Estigrade: Grading the Estimate, Not Just the Exam

Abstract

Estigrade is an experimental grading rule: before an exam, a student predicts their own score, and their final grade is adjusted by how accurate that prediction was. The aim is to reward self-knowledge, not just performance. This companion lays out the exact rule, what it does and does not guarantee, and the honest caveats the calculator's calibration and assumptions make explicit.

The rule

Let exam be the actual score, estimate the student's prediction, and gap the absolute difference between them. With a reward factor r and a penalty factor p:

final = exam + r * (100 - gap) - p * gap.

A perfect estimate (gap = 0) earns the full reward r * 100 on top of the exam score; a wild miss earns little reward and a large penalty. The calibration panel checks this against worked examples: a perfect estimate of an 80 with r = 0.1 gives 90, estimating 0 for an 80 gives 66, and with both factors zero the final grade is simply the exam score.

Why reward calibration at all

The pedagogical idea is metacognition: students who can accurately judge what they know study more efficiently and are less prone to over- or under-confidence. Asking for a prediction, and making it count, turns self-assessment into a graded skill. This connects to the broader literature on calibration of confidence, of which proper scoring rules (like the Brier score) are the formal backbone.

That said, the connection is an aspiration, not a result. The calculator implements the rule; it does not show that the rule improves learning. That would take a classroom study.

Two honest problems

The assumptions panel flags two issues worth taking seriously:

  1. The final grade is unbounded. The formula does not clamp to [0, 100]. With a high reward factor and a perfect estimate, a student can score above 100; a high penalty can push a final grade below 0. As stated, the rule needs an explicit cap.

  2. Truthful estimation may not be optimal. A grading rule that rewards accuracy is not automatically incentive-compatible. Depending on the reward and penalty factors and a student's own uncertainty, the score-maximizing prediction can differ from their honest expectation. Proper scoring rules are designed precisely to make honesty optimal; estigrade's linear form is not guaranteed to share that property, and checking when it does is the interesting mechanism-design question lurking underneath.

What the playground is

A transparent calculator for one exam and one estimate, with sliders for the reward and penalty factors. It is a tool for reasoning about the rule's shape and its edge cases, not evidence about its classroom effect. The robust content is the formula and its exact outputs; everything about learning outcomes and incentives is a hypothesis to be tested.

References

  • Literature on metacognition and the calibration of confidence in learning.
  • Proper scoring rules (e.g. the Brier score) as the formal theory of rewarding accurate probabilistic self-assessment.