> ## Documentation Index
> Fetch the complete documentation index at: https://docs.tradex.so/llms.txt
> Use this file to discover all available pages before exploring further.

# Expectancy and R

> An explanation of expectancy, R, and related concepts used in strategy analysis.

***

## Expectancy

Expectancy is the single most important piece of data for telling whether a strategy actually makes money — it looks at average profit, not win rate. In short, it tells you **how much you earn per trade, on average, with this strategy**.

***

### The Coin-Flip Game

Let's play a simple coin-flip game with these rules:

* Heads: +\$200
* Tails: -\$100

The win rate is obviously 50%. But what happens if you play this game 100 times?

```text theme={null}
A. 50 wins × $200 = +$10,000
B. 50 losses × $100 = -$5,000
```

Add the total gains (A) and total losses (B) and you get +$5,000. Divide by the number of games and you get \+$50 per game. That +\$50 is the expectancy.

It means **every time you play this game, you earn \$50 on average over the long run**.

Now let's keep the same game but change the payouts:

* Heads: +\$100
* Tails: -\$150

The win rate is still 50%, but the expectancy is -\$25. In other words, even with the same win rate, this is a game you are **guaranteed to lose**.

Starting to make sense?

***

### How to Read Expectancy

Here's how to interpret your per-trade expectancy. If your expectancy is +0.42R, read it like this:

> **"Every time I trade, I earn on average 42% of the risk (SL) I took on."**

If you risk \$1,000 on every trade, the results look like this:

* **+\$420** per trade on average
* **+$42,000** over 100 trades, **\+$420,000** expected over 1,000 trades

Of course, you don't earn exactly $420 every time. One trade might make \+$2,000 and another might lose -$1,000 — but the average converges to \+$420.

***

### Expectancy Benchmarks

| Expectancy          | Meaning                     | What to do                                             |
| :------------------ | :-------------------------- | :----------------------------------------------------- |
| **+0.5R or higher** | Very strong strategy        | Scale up your size and run it seriously                |
| **+0.2 – +0.5R**    | Stable, profitable strategy | Stay consistent and increase trade count               |
| **0 – +0.2R**       | Near break-even             | Improve your R/R or entry accuracy                     |
| **Negative**        | Losing strategy             | Stop immediately; analyze the cause or change strategy |

***

### 3 Ways to Improve Expectancy

1. **Raise your win rate**: Make your entry conditions stricter to improve accuracy.
2. **Raise your average win**: Improve your R/R by holding winners longer before taking profit.
3. **Cut your average loss**: On losing positions, stop out exactly as planned — no exceptions.

Most traders obsess over #1. But improving #2 and #3 is far easier and far more effective.

**Keep a 50% win rate and simply move your R/R from 1:1 to 1:2, and your expectancy jumps from 0 to +0.5R.**

***

## R

R is the unit of risk you take on in a trade — put simply, the distance to your stop-loss.

**Case 1. Trader A**

* Enters a Bitcoin long at \$90,000
* Stop-loss (SL): \$89,000

If A stops out, they lose $1,000. In other words, the risk taken in this trade is **1R = $1,000\*\*. Now let's express the outcomes in R:

* Take profit at $91,000 → made $1,000, so **+1R**
* Take profit at $91,500 → made $1,500, so **+1.5R**
* Take profit at $92,000 → made $2,000, so **+2R**
* Stop out at $89,000 → lost $1,000, so **-1R**

***

## Why Express Things in R?

You could express expectancy in plain dollars. But expressing it in R lets you **compare every trade on equal footing**.

Suppose trader A made these three trades:

| Trade | Symbol | Leverage | PnL      | Return | Risk at stop |
| :---- | :----- | :------- | :------- | :----- | ------------ |
| A     | BTC    | 5x       | +\$2,000 | +5%    | \$1,000      |
| B     | ETH    | 20x      | +\$750   | +20%   | \$500        |
| C     | SOL    | 2x       | -\$300   | -1.5%  | \$300        |

In dollar terms — +2,000 / +750 / -300 — it's hard to tell which trade was most efficient.

But in R terms — **+2R / +1.5R / -1R** — it's immediately clear the first was the most efficient.

Trader A's average expectancy is +0.83R, meaning **A earns 83% of their chosen stop-loss risk per trade**.

***

### The Win-Rate Trap

Expressed in R, expectancy follows this formula:

```text theme={null}
Expectancy (R) = (win rate × average win in R) - (loss rate × average loss in R)
```

**Case 1: A good trader**

* 40% win rate, average win +2.5R
* 60% loss rate, average loss -1R
* Expectancy = (0.4 × 2.5) - (0.6 × 1) = **+0.4R**

Even with just a 40% win rate, they earn 0.4R per trade on average. Over 100 trades, that's an expected +40R.

**Case 2: A dangerous trader**

* 70% win rate, average win +0.8R
* 30% loss rate, average loss -2.5R
* Expectancy = (0.7 × 0.8) - (0.3 × 2.5) = **-0.19R**

A trader with a 70% win rate who **loses money**. Small frequent wins, occasional huge losses.

**This is the win-rate trap — and exactly why expectancy matters more than win rate.**

Stop being fooled by win rates. With positive expectancy you survive, with negative expectancy you lose — every time.

***

### Relationship to Risk/Reward

This R concept is the foundation of expressions traders use all the time, like a **1:2 risk/reward ratio**. R/R of 1:2 = risking 1R to make 2R = an R/R ratio of 2.0. In other words, you risk losing 1 to your stop for the chance to make 2 at your target.