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# ATD (Automated Token Distributor)
## Overview
The Automated Token Distributor (ATD) is a core component of VALOR's token distribution strategy. This document explains the ATD’s budget distribution mechanisms.
{% hint style="info" %}
The below models can be updated due to the balance update
{% endhint %}
## 1. Budget Distribution
ATD’s budget distribution framework employs a probabilistic approach based on a standard normal distribution to allocate resources effectively across various tokens and market segments.
### Key Definitions and Variables
* **Normal Distribution (PDF)**: A probability distribution function used to allocate budgets fairly, with a mean of 0 and a standard deviation of 1.
* **Budget Allocation Ratios**: Ratios are derived from the PDF to determine the portion of the total budget allocated to each token.
* **Total Budget**: It is set at 110% of the inflow over 12 hours. It is rounded down to 9 decimal places, and the remainder is discarded.
### Process Explanation
1. **Total Budget Calculation**:
1. Case 1 (Accumulated Inflow < Accumulated Outflow):
* The total budget is set at 110% of the inflow over the past 12 hours plus any carried-over budget
$$
B\_{total} = \left\lfloor (1.1 \times Inflow) \times 10^9 \right\rfloor / 10^9
$$
* Here, $$Inflow$$ is the inflow over the past 12 hours.
2. Case 2 (Accumulated Inflow > Accumulated Outflow):
* The total budget is set at sum of each sSPL supply and ideal price.
$$
B\_{total} = \sum S \times P\_{idl}
$$
* Maximum budget = (Accumulated Inflow - Accumulated Outflow) \* 1.1
2. **Random Factor Generation**:
* Generate a random number within the range of \[-0.5, 0.5] from a normal distribution with a mean of 0 and a standard deviation of 1. This controls the variability in budget allocation.
* Calculate the probability density $$p(x\_i)$$ for each random factor $$x\_i$$. This density influences how the budget is divided. The probability density function is:
$$
p(x\_i) = \frac{1}{\sqrt{2\pi}} e^{-\frac{x\_i^2}{2}}
$$
3. **Budget Allocation**:
* Convert these densities into budget allocation ratios:
$$
R\_i = \frac{p(x\_i)}{\sum\_{j=1}^{9} p(x\_j)}
$$
* Allocate the total budget to various tokens using these ratios:
$$
B\_i = \left\lfloor R\_i \times B\_{total} \times 10^9 \right\rfloor / 10^9
$$
## 2. Price Setting
The ATD's price-setting mechanism dynamically adjusts token prices around an ideal price to reflect market values.
### Key Definitions and Variables
* **Ideal Price (**$$P\_{idl}$$**)**: The target price for the tokens.
* **Reference Price (**$$P\_{ref}$$**)**: The market price of the token in Black Market.
* **Next Price (**$$P\_{nxt}$$**)**: The price of the token after adjustment.
* **Standard Deviation (**$$\sigma$$**)**: Controls the spread of price values around $$P\_{idl}$$.
{% hint style="success" %}
These variables will be initialized on the procurement creation
{% endhint %}
### Standard Deviation Calculation
The standard deviation $$\sigma$$ is calculated as:
$$
\sigma = \sqrt{\frac{P\_{idl}^2}{2 \ln(10)}}
$$
This calculation determines the range of price fluctuations around the ideal price $$P\_{idl}$$, adjusting for market volatility.
### Price Determination Model
#### Random Price Determination Model
This model dynamically calculates the next token price using a probability distribution function centered on $$P\_{idl}$$.
**Detailed Process**
1. **Define Price Range**:
* Establish the effective price range for the next pricing cycle:
$$
\text{Effective Price Range} = \[P\_{ref} \times 0.9, P\_{ref} \times 1.4]
$$
2. **Generate PDF**:
* Create a normal distribution centered on $$P\_{idl}$$ with the calculated $$\sigma$$.
3. **Calculate Area Under Curve**:
* Determine the total probability area under the PDF within the defined range:
$$
A = \int\_{P\_{ref} \times 0.9}^{P\_{ref} \times 1.4} f(x) , dx
$$
4. **Generate Random Factor and Set Next Price**:
* Select a random value within the range \[0, A], and determine the corresponding price using the inverse cumulative distribution function (CDF):
$$
P\_{nxt} = f^{-1}(r)
$$
* Here, $$f^{-1}$$ is the inverse function of the CDF, accurately determining the price corresponding to the random value $$r$$.
5. **Final Quantity Adjustment**:
* Calculate the maximum quantity that can be purchased with the allocated budget:
$$
Q\_i = \left\lfloor \frac{B\_i}{P\_{nxt}} \right\rfloor
$$
* Round down to ensure accurate quantity calculation. (If $$Q\_i < 1$$, set $$Q\_i$$ to 1)
* Adjust the final price using the actual quantity purchased:
$$
P\_{final} = \left\lfloor \frac{B\_i}{Q\_i} \times 10^3 \right\rfloor / 10^3
$$
* The final price $$P\_{final}$$ is rounded down to 3 decimal places.
$$
B\_i^\text{new} = B\_i - (Q\_i \times P\_{final})
$$
## Data
| Token | Ideal Price ($VALOR) |
| ----------------------- | -------------------- |
| Voodoo Doll ($VD) | 5.5515 |
| Gold Teeth ($GT) | 6.8204 |
| JB Whiskey ($JBW) | 10.3219 |
| Canteen ($CT) | 11.2677 |
| G Badge ($GB) | 13.2835 |
| Holy Water ($HW) | 21.7118 |
| Used Engine ($UE) | 35.9697 |
| Enhanced Bullet ($EB) | 57.8595 |
| Oil Lighter Case ($OLC) | 72.0052 |
## Examples
### PDF and simulation when the ideal price is 2.28
### PDF and simulation when the ideal price is 50.4