Constants and Calibration Rationale

Core Library Reference

This page documents the calculation constants in the @opprs/core library. If you're using the REST API, these constants are applied automatically. This reference is for developers who want to understand the mathematical foundation or customize the calculations.

This section explains why each constant in the system has its current value. The constants are carefully calibrated to create a balanced, mathematically sound ranking system.

Design Philosophy

Most constants are chosen to:

1. Cap maximum contributions at specific thresholds
2. Create mathematical relationships between different components
3. Follow established rating systems (like Glicko)
4. Reflect real-world competitive difficulty

Many constants are interdependent - changing one often requires adjusting others to maintain system balance.

Base Value Constants

Constant	Value	Rationale
POINTS_PER_PLAYER	0.5	Chosen so 64 rated players yields exactly 32 points (0.5 × 64 = 32)
MAX_BASE_VALUE	32	Reasonable cap for tournament base value
MAX_PLAYER_COUNT	64	Player count where max is reached (32 ÷ 0.5 = 64)
RATED_PLAYER_THRESHOLD	5	Five events provides sufficient history to be "rated"

Key Insight: The 0.5 coefficient creates perfect linear scaling where the cap is reached at a reasonable tournament size.

Tournament Value Adjustment (TVA) Constants

Rating-based TVA

Constant	Value	Rationale
MAX_VALUE	25	Ensures rating TVA contributes 1/3 of the 75-point total TVA cap
COEFFICIENT	0.000546875	Reverse-engineered so 64 players rated 2000 contribute exactly 25 points
OFFSET	0.703125	Paired with coefficient: (2000 × 0.000546875) - 0.703125 ≈ 0.39 per player
PERFECT_RATING	2000	Reference rating for "perfect" player
MIN_EFFECTIVE_RATING	1285.71	Where formula crosses zero: (1285.71 × 0.000546875) - 0.703125 ≈ 0

Formula: (rating * 0.000546875) - 0.703125

The coefficients ensure 64 perfect players contribute exactly 25 points: 64 × 0.39 ≈ 25 ✓

Ranking-based TVA

Constant	Value	Rationale
MAX_VALUE	50	Largest component of TVA (2/3 of 75-point cap)
COEFFICIENT	-0.211675054	Calibrated so top 64 ranked players sum to exactly 50 points
OFFSET	1.459827968	Creates logarithmic decay favoring top-ranked players

Formula: ln(ranking) * -0.211675054 + 1.459827968

• Rank #1: ~1.46 points
• Rank #2: ~1.31 points
• Sum of ranks 1-64: ~50 points

Key Insight: The logarithmic formula heavily rewards top-ranked players, while the rating formula is more linear.

General TVA

Constant	Value	Rationale
MAX_PLAYERS_CONSIDERED	64	Limits calculation scope; prevents diminishing returns from large fields

TGP (Tournament Grading Percentage) Constants

Base Values

Constant	Value	Rationale
BASE_GAME_VALUE	0.04 (4%)	Base unit chosen so 25 meaningful games = 100% TGP
MAX_WITHOUT_FINALS	1.0 (100%)	Standard cap for simple tournaments
MAX_WITH_FINALS	2.0 (200%)	Allows qualifying + finals to each contribute up to 100%
MAX_GAMES_FOR_200_PERCENT	50	50 games × 4% = 200% (matches the math)

Format Multipliers

These reflect competitive difficulty:

Format	Multiplier	Effective %	Rationale
Four-player groups	2.0	8% per game	Most competitive format (PAPA-style)
Three-player groups	1.5	6% per game	Less competitive than 4-player
Unlimited best game	2.0	8% per game	Requires 20+ hours of qualifying
Hybrid best game	3.0	12% per game	Combines multiple competitive elements
Unlimited card	4.0	16% per game	Highest difficulty: unlimited practice + card format

Key Insight: Higher multipliers = harder formats = more TGP value per game

Ball Count Adjustments

Ball Count	Multiplier	Rationale
1-ball	0.33 (33%)	Less meaningful competition than standard 3-ball
2-ball	0.66 (66%)	Linear scaling between 1 and 3-ball
3+ ball	1.0 (100%)	Standard competitive format

Unlimited Qualifying

Constant	Value	Rationale
PERCENT_PER_HOUR	0.01 (1%)	Rewards longer qualifying periods
MAX_BONUS	0.2 (20%)	Caps at 20% bonus (achieved at 20 hours)
MIN_HOURS_FOR_MULTIPLIER	20	Must run 20+ hours to qualify for format multipliers

Finals Requirements

Constant	Value	Rationale
MIN_FINALISTS_PERCENT	0.1 (10%)	At least 10% must advance to ensure finals are meaningful
MAX_FINALISTS_PERCENT	0.5 (50%)	Maximum 50% prevents finals from being too inclusive

Event Booster Constants

Booster Type	Multiplier	Rationale
None	1.0 (100%)	Standard events, no adjustment
Certified	1.25 (125%)	25% boost for meeting certification requirements (24+ finalists, valid format)
Certified+	1.5 (150%)	50% boost requires 128+ rated players
Championship Series	1.5 (150%)	Same as Certified+ for series events
Major	2.0 (200%)	100% boost doubles the value of major championships

Key Insight: These create tiers that incentivize higher-quality tournaments.

Point Distribution Constants

Constant	Value	Rationale
LINEAR_PERCENTAGE	0.1 (10%)	Everyone gets some points
DYNAMIC_PERCENTAGE	0.9 (90%)	Heavily rewards top finishers
POSITION_EXPONENT	0.7	Creates curve less steep than linear but more aggressive than logarithmic
VALUE_EXPONENT	3	Cubic function creates exponential decay from 1st to last place
MAX_DYNAMIC_PLAYERS	64	Caps denominator so small tournaments don't over-penalize lower finishers

Formula:

power((1 - power(((Position - 1) / min(RatedPlayerCount/2, 64)), 0.7)), 3) * 0.9 * FirstPlaceValue

Key Insight: The 10/90 split ensures everyone gets participation points while creating significant reward for top performance. The exponents were tuned empirically to create a "fair" distribution curve.

Time Decay Constants

Time Period	Multiplier	Rationale
0-1 years	1.0 (100%)	Recent performance at full value
1-2 years	0.75 (75%)	25% annual decay begins
2-3 years	0.5 (50%)	Continues progressive decay
3+ years	0.0 (0%)	Complete removal after 3 years

Constant	Value	Rationale
DAYS_PER_YEAR	365	Standard year length for calculations

Key Insight: The 3-year window and 25% annual decay steps are standard in ranking systems, emphasizing recent performance while gradually phasing out older results.

Ranking System Constants

Constant	Value	Rationale
TOP_EVENTS_COUNT	15	Top 15 events count toward ranking (similar to IFPA)
ENTRY_RANKING_PERCENTILE	0.1 (10th)	New players start at 10th percentile (reasonable pessimistic assumption)

Glicko Rating System Constants

Constant	Value	Rationale
DEFAULT_RATING	1300	Standard Glicko starting rating (slightly below average)
MIN_RD	10	Minimum uncertainty for highly active players
MAX_RD	200	Maximum uncertainty (new/inactive players)
RD_DECAY_PER_DAY	0.3	~90 days of inactivity returns to max uncertainty (0.3 × 300 ≈ 90)
OPPONENTS_RANGE	32	Limits calculation to 32 players above/below (performance optimization)
Q	Math.LN10 / 400	Mathematical constant from Glicko formula (≈ 0.00575646)

Key Insight: These are standard Glicko parameters based on Mark Glickman's research, not arbitrary choices. The Q value is a mathematical constant: ln(10) / 400.

Validation Constants

Constant	Value	Rationale
MIN_PLAYERS	3	Absolute minimum for competitive validity
MIN_PRIVATE_PLAYERS	16	Higher bar for private tournaments
MAX_GAMES_PER_MACHINE	3	Prevents over-reliance on single machines
MIN_PARTICIPATION_PERCENT	0.5 (50%)	Data quality threshold for including results

Mathematical Interdependencies

Several constants are mathematically linked:

1. Base Value: 0.5 × 64 = 32 (points per player × max players = max value)
2. Rating TVA: Coefficients ensure 64 perfect players = 25 points
3. Ranking TVA: Logarithmic coefficients ensure top 64 = 50 points
4. TGP: 0.04 × 50 = 2.0 (base value × max games = max TGP)
5. Glicko Q: ln(10) / 400 is a mathematical constant, not arbitrary

WARNING

The system is highly calibrated. Changing one constant often requires adjusting others to maintain balance.

Summary

Most constants fall into three categories:

1. Mathematical calibrations (TVA coefficients, Glicko Q) - Derived from formulas
2. Empirical balance tuning (TGP multipliers, point distribution exponents) - Adjusted to feel "fair"
3. Standard values (Glicko defaults, 3-year decay) - Industry best practices

Together, these constants create a comprehensive ranking system where tournament value scales appropriately with field strength, format difficulty, and competitive level.