RiskScoreMeter

Where does this number come from?

This value is a Performance Rating. It's calculated based on your results (wins, losses, draws) and the ratings of your opponents in the selected games. It answers the question: "What Elo rating would a player need to have to achieve these results against this specific pool of opponents?"

For each game, an "expected score" \(E\) is calculated based on the rating difference. The formula is:

Where \(R_o\) is the opponent's rating and \(R_p\) is the performance rating we are looking for. The tool adjusts the value of \(R_p\) until the sum of expected scores from all games (\(\sum E_i\)) equals your actual score.

Is this for cheat detection?

No, this metric is not a direct indicator of cheating. A high performance rating on its own is not proof of foul play. Players can have lucky streaks or be genuinely underrated and improving rapidly.

So, what is it useful for?

It's a tool for measuring recent form and providing context:

• Form Check: It quickly shows if a player is performing significantly above or below their current rating. A 1500-rated player with a 1900 performance over their last 25 games is on a hot streak.
• Context for Other Metrics: A high performance rating, when combined with the "Legitimacy Analysis," can be more informative. For example, a performance rating that is statistically "Extremely Anomalous" is more significant than one that is just high but falls within a normal range of variance.

What is this analysis?

This tool measures how statistically surprising a player's performance is. It compares the score they actually got with the score they should have gotten based on their rating and their opponents' ratings. The key is the Z-Score, which tells us if a result is normal or a statistically rare event.

The Z-Score Formula

The Z-Score measures how many standard deviations a result is from the expected mean. The formula is:

• \(S_{obs}\) (Observed Score): The sum of the points you actually scored (Win=1, Draw=0.5, Loss=0).
• \(S_{exp}\) (Expected Score): The sum of the win/draw probabilities in each game, calculated using the player's actual rating. This is the statistically predicted outcome.
• \(\sigma\) (Standard Deviation): Measures the "amount of luck" or expected variance in the results. It's calculated as the square root of the sum of variances for each game: \(\sigma = \sqrt{\sum E_i(1-E_i)}\). A high \(\sigma\) means results are very variable, and it's easier to have long streaks (good or bad).

The Bell Curve Graph

The graph shows the probability of all possible outcomes. The center ('0') represents the expected performance. The marker shows where the player's actual performance landed. If the marker is in the big central hump, the performance was normal. If it's far out in the tails, it was a statistically rare event.