What does my rating mean?

Your rating is an estimate on your skill level, relative to all other users on the platform.

How is the rating calculated?

Your base rating is 1500.

For each rated contest you participated in, a rating delta is calculated which depends on your relative performance among all contestants.

Your rating is calculated by applying all the deltas obtained from all rated contests you participated in (capped above 1500)

We use a modified version of Elo adapted to multiplayer games. The effect we want to achieve:

• Slightly more than half of contestants will have a positive delta, the rest will have a non-positive delta.
• Delta depends on your and also your opponents' skill level, as illustrated below:
• Let A be a strong contestant. If A beats many weak contestants, A gets a smaller delta. If A beats many strong contestants, A gets a larger delta.
• Let B and C both be strong contestants. B has played many contests and has a high rating, while C is new and has rating = 1500. Since C has a lower rating before the contest, C will have a greater delta than B given that they score the same marks.

The specific algorithm used to compute the rating delta for a contest is described below.

For each participant $i$: $R_i$: Initial snapshot rating prior to the contest. $S_i$: Score achieved in the current contest ($0 \le S_i \le 1$). $c_i$: Number of prior scored contests played by user $i$. $K_i$: Weight factor controlling rating sensitivity. $K_i$ is derived using a piecewise step function based on contest history $c_i$: $$K_i = \begin{cases} 40 & \text{if } c_i < 10 \quad \text{(Provisional stage)} \\ 28 & \text{if } 10 \le c_i < 30 \quad \text{(Intermediate stage)} \\ 18 & \text{if } c_i \ge 30 \quad \text{(Established stage)} \end{cases}$$ For every ordered pair of participants $(i, j)$ where $j \neq i$, two metrics are produced: (1) Expected Score ($E_{ij}$): Based on the logistic distribution scaled down by $0.85$: $$E_{ij} = \frac{0.85}{1 + 10^{\frac{R_j - R_i}{400}}}$$ (*) It should be noted that instead of a zero-sum system like traditional elo, we scale the expected score by a factor of $0.85$ to encourage player participation (a positive-sum system) (2) Actual Score ($A_{ij}$): Normalized linear score comparison (spectrum: 1 for self win, 0 for opponent win) $$A_{ij} = 0.5 + \frac{S_i - S_j}{2}$$ The raw rating shift $\Delta R_i^{\text{raw}}$ sums performance differentials across all $N - 1$ opponents, scaled by $1 / \sqrt{N - 1}$: $$\Delta R_i^{\text{raw}} = \frac{K_i}{\sqrt{N - 1}} \sum_{j \neq i} \left( A_{ij} - E_{ij} \right)$$ (*) The standard choice for the dampening factor is $\dfrac{1}{N-1}$, but we use $\dfrac{1}{\sqrt{N - 1}}$ instead to introduce higher rating mobility. To protect system stability, constraints are applied: (1) Delta Clamping: Limits total raw change to the interval $[-200, 300]$: $$\Delta R_i^{\text{clamped}} = \max\left(-200, \min\left(300, \Delta R_i^{\text{raw}}\right)\right)$$ (2) The rating is capped above the base rating $1500$: $$R_i' = \max\left(1500, R_i + \Delta R_i^{\text{clamped}}\right)$$ Finally, the effective delta ($\delta_i$) is calculated and displayed: $$\delta_i = R_i' - R_i$$