Point Strategies
In a leaderboard with multiple houses (e.g., 4 houses), each house has a different number of students. Choosing the right scoring strategy is essential to ensure fair and motivating competition. Here are three scoring strategies, their formulas, and the pros and cons of each.
Variables Used in the Formulas
N
Definition: Total number of students across all houses.
Example: If there are 4 houses with 10, 15, 12, and 8 students respectively, then:
N = 10 + 15 + 12 + 8 = 45
H
Definition: Total number of houses.
Example: If there are 4 houses, then: H= 4
𝑆 𝑖
Definition: The number of students in house iii.
Example: If house 1 has 10 students, then: S1=10S_1 = 10S1=10
P i
Definition: Points awarded to house iii.
Example: If house 1 has earned a total of 150 points, then: P1=150P_1 = 150P1=150
1. Total Points (Default)
Formula:
Description: The total points for each house are calculated by simply summing all points awarded to that house.
Positives
Easy to understand and straightforward: This method is simple, as it only counts the total points accumulated by each house.
Rewards high participation: Houses with more active members or more opportunities to earn points will naturally score higher.
Negatives
Size bias: Larger houses (with more students) may have a higher total points score since they have more participants who can earn points.
Unfair to smaller houses: Smaller houses may be at a disadvantage since they have fewer students to contribute to the total points.
Best For
Scenarios where the number of students in each house is roughly equal.
When you want to reward absolute performance without adjusting for house size.
2. Average Points
Formula:
Where:
𝑆 𝑖 is the number of students in house iii
Description: The average points for each house are calculated by dividing the total points by the number of students in that house. This gives a per-student average score.
Positives
Balances size: This method removes the bias of larger houses by calculating points per student.
Fairer for smaller houses: Small houses are not disadvantaged because points are averaged based on their size.
Negatives
Doesn't reward high participation: A house with fewer points might still rank high if it has few members, as it's based on per-student averages rather than total contributions.
May discourage competition: Houses might feel less motivated to increase their total points if they can achieve a high rank by simply having a smaller number of students perform well.
Best For
Scenarios where fairness across different house sizes is crucial.
When the goal is to measure the average contribution per student, rather than total contribution.
3. Normalized Points
Formula:
Calculate the Average Number of Students per House:
Calculate Normalized Points for each house:
Description: This method scales each house’s points by comparing the average number of students per house to the actual number of students in the house. It adjusts each house’s points based on the size of the house, giving smaller houses proportionally higher points to compensate for their size.
Positives
Balances large and small houses: By normalizing points, smaller houses receive a score boost, which levels the playing field across houses of different sizes.
Encourages participation while ensuring fairness: Even though houses can earn more points through participation, normalization ensures that smaller houses are not left behind due to fewer members.
Negatives
Complexity: The calculation is more complex and might be harder to understand for participants compared to total or average points.
May not fully balance extremes: If there’s a very large difference in house sizes, this method may not completely level the field, as very large or very small houses could still have advantages.
Best For
Scenarios where houses vary significantly in size.
When the goal is to maintain fairness while still rewarding active participation.
Summary Table
Total Points
Simple and rewards participation.
Biased towards larger houses.
Use when house sizes are equal, or you want to reward absolute performance.
Average Points
Fair for smaller houses, balances size.
May discourage competition; not based on total effort.
Use when fairness by size is key, and you want to focus on per-student averages.
Normalized Points
Balances large and small houses while rewarding participation.
More complex to understand; may not fully balance extremes.
Use when house sizes vary and fairness + participation are both goals.
Choosing the Right Strategy
If house sizes are similar: Use Total Points for simplicity.
If fairness across house sizes is a priority: Use Average Points to ensure smaller houses aren’t disadvantaged.
If houses differ significantly in size: Use Normalized Points for both fairness and participation incentives.
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