Mathematical & Empirical Foundations
A quantitative behavioral testing engine mapping Keirsey Temperaments, Myers-Briggs (MBTI) archetypes, and Prospect Theory via World Athletics (IAAF) scoring formulas.
1. Theoretical Foundations & Prospect Theory
Unlike traditional Likert-scale self-reports prone to reference-group bias, our engine uses empirical wagering choices under real athletic physics constraints. Decisions reflect subjects' true loss aversion, expected value calculations, and decision weight.
Prioritizes risk mitigation, process discipline, and zero-foul baseline guarantees.
Thrives on atmospheric momentum, high-ceiling payoffs, and aggressive leverage.
Calculates mathematical expected value (EV) exploiting scoring formula non-linearities.
Values athletic determination, emotional momentum, and inspirational comeback arcs.
2. Decision Weighting & Scoring Equations
Wager Weighting Equation
Temperament Aggregation Formula
Risk & Behavioral Vector Calculations
3. Official IAAF Decathlon Scoring Equations
World Athletics calculates decathlon points using three canonical non-linear power-law formulas where P = floor(a * (X - b)^c) or P = floor(a * (b - T)^c):
| Discipline | Formula Type | a | b | c | Benchmark Mark | IAAF Points |
|---|---|---|---|---|---|---|
| 100m Sprint | Track: a*(b-T)^c | 25.4347 | 18.00 | 1.81 | 10.78s | 910 pts |
| Long Jump | Jump: a*(D-b)^c | 0.14354 | 220.00 | 1.40 | 710cm | 837 pts |
| Shot Put | Throw: a*(D-b)^c | 51.3900 | 1.50 | 1.05 | 15.20m | 802 pts |
| High Jump | Jump: a*(D-b)^c | 0.84650 | 75.00 | 1.42 | 208cm | 878 pts |
| 400m Sprint | Track: a*(b-T)^c | 1.53775 | 82.00 | 1.81 | 48.40s | 889 pts |
| 110m Hurdles | Track: a*(b-T)^c | 5.74750 | 28.50 | 1.92 | 14.50s | 911 pts |
| Discus Throw | Throw: a*(D-b)^c | 12.9100 | 4.00 | 1.10 | 46.50m | 798 pts |
| Pole Vault | Jump: a*(D-b)^c | 0.27970 | 100.00 | 1.35 | 500cm | 910 pts |
| Javelin Throw | Throw: a*(D-b)^c | 10.1400 | 7.00 | 1.08 | 64.00m | 798 pts |
| 1500m Run | Track: a*(b-T)^c | 0.03768 | 480.00 | 1.85 | 4:28.00 | 758 pts |
4. Response Timing & Deliberation Speed Analytics
The system records precise monotonic milliseconds for each question to compute total test duration, average deliberation speed per scenario, decision speed profiles (Instant & Intuitive, Balanced Deliberator, Deep Analytical Evaluator), and pacing drift (Accelerating, Decelerating, or Steady).
5. Dual-Championship Cross-Season Validation Framework
To verify whether decision patterns reflect true psychographic principles or transient reactions, the test evaluates 10 event dilemmas across two contexts: Scenarios 1–10 (Summer Outdoor World Championship) paired with Scenarios 11–20 (Winter Indoor Grand Prix). Matching choices yield a 0–100% Consistency Index and timing-consistency cross-insights.