Academic basis

The ASL model — where the APR comes from

The APR is built on the Arrow Score Level (ASL) model, a ballistic performance framework developed by Dr. Richard Park and Magnus Larven and published by Archery Australia in 2014. The paper set out to solve a specific problem: how do you compare scores shot under different conditions on a single, physically grounded scale?

Before the ASL model, comparing a 660/720 at 70m to a 290/300 at 18m was essentially impossible without a lookup table, and even those tables were arbitrary. Park and Larven observed that arrow grouping can be modelled as a two-dimensional Gaussian scatter — arrows cluster around the aiming point with a spread that follows predictable statistical laws. If you know the spread (sigma), you can calculate the expected ring value for any arrow fired at any face from any distance. Run that calculation in reverse and you can convert any competition score into the spread parameter that would have produced it, then translate that spread to the reference standard.

What "solving the ASL index" means

The ASL index is a number that describes how tightly your arrows cluster relative to what a perfect archer would achieve — it's an accuracy index, not a score. The model defines sigma (σ) as the standard deviation of arrow scatter in millimetres. A smaller sigma means tighter groups and higher scores.

The system works backwards from your score: given what you shot at a specific distance and face, it solves for the scatter value that would have produced that result. That scatter value is then translated to the reference distance and face — 70m on a 122cm WA target — to find the arrow average you would produce there. That reference arrow average × 100 is your APR.

In practice the solver runs an iterative search — it tries different ASL index values until the predicted score at your actual distance and face matches what you shot. Once found, that index is translated to the reference. This is what makes the system distance-agnostic: the physics of the scatter model does the translation, not an arbitrary lookup table.

Why a Gaussian scatter model works for archery

Archery errors — wind, form, release variation, sight movement — are largely independent small effects. The Central Limit Theorem tells us that the sum of many independent small errors tends toward a normal (Gaussian) distribution. This is exactly what you observe on a target face: arrows cluster around the aim point in a roughly circular spread, with fewer arrows at greater distances from centre. The ASL model formalises this, treating the two-dimensional scatter as a bivariate normal distribution with a single spread parameter σ.

The model isn't perfect — a real archer's scatter isn't perfectly symmetric, and outliers happen more often than a pure Gaussian predicts. But as a first-order approximation across a large population of competition scores, it is remarkably stable. In practice, the model's predictions align closely with what elite archers produce in competition — a useful cross-check that the physics are well-calibrated.

Scoring model

The 11-point scale

Standard WA competition scoring uses a 10-point scale, where the X (inner 10) counts as 10. The APR uses an 11-point model — the X scores 11 — for a reason that comes directly from the physics of the ASL model.

The ASL model computes an expected probability for each ring zone, including the X ring. If you collapse the X back to 10, you discard the information that the model is actually using to distinguish between archers at the high end. Two archers might both score 660/720 — but one achieves that with 45 Xs and the other with 15. Their sigma values are measurably different, and the 11-point model captures that difference. The 10-point model cannot.

For developing archers, the X ring is a pleasant bonus but rarely dominates the picture. For an archer competing at World Cup level, the 11-point model is essential: without it, the rating scale would compress near the ceiling and lose almost all discriminating power at the levels where the system is most useful.

When X counts are not recorded for a round (common at smaller indoor events), the system falls back to a 10-ring model. The operator marks this at import time. Both models produce valid APR values. A round without X tracking still generates a fully usable rating — it simply can't access the space above a pure-10 score.

APR differences as arrow score differences

Because APR = arrow average × 100, the gap between two ratings translates directly into a concrete accuracy difference. 10 APR points = 0.1 per arrow on the 70m/122cm reference. Over a 72-arrow round, that is roughly 7 score points.

From score to rating

The full calculation pipeline

Every imported score passes through two distinct phases before it affects a rating. The phases are separated deliberately — Phase 1 does the ballistic work; Phase 2 does the statistical rating update. Keeping them separate means the rating aggregation chain can be replayed quickly without recalculating all the arrow physics.

Phase 1 — ASL computation

1. Score → arrow averageYour total score is divided by arrow count to get a raw arrow average. A 660/72 arrows is 9.167 per arrow. X counts, if available, are incorporated using the 11-point model.
2. Arrow average → sigmaGiven the arrow average at the actual distance and face, the ASL model numerically solves for the sigma that would produce that average. This is the core inverse problem — the ballistic translation step.
3. Sigma → reference arrow averageThe same sigma is now applied to the reference distance (70m) and face (122cm). The model computes the expected arrow average there. Multiply by 100 and you have the raw APR for this score.
4. Field calibration (where applicable)When a calibration group (same event session: bow style family and age tier) has enough archers with prior competition history, the system compares the group's actual raw APR average to what those archers would be expected to average from their other events. If the session fell meaningfully below that expectation, the same upward APR adjustment is applied to every archer in the group. The calibration factor and points are stored alongside each score.

Phase 2 — Weighted rating aggregation

Once field-adjusted APR values are stored, the rating is computed as a weighted average of all event APR results. This is the same family of methods used by World Athletics, the Official World Golf Ranking, and the PDGA disc golf rating system — each combines independent measurements from qualification-style performance rather than elimination bracket results, which fits archery qualification rounds.

Each score contributes to the rating with a weight that combines two factors: recency (more recent scores carry more weight, via exponential decay with λ (configurable, default 0.7): weight includes e^{−λ × age in years}) and event weight (major championships carry more influence than smaller events). A World Cup score at 1.75× weight from last month contributes more than an older club score from a previous season. The result converges quickly to an archer's true performance level and remains responsive to genuine improvement or decline.

Conditions correction

Field calibration

Competition conditions — wind, rain, difficult lighting, extreme heat — can systematically depress scores across an entire session. When this happens, every archer in the session is affected equally, and the APR model should reflect their true ability level rather than penalising them for conditions outside their control.

The field calibration system detects and corrects for this. After computing raw APR values for all scores in an event, the system identifies calibration groups — archers who competed in the same session under the same conditions. A calibration group is defined by event, bow style family, and age tier:

• Recurve-family (recurve, barebow, traditional, longbow, VI1, VI2/3) shoot in the same calibration family; Visually Impaired Class 1 (VI1) and Classes 2/3 (VI23) are separate rating pools and calibration groups.
• Compound-family (compound, fixed pins, W1) shoot together
• Within each family, senior/masters divisions shoot together, and youth divisions (U18, U21) shoot together separately

For each calibration group, the system computes what that group of archers would be expected to average based on their historical performance at other events. If the group's actual performance falls significantly below expectations — more than 2% below the expected mean — a conditions adjustment is applied.

Calibration only applies upward — the system corrects for conditions that hurt performance, not for unusually good conditions. An archer who shoots well in perfect weather earned that score. Calibration fires only when the group has at least 10 archers with established histories (3+ prior events), ensuring the expected mean is statistically reliable.

Where a calibration adjustment was applied, a footnote appears alongside the event APR on the archer's profile and on the event results page, showing the adjustment in APR points. The underlying raw APR is always stored and accessible.

Confidence and scale

Rating phases and what your number means

Select your bow style to see calibrated benchmarks:

Profile diagnostics

Rating deviation, consistency, and peak potential

Three numbers appear alongside your APR on the profile page. They are fully independent — each answers a different question, and you can have almost any combination of values across the three.

Rating deviation in detail

RD reflects the statistical uncertainty in your rating based on the volume and consistency of your competition history. It has nothing to say about how consistently you shoot within a round — it is purely a measure of how much competition evidence the system has accumulated about you. An archer with narrow RD (±25) has a well-established rating. One with ±150 could realistically sit anywhere across the full width of that uncertainty band around their listed rating — the true level isn't yet known. A large RD is fixed by competing more. A low consistency score is fixed on the practice range. These two things are completely independent.

Consistency score in detail

For each score with arrow data, the system compares your actual ring-value distribution to the distribution the ASL model predicts for an archer at your rating level. The comparison uses a statistical goodness-of-fit test — the result is scaled to a 0–100% range where 100% means your arrow distribution matched the model's predictions perfectly.

A high score means your arrows fell in the rings approximately as often as the model predicts — no systematic bias, no wild-end outliers pulling the distribution out of shape. Two archers can share the same APR with very different consistency scores: one might produce steady 55–57 point ends; another might shoot a 61 followed by a 47 and still average the same number. Their rating is identical; their consistency is not.

Peak potential APR in detail

The system identifies your weakest arrows — those falling in the lower tail of the distribution expected for your skill level — removes them, and re-solves the skill level implied by the remaining arrows. The result is converted to the reference scale as usual. The corresponding peak potential score is also calculated — what you'd shoot over a full round at that APR.

A small gap (20–30 points) between your APR and peak potential means your arrow distribution is already fairly tight — you're shooting close to your full ability. A large gap (80–100+ points) means a handful of significantly off arrows are holding your average down. That is actually encouraging: it means your best shooting is well ahead of your typical result, and there's a clear, quantifiable target to aim at in training.

Score alone vs. arrow data

A round total is sufficient to calculate a valid APR and update your rating. All it takes is the final score, the distance, the target face, and the bow style. Consistency score and peak potential, however, require knowing which ring value each individual arrow scored — a round total is an average that cannot be decomposed. End-by-end scores (the minimum) allow both diagnostics to be calculated. Full arrow strings allow them to be calculated more precisely.

All World Archery imports record individual arrow values end-by-end, so consistency and peak potential are available for every World Cup, World Championship, and Olympic Games score in the system. Events sourced from other result systems may provide totals only, in which case the profile notes these metrics as unavailable for those specific scores. There is no disadvantage to the rating itself — the arrow data only unlocks the additional diagnostics.