# Sticker stats
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All the numbers below are subject to change depending on the game balance and player feedback.
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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.
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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
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## Prediction point computation
Prediction point =
* 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?
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..
## 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.*