The measure
What PQ is
PQ (Pickleball IQ) is a standard score for one construct: the quality of a player's tactical decisions, measured on written rally scenes. It is reported on a 50 to 150 scale with mean 100 and standard deviation 15, the architecture used by IQ-style standard scores, and every score is reported with its standard error.
Norms are model-based today and will be replaced by measured norms as real test-taker results accumulate; every PQ is reported with its standard error. Percentiles are model percentiles: they locate a score inside the model's reference population, and they will be re-based on measured norms as the test-taker record grows.
The model
How a sitting is scored
Items are generated, not banked. Each scene is built on the server from the decision rules of Tactics 101, 201 and 301, across twelve tactical dimensions and three tiers. A scene a member has already answered is held back from that member's later sittings.
Item parameters are modelled. Every generated item carries a difficulty and a discrimination. Difficulty comes from a linear logistic model (LLTM) over the item's book tier and scene features, such as a left-handed partner, score pressure and ball height. Discrimination is modelled from the item's family and features and is bounded between 0.6 and 1.8. Section 5 describes how real responses replace these model values over time.
Ability is a latent trait. Scoring is a two-parameter logistic (2PL) item response model. After each answer, ability (theta) is re-estimated by maximum a posteriori estimation under a N(0, 2²) prior, and PQ = 100 + 15θ, clamped to the 50 to 150 scale.
The test adapts. The sitting follows a twenty-slot plan across the twelve dimensions, weighted toward the member's measured weaknesses. Within each slot, the next scene is the candidate whose difficulty sits closest to the current theta estimate, which is the maximum Fisher information choice: no scene is wasted on what the member has already proven. This is the architecture the GRE and GMAT use, pointed at rally decisions.
Keys are priced, not asserted. Every option is priced in expected win probability by the value model. At the 301 tier, answers earn expected-value partial credit at the level profile the first scoring pass implies, instead of being graded against a single fixed key. Where the model's best play and the strategy rulebook disagree, the scene is flagged contested and its margin is shown. In the published key audit, the model's best play agreed with the rulebook on 89.8% of 10,800 audited scenes.
One official score
The combined-estimate doctrine
A member has exactly one official PQ. Every scored PQ-test response the member has ever given, from adaptive sittings and from the book quizzes, is pooled and re-estimated as a single 2PL MAP ability. A new sitting refines that estimate and narrows its standard error; it never simply replaces the record with the newest score. Where item-level responses are unavailable for an older record, sittings are combined by inverse-variance weighting of their thetas instead.
Per-attempt scores stay visible in the member's history, unchanged. A re-score under a changed model may appear only inside Item Analysis, labelled with its method and its ±SE likely range, and it never overwrites the official score. Certificates and diplomas are awarded on the combined estimate, never on a single lucky sitting.
Precision
What the standard error means
Every PQ carries a posterior standard error (SE), computed from the Fisher information at the final theta estimate, prior included. The SE is the uncertainty of the measurement, in PQ points (theta SE × 15). A member's true level most likely sits within about one SE of the reported score, and within about two SEs with roughly 95% confidence.
Read band boundaries with the SE in hand: the difference between PQ 114 and PQ 115 is smaller than the standard error of a single sitting, which is exactly why certificates follow the pooled estimate rather than one sitting. Pooling is the precision mechanism: on the current record, a single adaptive sitting carried an SE of 0.49 (about 7 PQ points), while pooled estimates sit at a median SE of 0.25 (about 4 PQ points).
Item-bank maintenance
How the bank relearns
A nightly recalibration refits the generated bank from real member responses. Difficulty is refit by maximum-likelihood steps given each sitting's theta; discrimination is refit from the item's point-biserial correlation with the sitting total. Empirical values never replace model values outright; they are blended in by sample size, so an item nobody has answered keeps its model prior and a heavily answered item is mostly empirical.
| Parameter | Empirical value enters at | Blend weight |
|---|---|---|
| Difficulty (b) | n ≥ 10 responses | n / (n + 40) |
| Discrimination (a) | n ≥ 60 responses | n / (n + 120), result clamped to 0.6 to 1.8 |
The blended parameters are what item selection and scoring actually use, so the bank relearns from every sitting. Only measurement counts: daily worksheets and Training Lab practice are training and never enter calibration.
Evidence
Evidence on record, 7 November 2026
PQ is a young measure and this section says exactly how young. Every figure below is computed from the production record on the date shown; the counts are small, and they are printed rather than rounded into a story.
| Fact | On record |
|---|---|
| Member accounts | 7 |
| Stored PQ test records | 24 (23 predate item-level storage) |
| Item-level adaptive sittings | 1, with stored posterior SE 0.49 (about 7 PQ points) |
| Members holding a pooled estimate | 4, median posterior SE 0.25 (about 4 PQ points) |
| Stored book-quiz responses feeding pooled estimates | 247 |
| Calibration state | 20 scored responses across 20 generated items; no item has reached the n ≥ 10 blend threshold, so every item parameter in use today is the model prior |
What is not yet claimed. No reliability coefficient, no test-retest figure and no external validity correlation is published today, because the record does not yet support them honestly. They will be published here, with their sample sizes, when the record reaches:
- Marginal reliability (1 − mean SE² / Var θ̂): at 30 members holding pooled estimates. Today: 4.
- Test-retest stability (first sitting against later sittings): at 20 members with two or more adaptive sittings. Today: 0.
- Item exposure and fit tables: as generated items pass n ≥ 10 responses each. Today: 0 items.
- Criterion studies (PQ against playing level and match outcomes): designed, not yet run. No validity coefficient is claimed until one is measured.
Retakes
Retake policy
Retakes are unlimited. Sittings are rate-limited only against automated abuse. Retaking cannot game the score: because every response pools into the one official estimate, a single fortunate sitting moves a member's PQ only in proportion to the information it adds, and its effect shrinks as the member's record grows. There is no best-of selection anywhere in the system: not in the dashboard, not in the certificate, not in the peer comparisons.
Currency and verification
What a credential certifies, and for how long
A PQ certificate certifies the holder's combined PQ at its issue date. PQ is a current-state estimate, not a lifetime rank: it moves as the holder keeps measuring. Credentials do not expire, and the verification page shows both sides of that fact: the PQ at issuance, and the holder's current combined PQ and standing at the moment of the check.
Every certificate and diploma issued from 7 November 2026 carries a per-credential serial (format PQV-XXXXXXXX) printed on the PDF. Enter it on the verification page to confirm the credential: the page shows whether it is valid, the holder's name, the credential and award, the PQ at issuance for certificates, and the issue date. Nothing else is exposed: no email address, no account details.
Legacy credentials: PDFs printed before per-credential serials carry only the member number (for example PT-000001). The verification page accepts a member number and shows that member's credential standing; support can also confirm any legacy credential at support@pickleball-tactics.com.
Test conditions
Conditions of measurement
PQ is taken online, unproctored and self-administered, on the honor system, with no identity check. That is stated plainly because it bounds what a PQ means: it is a psychometrically scored measure built for training decisions, league-of-one progress tracking and placement into the Academy curriculum, not a proctored examination result. Treat it the way you would treat a well-built self-report instrument: meaningful, improvable, and not a ranking to hire or select by.
Reviews
Score and item reviews
Measurement that cannot be challenged should not be trusted. Any member may challenge:
- Item content or its key: a scene whose priced best play looks wrong, with the scene identified from the dashboard's item views.
- A scoring or record error: a sitting, response or estimate that does not match what happened.
- A credential record: a certificate, diploma or verification entry that is wrong.
Send the challenge through the contact form under the category Score and item review, or write to support@pickleball-tactics.com. If a key is wrong, the item is corrected or retired, every pooled estimate the key touched is recomputed under the corrected key, and the change is logged in this brief. If a record is wrong, it is corrected and the correction is confirmed by email. Review outcomes are decided on the measurement evidence, and the reason is given either way.
Governance
Who maintains the standard
Today the PQ standard, the Tactics books, the answer keys and the engine are maintained by one person: Richie T. Kim, Ph.D. That concentration is named here rather than hidden. Independent stewardship of the PQ standard is being established through a nonprofit measurement institute, which will hold the standard and license it back at arm's length; until it is seated, this brief is the public maintenance record, and the review path above is open to anyone.
Change log · v1, 2026-11-07: first publication. Model, doctrines, blend rules, evidence counts and review path as of this date.