Greatness Index Calculation

1. Placement Inversion

To rank players on the all-time scale, we begin by transforming placements into higher values. Lower placement values are considered better, so the formula incorporates a method to convert these placements into values that accurately represent a player's performance.

After the conversion, players who attain 1st, 2nd, and 3rd places will have their converted values look something like 50,000, 40,000, and 30,000, respectively.

The Event-Specific Formula:

The formula below is used to transform a player's placement into a component that will be part of their overall greatness score.

1. Base Transformation:

First, we transform the placement by taking the reciprocal of the player's placement, scaling it by 10, and normalizing it by dividing by 15:

$$\frac{10}{\text{Placement}} \times \frac{1}{15}$$

2. Region Multiplier:

For more details, refer to the Region Multiplier documentation.

Next, we apply the Region Multiplier to adjust the score based on the player's region:

$$\left( \frac{10}{\text{Placement}} \times \frac{1}{15} \right) \times \text{Region Multiplier}$$

3. Seasonal Multiplier:

For more details, refer to the Seasonal Multiplier documentation.

We then incorporate the Seasonal Multiplier, which accounts for changes in competitiveness across different seasons:

$$\begin{aligned} & \left( \frac{10}{\text{Placement}} \times \frac{1}{15} \times \text{Region Multiplier} \right) \\ & \times \text{SEASONAL-MULTIPLIER} \end{aligned}$$

4. Game Mode Multiplier:

For more details, refer to the GameMode Multiplier documentation.

The Game Mode Multiplier is applied next, reflecting the difficulty and competitiveness of the game mode in which the player participated:

$$\begin{aligned} & \left( \frac{10}{\text{Placement}} \times \frac{1}{15} \times \text{Region Multiplier} \right) \\ & \times \text{SEASONAL-MULTIPLIER} \\ & \times \text{GAMEMODE MULTIPLIER} \end{aligned}$$

5. Player Contribution:

For more details, refer to the Player Contribution documentation.

Finally, the Player Contribution factor is included, which adjusts the score based on the individual player's performance.

Full Formula:

Event Score:

$$\begin{aligned} & \left( \frac{10}{\text{Placement}} \times \frac{1}{15} \times \text{Region Multiplier} \right) \\ & \times \text{SEASONAL-MULTIPLIER} \\ & \times \text{GAMEMODE MULTIPLIER} \\ & \times \text{PLAYER CONTRIBUTION} \end{aligned}$$

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2. Summing the Events Together

The greatness score for each event will be summed for all relevant S-Tier events the player participated in. For example, if the player participated in 5 S-Tier events, the summation will be:

$$\begin{array}{l} \text{GreatnessScore\_Event1} + \text{GreatnessScore\_Event2} \\ + \text{GreatnessScore\_Event3} + \text{GreatnessScore\_Event4} \\ + \text{GreatnessScore\_Event5} \end{array}$$

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3. Earnings Incorporation

For more details, refer to the Earnings documentation.

Incorporating earnings into the calculation, the greatness score is now calculated as follows:

$$(\text{GreatnessScore\_Event1} + \text{GreatnessScore\_Event2} \\ + \text{GreatnessScore\_Event3} + \text{GreatnessScore\_Event4} \newline + \text{GreatnessScore\_Event5}) + (\text{Earnings Score})$$

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4. Finally, We Account For Consistency

For more details, refer to the Consistency documentation.

The final greatness score calculation, accounting for all factors, is:

$\text{FINAL GREATNESS SCORE = }$

$$\begin{aligned} & \left( \text{GreatnessScore\_Event1} \right) \\ & + \left( \text{GreatnessScore\_Event2} \right) \\ & + \left( \text{GreatnessScore\_Event3} \right) \\ & + \left( \text{GreatnessScore\_Event4} \right) \\ & + \left( \text{GreatnessScore\_Event5..} \right) \\ & + \left( \text{Earnings Score} \right) \\ & + \left( \text{Consistency Score} \right) \end{aligned}$$