# expected value

Calculates the expected return on a trade based on the composite probability estimate and current market price.

## Formula

```
EV = (Estimated Probability * Payout) - Cost

Where:
  Payout = 1.00 (prediction markets pay $1 on YES if correct)
  Cost = Current YES Price
```

Simplified:

```
EV = Estimated Probability - Market Price
```

## Related Metrics

| Metric        | Formula            | Meaning                                       |
| ------------- | ------------------ | --------------------------------------------- |
| **EV**        | `p_est - p_market` | Raw expected value per dollar at risk         |
| **ROI**       | `EV / p_market`    | Percentage return on investment               |
| **Breakeven** | `p_market`         | Minimum true probability needed to break even |

## Example

A market trades at 40% YES. Your composite probability estimate is 55%.

```
EV = 0.55 - 0.40 = $0.15 per share
ROI = 0.15 / 0.40 = 37.5%
Breakeven = 40%
```

You need the event to have at least a 40% true probability to break even. Your model says 55%. The 15-cent edge is your expected profit per share.

## For NO Trades

When the model suggests a NO position:

```
EV (NO) = (1 - Estimated Probability) - (1 - Market Price)
        = Market Price - Estimated Probability
```

If the market is at 70% and your estimate is 50%:

```
EV (NO) = 0.70 - 0.50 = $0.20 per share
ROI = 0.20 / 0.30 = 66.7%
```

## Edge Categories

| Edge Size    | Interpretation                                              |
| ------------ | ----------------------------------------------------------- |
| **>15%**     | Strong edge. Verify signals aren't correlated.              |
| **5-15%**    | Moderate edge. Standard opportunity.                        |
| **2-5%**     | Marginal edge. Check taker cost.                            |
| **<2%**      | Negligible. Taker cost likely erases it.                    |
| **Negative** | No edge. Model agrees with market or favors the other side. |

## Interaction with Other Models

* **Kelly Criterion** uses EV to determine position size
* **Monte Carlo** provides a distribution that EV summarizes as a single number
* **Taker Cost** reduces your realized EV by the cost of execution
* **Bias Zones** flag markets where systematic biases inflate or deflate EV estimates


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