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

# Trading ELO

> How the composite trader rating works

Trading ELO is a composite rating from **0 to 2,400** that measures your overall quality as a trader. Unlike Arena ELO (which tracks duel wins), Trading ELO evaluates your real trading performance -- risk management, returns, and capital deployed.

## The formula

Your Trading ELO is the product of three independent factors, each scored between 0 and 1:

$$
\text{ELO} = 2400 \times \text{riskFactor} \times \text{growthFactor} \times \text{capitalFactor}
$$

Each factor is **disqualifying** -- if any one of them is zero, your entire score is zero. Great traders need all three: disciplined risk, positive returns, and real capital at stake.

## The three factors

### 1. Risk Factor (Sortino Ratio)

Measures how well you manage downside risk. Uses the [Sortino ratio](https://en.wikipedia.org/wiki/Sortino_ratio), which only penalizes negative volatility (unlike Sharpe, which penalizes all volatility).

$$
\text{riskFactor} = \frac{\min(\text{Sortino}, 5)}{1 + \min(\text{Sortino}, 5)}
$$

* Sortino is capped at **5** to prevent traders with zero losing days from maxing out
* Maximum possible riskFactor: **0.833** (at Sortino = 5)
* Negative or zero Sortino = 0 (no credit for poor risk management)
* Sortino is annualized: `(mean return / downside deviation) x sqrt(252)`

### 2. Growth Factor (ROI)

Measures your return on capital. Uses a sigmoid curve applied to the log of returns, which naturally handles both gains and losses.

$$
\text{growthFactor} = \text{sigmoid}(\text{sign}(\text{ROI}) \times \ln(1 + |\text{ROI}|))
$$

Where `sigmoid(x) = 1 / (1 + e^(-x}))`.

* ROI is calculated as `realized PnL / peak account value`
* Positive ROI pushes the score above 0.5; negative ROI pushes it below
* The log transform means doubling your money (+100%) and halving it (-50%) are treated symmetrically
* Handles leveraged losses (ROI below -100%) safely

### 3. Capital Factor (Peak Capital)

Measures how much real capital you have at stake. Uses a Hill curve that rewards larger accounts but with diminishing returns.

$$
\text{capitalFactor} = \text{sigmoid}(\ln(1 + \text{peakCapital} / 1000))
$$

* **\$1,000** is the reference point (produces a factor of \~0.62)
* **\$10,000** produces \~0.76
* **\$100,000** produces \~0.88
* Zero or negative capital = 0

This factor ensures that ELO reflects real conviction -- trading with significant capital, not just small test positions.

## Confidence ramp

To prevent traders with very few trades from dominating the leaderboard, a confidence adjustment is applied:

* **Minimum 2 closed positions** required for a Sortino ratio to be calculated at all
* Below **5 closed positions**, your ELO is linearly attenuated toward the baseline
* At 5+ closed positions, you receive full credit

$$
\text{final ELO} = 200 + (\text{formula ELO} - 200) \times \min\left(\frac{\text{closed positions}}{5}, 1\right)
$$

The **floor is 200** -- no trader's ELO drops below this, even with a negative Sortino.

## How it updates

Trading ELO is recalculated every 5 minutes by a background job. It pulls your latest:

* **Sortino ratio** from closed position returns
* **Season PnL** from wallet performance metrics
* **Peak account value** (high water mark) from periodic snapshots

Your ELO is scoped to the current season period and displayed on your profile and the leaderboard.

## Key differences from Arena ELO

|                      | Trading ELO                | Arena ELO                    |
| -------------------- | -------------------------- | ---------------------------- |
| **Range**            | 0 -- 2,400                 | 1,200+ (unbounded)           |
| **Based on**         | Real trading performance   | 1v1 duel wins/losses         |
| **Inputs**           | Sortino, ROI, peak capital | Win/loss vs. opponent rating |
| **Starting value**   | 200 (baseline)             | 1,200                        |
| **Update frequency** | Every 5 minutes            | After each duel settles      |