- Overview
- Reward Pool
- Points Calculation
- Penalty for Losing
- Losing Points
- Stake “At Risk”
- Point Conversion to $NRN Reward

### Overview

In this section we discuss the methodology of how $NRN rewards are distributed to the **Gamers** via the **Ranked Battle** competition.

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**There are 3 main drivers that determine the amount of $NRN rewarded: **

1️⃣ Your NFT’s performance in the current **Round** of competition.

2️⃣ The amount of $NRN staked on your NFT throughout this Round of competition.

3️⃣ Your NFT’s current **Elo**.

### Reward Pool

A **Reward Pool** of $NRN will be distributed at the end of each Round of the Ranked Battle competition. The size of the Reward Pool is determined by ArenaX Labs on a discretionary basis.

The $NRN reward received by an individual NFT is based on the three drivers mentioned above. Each NFT accumulates **Points**, which are claims on the Reward Pool, during a Round. The Points are settled for $NRN from the Reward Pool at the end of each Round. The Reward Pool will be divided proportionally amongst all NFTs with positive Point totals at the end of each Round.

To keep terms consistent, we will use **“Challenger”** and **“Opponent”** to denote the NFTs **instigating** and **being matched** for Ranked Battles, respectively.

It is important to note that only the Challenger NFT accrues Points during a match. For the Opponent NFT, the outcome does not impact their Point total. However, it does impact their Elo score¹.

Also, a player may stake as many $NRNs on their Challenger NFT at the beginning of a Round. They can also increase their stake during a Round. However, if they choose to reduce their stake during a Round they are no longer able to increase stake until the following Round. This is to prevent people from gaming the staking system by selectively reducing stake before ranked matches.

### Points Calculation

Points for the Challenger NFT are calculated based on the following formula:

**Points = Battle Results * Staking Factor * Elo**

➡️ **Battle Result** is either 0 for a loss or tie, and 1 for a win.

➡️ **Staking Factor** is a number representing the amount of $NRN a player has staked behind their Challenger NFT for the Round. The more $NRN a player stakes, the more Points their Challenger NFT can accumulate. The Staking Factor is the most important driver out of the three. If a player does not stake $NRNs, their NFT will not accrue Points or $NRN rewards (i.e Staking Factor would be 0 and the product of the equation is 0). The Staking Factor is a quadratic derivative of the actual stake. This means that the relationship between the stake and potential Points which an NFT can earn is non-linear. The impact of the marginal $NRN staked decreases as more $NRN is staked (i.e. the 1,000th $NRN staked will be less impactful than the first $NRN staked)².

➡️ **Elo** is the Elo score of each Challenger NFT and represents its skill level relative to other NFTs. Elo score has a mean of 1500. The higher the Elo score, the more Points will be awarded to the Challenger NFT should they win a match. Rewarding for Elo directly rewards for player skill, as higher-skilled players will have higher Elo NFTs.

### Penalty for Losing

Ranked Battle is a competitive arena. To ensure the proper incentives, there are risks involved for losing matches. Points gained during a round are not considered safe until the round is over. The penalty for losing matches:

1️⃣ Loss of points accumulated in the current Round, and;

2️⃣ A potential loss of stake.

**Losing Points **

If a Challenger NFT has positive Points in the current Round, the penalty for losing a match, in addition to dropping in Elo rank, is a loss of Points. We note that a Challenger NFT cannot have negative Points. When a Challenger NFT reaches 0 Points, further losses will result in their stake being placed in a new mode called “at risk”.

### Stake “At Risk”

When a Challenger NFT loses, and has 0 Points in the current Round, a small portion of their stake (not Points) is placed** ****“**** at risk”.** At the end of each Round, the

*at risk*stake is lost permanently. Furthermore, a Challenger NFT cannot earn $NRN rewards if they have any stake

*at risk*. Challenger NFTs can regain their

*at risk*stake by winning matches before the end of the Round.

**Example: **

A player stakes 1,000 $NRN on their Challenger NFT and has 0 Points in the current period. Assume that the penalty for a loss is 0.1% (10bps) of the stake.

The Challenger NFT loses a match and the penalty is 1,000 * 0.1% = 1 $NRN.

The Challenger NFT loses another match, and the penalty is again 1,000 * 0.1% = 1 $NRN.

There are now 2 $NRNs *at risk** *for the Challenger NFT.

**Consider the following scenarios:**

**Scenario 1: **If the Challenger NFT stops playing in the current Round, the 2 $NRNs *at risk* are lost permanently. The player will have 998 $NRNs staked on the Challenger NFT for the following round.

**Scenario 2:** If the Challenger NFT wins the following match, they will regain 1,000 * 0.1% = 1 $NRN. If it stops playing thereafter, at the end of the Round, only 1 $NRN will be lost permanently.

**Scenario 3:** If the Challenger NFT wins the two following matches, they will regain 2 $NRN. It would be out of the *at risk* state, and any additional matches they win will accumulate Points claimable in the Reward Pool.

We note that, as long as the original stake does not change, the amount being put at risk every time when the fighter loses will be the same. We also note that in Scenarios 2 and 3, the fighter regained *at risk* stake but did not gain any reward Points for winning because they need to climb out of the deficit first.

### Point Conversion to $NRN Reward

Points are settled for $NRN from the Reward Pool at the end of each Round. The Reward Pool will be divided proportionally amongst all Challenger NFTs with positive Point totals at the end of each Round. See example below.

**Assumptions:**

➡️ Reward Pool: 1,000 $NRN

➡️ Total Points Accumulated by All Challenger NFTs within a Round: 100 Points

➡️ Points Accumulated by Challenger NFT: 10 Points

**$NRN Reward:**

🪙 Challenger NFT would receive $(\frac{10}{100})$ *1,000 = 100 $NRN at the end of the current ranked period.

Notes:

- Elo impact prevents stale models in the Arena. This helps to keep the Ranked Battle competitive.
- Quadratic staking is implemented to prevent whales from crowding out the Reward Pool. This creates a more level playing field for beginners and intermediate players in the game, who tend to have lower $NRN balances to stake.