How ratings work
Every topic has ratings that move as you practise. This is how to read them.
What a rating is
Each topic gives you three ratings, one for each question format. They move independently, so a strong Drill number does nothing for your Exam 2 number.
Fast recall and procedural fluency. Single-step problems.
Exam-style questions worked by hand. No calculator assistance.
Exam-style questions with the CAS calculator available.
Every rating starts at 1500.
Rating tiers
Each rating gets a label from its number.
What the ? means
Behind each rating is a second number, the rating deviation. It measures how sure the system is about where you sit. The ? shows while that deviation is still large.
Every marked attempt in a format shrinks its deviation. Once it drops under the cutoff, the ? goes away for that format.
How one question moves it
Every marked question is a rated opponent. Questions carry their own rating, and yours moves depending on how you did against what the system expected.
A well-rated question at your level is close to a coin flip. Do better than expected and your rating rises. Do worse and it drops.
Partial marks count as a partial result, but the scale is tilted. On a question at your level you need most of the marks to break even, so dropping a few still costs you.
Bigger surprises move the number more. A large deviation moves it more too, and as your deviation shrinks each result moves it less.
Topic and subject averages
Your three format ratings average into a topic rating, and your topics average into a subject rating.
The Glicko-2 system
Axiom uses Glicko-2, Mark Glickman's rating system. Each rating is three numbers: the rating \( r \), the rating deviation \( RD \) and the volatility \( \sigma \). The tier table and the ? are built on the first two.
After a rated result against a question \( j \), the update runs on an internal scale:
\( g \) discounts an opponent whose own rating is uncertain, and \( E \) is the expected score:
\( v \) is the estimated variance of your rating from this result and \( \Delta \) the estimated improvement, with \( s_j \) the score:
The new volatility is \( \sigma' = e^{A/2} \), where \( A \) is the root of \( f(x) = 0 \), found with the Illinois iteration in the paper. \( \tau \) sets how quickly volatility is allowed to change.
Then the deviation and the rating update:
and convert back:
The deviation is how sure the system is. It starts wide, narrows with each result, and is widened a little by volatility before every update so it never locks solid.
Volatility is how erratic your results have been. A run of surprises pushes it up, which lets a student who is improving move faster than one whose results are steady.