    Adopt pyramid-style position increases (only add positions when profitable)
    Use market money to fund position increases

V. Extended thinking on the trader's formula

1. Shitaimeiya's trading results formula

American futures expert Shitaimeiya proposed a more macro formula: trading results = market understanding × (trading strategy + self-awareness) this formula emphasizes that market understanding is fundamental

Trading strategy and self-awareness are equally important

Long-term trading performance is the result of the trader's overall investment

2. Fisher's formula and market activity

Fisher's formula (MV=PT) reveals the relationship between market activity and price:

Increased market activity (V increases) will lead to price P rising

This provides a macro perspective for judging market trends

  1. Estimated win rate

    • Set stop-loss (risk)

      Mark the target (return)

    Apply the formula for verification:
    Calculate win rate × expected return vs loss probability × risk

    Only consider trading when the left side is greater than the right side

    Small position practice:

    Practice with a small position of 'completely not caring about losses'

    First stabilize the Z-score above 2, then consider scaling up

    Continuous optimization

    • Record the win rate, risk, and return of each trade

      Regularly review and adjust parameters

Key reminder: perfect trading does not exist, continuously executing trades with positive expectations, small advantages will accumulate into considerable profits over time.

The trader's formula provides a scientific evaluation framework for trading decisions, but ultimate success also depends on the trader's discipline and psychological control abilities. As emphasized in (Reminiscences of a Stock Operator), the hardest thing to overcome in the market is not the market itself, but the trader.