TOC Bid Ranking System
A transparent achievement ranking grounded in the structure of single-elimination brackets and official TOC bid tiers.
Purpose
The TOC Bid Ranking System converts elimination results into a single, comparable achievement score.
It does this by combining two facts the national circuit already treats as meaningful:
- How deep a competitor advanced in elimination rounds.
- The official TOC bid tier of the tournament.
The system is deliberately an achievement ranking, not a predictive skill rating. It does not model opponent quality, bracket variance, prelim records, or continuous strength of schedule. Those factors matter, but incorporating them requires opacity, ongoing parameter tuning, and contested assumptions.
The result is a fully auditable score that rewards deep runs at harder tournaments and can be verified by hand from public results.
Core Principle
Each elimination round advanced is approximately twice as hard as the previous one.
This follows directly from the mathematics of single-elimination brackets. As weaker entries are removed, the remaining field grows stronger on average. The same geometric increase applies to official TOC bid tiers, which already represent the community’s consensus ranking of relative tournament strength.
Because both depth and tier follow a doubling structure, performance can be expressed with a single exponential:
[ \text{Score} = 2^{w + d} ]
No subjective weights are introduced. The system simply makes the existing bracket and bid architecture numerically explicit.
Scoring a Single Result
Every result is defined by two observable inputs only:
- (w) — number of elimination wins in bid-relevant rounds (placement depth)
- (d) — official TOC bid-tier index of the tournament
Placement Depth ((w))
| Placement | Elim Wins ((w)) | Base Points = (2^w) |
|---|---|---|
| Ghost Bid | 0 | 1 |
| Octofinals | 1 | 2 |
| Quarterfinals | 2 | 4 |
| Semifinals | 3 | 8 |
| 2nd Place | 4 | 16 |
| 1st Place | 5 | 32 |
Interpretation: every additional elimination win is worth as much as all previous wins combined.
Tournament Difficulty ((d))
| Bid Level | Index (d) | Multiplier = (2^d) |
|---|---|---|
| Finals-bid | 0 | 1 |
| Semis-bid | 1 | 2 |
| Quarters-bid | 2 | 4 |
| Octos-bid | 3 | 8 |
Interpretation: each step up the official TOC bid ladder doubles the weight, reflecting a substantially stronger national field.
Combined Score
[ \text{Score} = 2^{w + d} ]
The exponent (w + d) is an integer achievement level. The exponential scale ensures that major accomplishments separate cleanly from lesser ones.
Seasonal Ranking
A competitor’s seasonal score is the simple sum of all individual tournament scores.
- Every result retains its full value permanently.
- There is no cap, no decay, and no re-weighting.
- Rankings are ordered by this total.
This preserves the purest form of the geometric logic: each achievement stands on its own, and a season is the straightforward accumulation of those independent achievements.
Example Equivalences
The following results all equal 32 and are treated as equivalent under the system:
- 1st Place at a Finals-bid tournament
- Quarterfinals at an Octos-bid tournament
Further calibrated equivalences appear in the matrix below.
Matrix of Meaningful Outcomes
Finals-bid (×1)
- Ghost (Semis ghost): 1
- 2nd Place: 16
- 1st Place: 32
Semis-bid (×2)
- Ghost (Quarters ghost): 2
- Semifinals: 16
- 2nd Place: 32
- 1st Place: 64
Quarters-bid (×4)
- Ghost (Octos ghost): 4
- Quarterfinals: 16
- Semifinals: 32
- 2nd Place: 64
- 1st Place: 128
Octos-bid (×8)
- Ghost (Doubles ghost): 8
- Octofinals: 16
- Quarterfinals: 32
- Semifinals: 64
- 2nd Place: 128
- 1st Place: 256
Design Choices and Intentional Trade-offs
The system is deliberately minimal. The following limitations are acknowledged and accepted as the price of transparency and structural grounding:
| Issue | Approach | Rationale |
|---|---|---|
| Discrete / contested bid tiers | Uses official TOC tiers exactly as published | The TOC advisory process is the existing community consensus. Re-ranking tournaments inside a tier reintroduces subjectivity the system was designed to avoid. |
| Field size and true strength of schedule | Not modeled | Capturing continuous SOS requires historical data, opponent tracking, and contested parameters. The exponential gaps already provide strong separation between tiers. |
| Credit for beating specific strong opponents | Not awarded | The ranking measures accomplishment (depth + official tier), not path-dependent bracket outcomes. Opponent quality belongs to predictive ratings. |
| Tournament volume | Full sum of all results | The calibration of (2^{w+d}) already makes extreme lower-tier farming costly. A single Octos-bid championship (256) requires eight Finals-bid titles or four Semis-bid titles to match. Reasonable volume cannot overtake elite depth. |
These are not unresolved flaws. They are explicit trade-offs that keep the metric auditable, explainable, and free of hidden coefficients.
Why the Calibration Holds
Because the scale is exponential, the protective effect against pure volume is built-in:
- 1 Octos-bid title = 256
- Equivalent to 8 Finals-bid titles, or 4 Semis-bid titles, or 2 Quarters-bid titles
In a real season the supply of high-value tournaments is limited and the cost of attending them is real. The system therefore rewards sustained excellence at the top of the bid ladder far more than accumulation of marginal results, without needing artificial caps or decay functions.
What This System Is (and Is Not)
It is
- A transparent quantification of the achievement hierarchy already implicit in TOC bids and single-elimination structure.
- Fully reproducible from public results.
- Stable: a result’s value never changes after it is earned.
It is not
- An Elo or opponent-adjusted skill rating.
- A claim about who is “better” in an absolute sense.
- An attempt to second-guess the official TOC bid list or to model prelim strength, speaker points, or bracket luck.
Those goals require different tools. This system exists to make the existing bid-and-bracket hierarchy numerically precise and publicly comparable.
School Rankings
School rankings extend the same achievement logic from individuals to programs.
A school’s score is the sum of the Bid Scores of all its competitors in the event.
Ranking Order
- Total Bid Score — sum of every competitor’s seasonal Bid Score from that school
- Number of TOC-qualified entries
- Total number of bids earned by the school
- Exact ties remain ties
Rationale
This ordering is deliberately consistent with the individual ranking:
- Primary key remains pure achievement quality (Total Bid Score).
- Breadth of qualification is used only as a tiebreaker, not as the main ranking criterion.
- Raw bid volume is the final tiebreaker.
A program that produces one or two high-scoring national contenders will correctly outrank a larger group of marginal qualifiers. At the same time, a deep and consistently strong squad will still accumulate a higher total than a one-person program in most realistic cases.
The alternative — ranking primarily by number of qualifiers — would invert the system’s core principle by privileging participation count over the quality of results the system was built to measure.
Summary
Single tournament
[
\text{Score} = 2^{w + d}
]
Season (Individual)
[
\text{Season Score} = \sum \text{all individual scores}
]
Season (School)
[
\text{School Score} = \sum \text{Bid Scores of all competitors from the school}
]
Where (w) is the number of bid-relevant elimination wins and (d) is the official TOC bid-tier index.
School rankings then apply the ordered tiebreakers: Total Bid Score → Number of qualified entries → Total bids.
The ranking that results is a direct, structural measure of seasonal achievement at both the individual and program level.
This document is the official methodology. The system prioritizes clarity, auditability, and fidelity to the bracket-and-bid architecture over marginal gains in predictive granularity. Edge cases and feedback are welcome; changes that sacrifice transparency will be resisted.