# Reward System

LETSTOP’s reward system uses a sophisticated mathematical framework to calculate token rewards based on **riding behavior, subscription tier, user attributes, and system constraints**. It is designed to **incentivize safe driving, consistent engagement, and responsible app use** while maintaining overall economic stability.

***

#### Ride Quality Assessment

Each ride is evaluated using a **driving score**, which quantifies rider behavior:

$$
It = (TD \* SV1)/InDS = max(0, 1 - (NoTIm/It))
$$

Where:

* **TD** = time driven (ride duration)
* **NoT** = number of touches (phone interactions)
* **DS** = driving score (0–1)
* **SV1, InDS** = system constants

This score rewards **longer rides with minimal phone interaction**, promoting safe driving behavior.

***

#### Base Credit Calculation

The driving score is converted into **base credits** using a polynomial function:

$$
BSC = SV2 \* DS⁴ - SV2 \* DS³ + (1/2)SV2 × DS² + (3/14)SV2 × DS
$$

This ensures higher driving scores contribute **nonlinearly** to rewards, amplifying the benefit of consistently safe rides.

***

#### Distance and Time Factors

Ride distance and duration further influence rewards through **kilometer and time multipliers**:

$$
KMM = SV3 \* √KMDTM = SV4 \* TD + SV5 \* √TD
$$

Where:

* **KMD** = kilometers driven
* **KMM** = kilometer multiplier
* **TM** = time multiplier

These factors scale rewards based on actual effort, ensuring that longer and more involved rides are rewarded proportionally.

***

#### Progressive Reward Structure

**Subscription Benefits**

Subscription tiers determine the **full-reward segment size** and **multiplier**. Higher tiers receive **larger full-reward segments** and **higher multipliers**, providing greater incentives for active and premium users.

| Subscription | First Segment | Regular Segments | Multiplier |
| ------------ | ------------- | ---------------- | ---------- |
| Lite         | X km          | Y km             | 1.0        |
| Plus         | 3X km         | 3Y km            | 1.2        |
| Pro          | 7X km         | 3Y km            | 1.5        |
| Platinum     | 10X km        | 3Y km            | 5.5        |
| Custom       | 11X km        | 3Y km            | 6.0        |
| Elite        | 12X km        | 7Y km            | 7.0        |

***

**Distance-Based Decay Model**

Rewards decay progressively based on accumulated daily distance:

For position **p km** in daily riding:

* If **p < F** → full rewards (Multiplier = 1.0)
* If **p ≥ F** → decay applies:

$$
Segment number = 1 + ⌊(p-F)/R⌋

Decay factor = 0.5^(Segment number)
$$

Where:

* **F** = first segment size (varies by subscription)
* **R** = regular segment size (varies by subscription)

This ensures that **initial kilometers earn full rewards**, while very long rides receive gradually reduced rates to maintain balance.

***

#### Comprehensive Reward Calculation

Each ride is divided into segments, and the reward for each segment is calculated as:

$$
SegmentReward\_i = M \* C \* d\_i \* B \* MultiplierAt(p\_i)
$$

Where:

* **M** = subscription multiplier
* **C** = touch count penalty derived from driving score
* **d\_i** = distance within segment i
* **B** = base token rate derived from ride quality
* **p\_i** = position at segment start = T + ∑(j=0 to i-1) d\_j
* **T** = total distance already ridden today

The **total reward** for the ride is the sum of all segment rewards:

$$
Reward = ∑(i=0 to n-1) SegmentReward\_i
$$

***

#### Credit Balance Influence

A user’s **existing credit balance** also impacts rewards. LETSTOP applies a **logarithmic scaling function with diminishing returns**:

$$
CM=1+α\*ln(1+CB/β​)
$$

Where:

* **CM** = credit multiplier applied to ride reward
* **CB** = your current credit balance
* **α** = scaling factor (determines how much balance affects rewards)
* **β** = normalization constant (ensures the boost is reasonable)

This approach:

* Rewards consistent participation
* Accelerates engagement for new users
* Caps excessive accumulation at high balances

The **credit-based reward** is combined with ride quality, subscription multipliers, and vehicle or level bonuses to determine the **total tokens earned per ride**.

***

#### System-Wide Balance

To maintain overall economic stability, a final adjustment ensures proportional token distribution:

<p align="center"><span class="math">AdjustedReward = Reward * (SystemAllocation / ∑(all rides) Reward)*CM</span></p>

This prevents inflationary reward spikes and preserves fairness across all users.

***

#### Key System Benefits

* Rewards **safe riding** and minimal phone interactions
* Higher subscription tiers gain **larger full-reward segments** and **higher multipliers**, including Platinum, Custom, and Elite tiers
* Encourages **consistent daily riding** over sporadic long rides
* Integrates **user credit balance** to reward long-term engagement
* Maintains **economic stability** and proportional token distribution


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