# Sticker stats

{% hint style="info" %}
All the numbers below are subject to change depending on the game balance and player feedback.
{% endhint %}

Our target is to give the following power increase per sticker:

* 4% as a base power increase to the Pookyball for a Level 0 Common Sticker
* Increased by a 1.25% multiplier to the base number per level
* Max level of a given rarity has the same boost of Level 0 of the next rarity 

| Rarity & level    | Average power increase |
| ----------------- | ---------------------- |
| Common, lvl0      | +4%                    |
| Common, lvl40     | +6%                    |
| Rare, lvl0        | +6%                    |
| Rare, lvl60       | +9%                    |
| Epic, lvl0        | +9%                    |
| Epic, lvl80       | +13%                   |
| Legendary, lvl0   | +13%                   |
| Legendary, lvl100 | +18%                   |

* To achieve this, we have looked at the probabilities of given events happening (for random stickers) or have looked at how often you can deterministically benefit from the sticker
  * *Example 1 : a Club sticker benefits in 1 match out of a matchday of 10 matches. As such, it has a deterministic rate of 10%.*
  * *Example 2 : a sticker giving extra points if the score ends up being 1-1 has a 11% probability of activating*
* However, variance is quite powerful in Pooky. As such, we’ve applied a variance correction formula to the points given. We calculate it by putting the event probability rate at the power (-0.5).
  * $$(VCF) VarianceCorrectionFactor = 0.5$$
  * $$point.multiplier = probability ^{-VCF}$$
  * *Example : a sticker with a 10% probability will have a variance-corrected factor of (10% ^ (-1/2) = 3,16. For a level 0 common, it means it would grant 4% \* 3,16 = 12,65% extra points when it activates.*
* The point multiplier has a maximum, currently set at 6. This means any event with less than 2.78% chance of happening will offer the same point boost, regardless of the final probability.

{% hint style="info" %}
All of the below can be adjusted for balance purposes and depending on how the football games change with time:

* the VCF 
* the point multiplier maximum
* the underlying probabilities 
  {% endhint %}

## Prediction point computation <a href="#balancing" id="balancing"></a>

Prediction point =&#x20;

* sum of:   Base Points multiplied by their respective attributes (from both Pookyball and Attribute Stickers);
* multiplied by:    (1 + Sum of Pookyball Boosts)
* multiplied by:    (1 + Sum of Sticker Boosts)
* multiplied by:    (Pressure Factor)

## How are the stickers balanced when they don't award exactly linear, probability-based points? <a href="#balancing" id="balancing"></a>

Pooky is a game where 5% extra points can mean a lot of places in the leaderboards.

Our reward distribution is exponential, meaning that ranking 1st + Last is much better than ranking in the middle twice.

In order to take this into account, we’re giving less points to stickers that have a high variance - because when this high variance happens, you get exponentially more rewards through that matchday. As Pooky looks to reward skill, we have implemented a formula that puts the probability of a given event at a negative power, between 0 and 1.

For instance, with a 0.5 VCF, an event that has 10% of happening, will give 3.1x more points than an event that has 100% of occurring - because a lucky amount of occurrences can boost you significantly. Without this factor, just 2 of the 10% occurrences would amount to 2x the boost of the “guaranteed” sticker… and getting 2/10 correct at 10% probability is 19.3% proba, 3/10 is still 5.7%!

We will heavily monitor the factors, notably the VCF, to ensure that all stickers have a close power level when used optimally..&#x20;

## Detailed sticker stats

*For simplicity, this spreadsheet contains the latest data about stickers. It will be updated on a regular basis up until the release of Stickers.*

<https://docs.google.com/spreadsheets/d/1rPkh9vei0ZPkr8CPC72I0GUw-gSaJV2QUAu0QuptinE/edit#gid=1641744608>


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