Scores and Sigma Explained

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Scores and Sigma Explained

How a rare item's score and sigma are calculated, and what they mean.

Dec 18, 2021


Categories

General

Date

Dec 18, 2021

Post by

ozzy


Score

A rare item's score is calculated by multiplying each roll by the weight for that mod. The intention is for a "perfect" ring to have a score of 100.

This value is static. It is calculated purely off of the ring itself, and does not take in to account the rest of the rings in the database. It will not change, unless the weights change.

The math is straight forward:
Ideal score = sum of top 6 weights for the specific useCase
Weight for each mod = (roll / max roll) * ModWeight
Total weight for each rare item = sum of weights for each mod
Score = Total weight / ideal score * 100

Sigma

The sigma value represents how many standard deviations above or below the average the score is.

Because this value depends on the average and standard deviation of the total population then it will change as more items are added to the database. If you notice the sigma score changing over time just be patient. As the database grows larger these fluctuations should get smaller and smaller.

For example, if the average score for all rings is 40, and the standard deviation is 10:

Score Sigma
20 -2
30 -1
40 0
50 1
60 2

To calculate the standard deviation we assume a normal distribution.

By M. W. Toews - Own work, based (in concept) on figure by Jeremy Kemp, on 2005-02-09, CC BY 2.5, https://commons.wikimedia.org/w/index.php?curid=1903871

You can use the sigma value to assess how this ring stacks up vs the other rings in the database.

Sigma Better than % of all other items
-2 2.3%
-1 15.9%
0 50%
0.5 69.1%
1 84.1%
1.63 90.3%
2 97.7%
Is this Charsi food?

The color coding on this site is based off of the maximum sigma value from all possible use cases.

Color Charsi message Minimum sigma Better than % of all other items
green Definitely Keep 1.0 84.1%
yellow decent 0.0 50.0%
red Charsi Food! N/A N/A

If the sigma value is near the threshold between two of these states, then you may observe it switch back and forth as more items are added to the database.

When in doubt, use your own discretion and judge the ring based off of the score, which will remain static regardless of how many items are in the database.


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