Three ways to measure your cognitive performance
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Adaptive Cognitive Efficiency - Version 1
This algorithm distinguishes between "Processing Power" (Difficulty) and "Processing Efficiency" (Time/Stability). Unlike standard tests, accuracy is a binary gate, not the score itself. You only accrue points if you are accurate; the amount of points is determined by how efficiently you arrived at the truth.
Time-Decayed Exponential Model
This formula prevents the "infinity score" glitch while aggressively rewarding speed and stability.
| Variable | Name | Type | Definition |
|---|---|---|---|
| Ai | Accuracy Vector | Binary | 0 if incorrect/skipped, 1 if correct |
| Di | Difficulty | Integer | The complexity rating of the specific question (1-5) |
| Ti | Actual Time | Float (ms) | Time elapsed from question render to final submission |
| Ttarget | Target Time | Float (ms) | The "Elite Benchmark" - time a top 1% performer takes at this difficulty |
| Ci | Change Count | Integer | Number of times the answer selection was toggled before submission |
The "Knobs" that control the algorithm
| Constant | Value | Description |
|---|---|---|
| λ (Lambda) | 0.7 | The Decay Factor. A higher value makes the score drop off faster as time passes. λ = 0.7 ensures that meeting Ttarget exactly retains ~50% of max potential points. |
| α (Alpha) | 0.05 | The Uncertainty Penalty. The percentage of score lost per answer toggle (5%). |
Difficulty is raised to the power of 1.5 rather than kept linear. Solving a Difficulty 10 problem is exponentially more valuable than a Difficulty 1 problem. This prevents gaming the system by answering easy questions quickly.
As Ti increases, the multiplier approaches 0, but never becomes negative. If you answer faster than the target time, the exponent becomes smaller, pushing the multiplier closer to 1 (Maximum Efficiency).
Penalizes "guessing" or "fidgeting." Each answer change removes 5% of the raw score. The max() function ensures that even 20+ toggles still allows 50% of points if you eventually get it right.
How the algorithm determines which question is served next
The adaptive engine looks at the Performance Ratio (P) = Ti / Ttarget, not the Score itself.
| Condition | Logic | Next Question | Interpretation |
|---|---|---|---|
| Ai = 0 | Incorrect | Difficulty -1 | User hit failure point. Reduce load. |
| P < 0.5 | "Super Speed" | Difficulty +2 | User is bored/overqualified. Aggressive jump. |
| 0.5 ≤ P ≤ 1.0 | "In Flow" | Difficulty +1 | User is performing optimally. Standard progression. |
| P > 1.0 | "Struggling" | Difficulty +0 | User got it right, but too slowly. Do not increase difficulty. |
In an efficiency test, skipping is a strategic resource.
Si = 0(No points awarded)Difficulty +0(No change)The Total "Elite Quotient" is not just the sum. It is the sum normalized by the highest difficulty reached.
This normalization ensures that reaching higher difficulties is rewarded, even if you don't answer as many questions. A user who answers 10 questions at Difficulty 8-10 will score higher than someone who answers 50 questions at Difficulty 1-3.
What the system needs to make ACE work
Every question must contain a validated Ttarget (Target Time) based on empirical data from top performers at each difficulty level.
Capture onclick events for Change Count (Ci) and precise timestamps for Actual Time (Ti).
The scoring function must be computed server-side immediately after each question submission to determine the next difficulty level.
The ACE Algorithm is designed to measure cognitive efficiency, not just knowledge. It rewards quick, confident, accurate problem-solving at increasing levels of complexity.