Activity Leaderboard

🜂 Activity Leaderboard

The Ometeotl Activity Leaderboard distributes 1000 activity-shares among contributors based on their recent, weighted activity. It rewards sustained, high-quality contributions while ensuring every contributor — even occasional ones — receives recognition.

The founder is excluded from share allocation and displayed out-of-competition.

View current standings →

How It Works

The leaderboard pipeline runs in four stages:

Raw Score  →  z-score  →  Adjusted Score  →  Activity-Shares

Stage 1 — Raw Activity Score

Every contribution is weighted and decayed over time:

S(u) = Σ  weight(event) × recency(age)

Event	Weight	Rationale
Merged PR	10	Core contribution — reviewed and integrated
Commit in merged PR	3	Rewards granular, iterative work
PR review	4	Code review is high-value mentorship
Issue opened	2	Surfaces bugs and proposes features
Comment (issue/PR)	1	Encourages community discussion
Lines changed	0.01/line	Minor volume bonus (capped at 200 lines/PR)

Recency decay uses an exponential half-life of 90 days:

r(t) = 2^(−t / 90)

A contribution keeps 50% of its value after 3 months, 25% after 6 months, and ~6% after a year. It never reaches zero.

Recency Decay

Stage 2 — z-score Normalization

Raw scores are standardized across all contributors (founder included):

z(u) = (S(u) − mean) / std_dev

This removes scale dependence: z = 0 always means “average contributor.”

Stage 3 — Adjusted Score

The standardized score is transformed through a non-linear function designed to:

Anchor the average contributor at a predictable value (f(0) = 1 always)
Generously reward exceptional contributors (super-exponential growth)
Symbolically recognize occasional contributors (approaches 0 but never reaches it)

f(z) = exp(sinh(z) / k)

Adjusted Score Function

The key mathematical properties of this function:

f(0) = 1 for all k — the average contributor has a fixed, predictable score
Super-exponential growth for z > 0 — top contributors are rewarded aggressively
Approaches 0 for z < 0 but never reaches it — no one gets zero shares
Monotonically increasing — more activity always means a higher score
Single parameter k controls the entire distribution shape

Stage 4 — Adaptive Smoothing (k)

The smoothing factor k adapts to community size:

k = max(3, 12 − n_active)

Where n_active = number of contributors with activity in the last 180 days.

Adaptive k

Phase	n_active	k range	Effect
Protective	1–8	11 → 4	Smooth distribution — prevents one person from dominating a small pool
Mature	9+	3 (floor)	Full differentiation — exceptional contributors are generously rewarded

This means the leaderboard automatically becomes more competitive as the community grows.

Activity-shares are proportional to adjusted scores (founder excluded), totaling 1000:

shares(u) = (f(z(u)) / Σ f(z(uᵢ))) × 1000

Share Allocation

Example

With 9 active contributors and k = 3:

Rank	z-score	Shares	Profile
1	+2.50	433	Star contributor — generously rewarded
2	+1.94	179	Strong contributor
3	+1.38	107	Above average
5	+0.25	63	Average — stable, predictable share
7	−0.88	41	Below average — still meaningful
9	−2.00	17	Occasional — symbolic but non-zero

Relationship with the Rank System

The leaderboard is complementary to the rank system (Path of the Serpent):

	Rank System	Activity Leaderboard
Nature	Lifetime milestone	Dynamic snapshot
Based on	Total merged PRs	Weighted, recency-adjusted activity
Direction	Only goes up	Fluctuates with activity
Purpose	Status and identity	Incentive and recognition

You can be a high-ranking Otomi with few current shares (if inactive recently), or a new Eagle Warrior with a strong share from a single impactful PR.

Transparency

All parameters are in leaderboard/config.json — version-controlled and auditable
Raw data is exported to leaderboard/leaderboard-data.json after each computation
The formula is public and deterministic: anyone can reproduce the results
Full mathematical specification: LEADERBOARD_SPEC.md

Current Standings