Initial Calculations
- We calculate the total prize pool by taking 70% of all entry fees.
- We calculate each player's individual share by dividing the total pool equally.
- We calculate the median score (cutoff score) by finding the score of the player at the midpoint of the leaderboard.
The cutoff score is a key input for calculating bonus rewards.
Total Pool
7000
coinsIndividual Share
70
coinsTier Rewards
After establishing the base values, we calculate coin rewards for each tier.
| Tier | Multiplier |
|---|---|
| Top 1% | 15× |
| Top 5% | 10× |
| Top 10% | 8× |
| Top 20% | 5× |
| Top 30% | 3× |
| Top 50% | 1× |
Each player in the top 50% gets at least a minimum prize. To find this prize, we multiply their individual share by their tier's multiplier shown above.
If scores are tied at the 50% mark, more than 50% of players may receive a prize.
Exceptionally high scores may receive a bonus reward instead, see next section for how this works.
Bonus Rewards
In some cases where a player scores significantly higher than others and there are just a few players above their score, we calculate a bonus reward for them.
If this bonus amount is higher than their normal tier award, we award the bonus instead.
In most cases, players will receive their normal tier-based rewards.
We take the higher of the two prize amounts for each player.
Then
we scale all prizes down to make sure they add up to the total
prize pool.
This process is explained further in the
next section.
Tier Prize
700
coinsBonus Prize
426
coinsAdjustment Process
The initial prizes add up to more than what's available in the prize pool. This happens for two reasons:
First, when we multiply the individual share by 15x, 10x, 8x etc. in the tier awards, these multipliers naturally add up to more than 100%.
Second, some players may receive higher amounts than their normal tier award due to bonus rewards. This makes the total even larger than what we have available.
To fix this, we reduce everyone's prize by the same percentage so the total matches what's available in the pool.
We apply this adjustment to each player's higher prize amount, whether it came from normal tier awards, or from bonus rewards.
After we calculate all prizes, some coins are usually left over because we round the numbers.
The next section explains what happens to these leftover coins.
Remaining Coin Distribution
If there are any coins left over, we distribute them in two steps.
In step one, we split the leftover coins between tiers based on how much weight each tier has, as shown in the table below.
| Tier | Weight |
|---|---|
| Top 1% | 32× |
| Top 5% | 16× |
| Top 10% | 8× |
| Top 20% | 4× |
| Top 30% | 2× |
| Top 50% | 1× |
If there are still coins left after sharing them by weight, we do a second round.
In this round, we give out the remaining coins one by one. We start with players in the highest tier and work our way down until all coins are given out.
Edge Cases
Tied Scores
- Players with tied scores must receive equal prizes
- All players tied at cutoff score are included in prize pool
- This may result in slightly more than 50% of players receiving prizes
Tied scores in remaining coins second pass
- If there aren't enough coins to give +1 to all tied players, that group is skipped
- The algorithm continues to the next group of players
- This ensures tied players always receive equal prizes
Minimum Player Count
- All Quizzes require at least 2 players
- When only one player is present, no prizes are awarded. The player is refunded their entry fee.
Very Small Prize Pools
- Any decimal amounts are rounded down to whole coins
- Players must receive at least 1 coin as a prize
- Top players still get more coins even in small prize pools