How We Calculate

Example: How your skill score is calculated

You solved Puzzle X in 45 min, 3 months ago.

Out of 50 first-attempt solvers, 38 were slower — your percentile = 0.78

Puzzle X is Challenging (difficulty 1.18) — difficulty weight = 1.09

Weighted percentile: 0.78 × 1.09 = 0.85

Solve is 3 months old (within plateau) — age weight = 1.00

Your skill score = weighted median of all such entries, where recent solves have more influence.

Skill recency weighting

Your skill tier reflects your current ability. Recent puzzles have more influence than old ones via a gentle time decay with a 6-month plateau.

Rating recency weighting

Portfolio entries are gently decayed by age so recent results matter more, while older strong results still count. A 3-month plateau keeps very recent results at full value.

Example: Cold Solver vs Grinder

Same Hard puzzle (difficulty 1.35, weight 1.175), solved last month (decay = 1.0):

Player A wins decisively — raw cold-solving talent leads, but B gets partial credit for improvement.

Anti-gaming properties

• Grinding same puzzle: Only affects one best-time entry (25% weight). First-attempt score is locked.
• Volume accumulation: Cap of 100. After 100 puzzles, more solves only help if better than your weakest entry.
• Easy puzzle farming: Difficulty weighting makes hard puzzles worth more at the same percentile.
• Inactivity: Time decay gradually reduces older results. Stay active to maintain your rating.

Improvement ratios

We compute improvement ratios — how much faster players typically get between consecutive attempts (1st→2nd, 2nd→3rd, etc.). These are computed from real data across all players and puzzles, stratified by the time gap between attempts.

ratio(N→N+1) = median(time_attempt_N+1 / time_attempt_N)

Sources (priority order):
  1. Your personal ratio (from all your repeat solves)
  2. Global ratio (from all players, per piece count)
  3. Default: 0.90

Gap correction: your personal ratio is adjusted
by global gap-bucket data to account for memory fading.

Time gap between attempts affects how much you remember. Ratios are bucketed by gap duration:

Personal prediction (1+ prior solves)

When you've solved the puzzle before, we predict your next time using improvement ratios blended with Holt's damped trend smoothing. With fewer prior solves, the improvement ratio dominates. With more history, Holt's trend takes over.

ratio_prediction = last_time × improvement_ratio(N→N+1, gap)

Blending with Holt's damped trend (α=0.5, β=0.4, φ=0.8):
  N = 1:   100% ratio prediction
  N = 2-5: blend (Holt's weight = (N-1)/5)
  N ≥ 6:   100% Holt's damped trend

Floor: max(predicted, best_time × 0.70)

The blending ensures smooth transitions: with few data points, cross-puzzle improvement patterns guide the prediction. As puzzle-specific history grows, the trend model takes over.

Statistical prediction (first-time puzzle)

When you haven't solved this puzzle before, we combine your baseline with the puzzle's difficulty:

Your 500pc baseline: 55 min

Puzzle difficulty: 1.15 (Challenging)

Predicted time: 55 × 1.15 = ~63 min

Range uses P25–P75 of the puzzle's difficulty indices: baseline × P25 to baseline × P75. Safety bounds keep the range between 30% and 300% of the predicted time.