# Off-Peak Analysis

## Off-Peak Period: Two Possible Approaches

### 1. Based on Peak Revenue (PR)

A time period is off-peak if its **CONSISTENTLY** **RECURRING** revenue is below a certain percentage of the peak revenue.

**Formula:**

$$
OPR\_t < \alpha \cdot PR
$$

where:

* $$OPR\_t$$ = Off-Peak Revenue at time ( t )
* PR = Peak Revenue
* $$\alpha$$ = Threshold percentage (e.g., 70% of PR)

### 2. Based on Average Revenue (AR)

A period is off-peak if its revenue is significantly below the daily or weekly average revenue.

**Formula:**

$$
OPR\_t < \beta \cdot AR
$$

where:

* $$\beta$$ is the threshold factor (e.g., 80% of AR)

***

## Deriving Revenue Difference Between Off-Peak and Normal Days

To quantify the financial impact of off-peak periods, we need to determine the revenue difference between off-peak and normal periods.

### Revenue Difference Formula

$$
\Delta R = (AR - OPR) \times T\_{off}
$$

where:

* $$\Delta R$$ = Lost revenue due to off-peak periods
* AR = Average Revenue per unit time (hour, day, week)
* OPR = Off-Peak Revenue per unit time
* $$T\_{off}$$ = Total duration of off-peak periods

### Percentage Revenue Loss Due to Off-Peak Periods

$$
\text{Loss Percentage} = \left( \frac{AR - OPR}{AR} \right) \times 100
$$

This formula helps estimate how much revenue is lost during off-peak times.

***

## Example Calculation

Let’s assume:

* **Peak Revenue (PR)** = $10,000 per day
* **Average Revenue (AR)** = $7,000 per day
* **Off-Peak Revenue (OPR)** = $4,500 per day
* **Off-Peak Time Share (**$$T\_off$$**) = 5 hours out of a 12-hour business day**

### Revenue Difference Calculation

$$
\Delta R = (7,000 - 4,500) \times \frac{5}{12} = 2,500 \times 0.4167 = 1,041.67
$$

Thus, the revenue shortfall per off-peak period is **$1,041.67**.

### Percentage Revenue Loss

$$
\left( \frac{7,000 - 4,500}{7,000} \right) \times 100 = \left( \frac{2,500}{7,000} \right) \times 100 = 35.71%
$$

So, off-peak periods account for **35.71% revenue loss** compared to normal periods.

***

## Using This Formula for Forecasting

By adjusting the **(** $$\alpha$$ **)** and **(** $$\beta$$ **)** values, a business can:

* Predict revenue differences for different off-peak time scenarios.
* Determine the discount rates or incentives required to mitigate the impact of off-peak losses.
* Optimize pricing strategies for subscription models based on expected revenue fluctuations.


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