Group Size Projection
Enter your bow setup, arrow specs, tuning depth, and conditions. The model uses an error-budget (RSS) approach — each factor contributes an independent standard deviation; they combine as √(sum of σ²), not as a simple sum. See which factors are costing you the most spread, and what the biggest upgrade is. How the math works ↓
How the model works
Each input factor contributes an independent 1D standard deviation (σ) to the total error budget. Factors combine as root-sum-of-squares: σ_total = √(σ_platform² + σ_arrows² + σ_tuning² + σ_FOC² + σ_fletching² + σ_wind²). Group diameter = σ_total × 3.5, which approximates the expected extreme spread of a 10-arrow group under bivariate normal distribution.
Range: Hooter Shooter + best-case setup at 40 yards indoor → ~0.35". Budget bow + store arrows + no tuning + heavy outdoor wind → ~6". Human error is the dominant factor in most hunting setups.
Platform
Combines bow geometry (ATA length, cam aggressiveness, component tolerances) with shot-to-shot human form variation for a competent field archer. Longer ATA produces more stable geometry at full draw and is more forgiving of torque and timing variation. Hooter Shooter removes all human σ and isolates purely mechanical spread.
Arrow straightness & consistency
Straightness tolerance is the most direct proxy for shaft-to-shaft uniformity. Within a straightness grade, spine consistency and weight consistency also contribute. Tighter tolerance = tighter groups, especially at distance. Store-bought arrows are modeled with an unknown but typically wide tolerance spread.
Tuning depth
Tuning aligns arrow launch conditions to the specific bow. DIAG — dead-on nocks, walk-back, French tune, distance verification — is the most thorough method. Each tier removes a layer of systematic launch error. Untuned arrows produce repeatable but setup-dependent flight errors that widen groups without a clear directional pattern.
FOC
Higher front-of-center increases arrow stability in flight and reduces sensitivity to imperfect release and wind gusts. Below ~10% FOC, arrows are noticeably less stable and more vulnerable to form variation. Above ~15%, the benefit plateaus for most compound setups.
Fletching
Larger, helically-mounted vanes correct arrow flight faster and more aggressively after the launch. This reduces residual scatter from small release inconsistencies. Small or straight vanes correct more slowly, leaving more flight-path variation to accumulate over distance.
Wind variation
Steady wind shifts point of impact but does not by itself open groups. What opens groups is shot-to-shot variation in wind timing and gusts — each arrow encounters slightly different conditions during its flight. Smaller diameter and heavier arrows are less affected per unit of crosswind force. Wind contribution scales with distance^1.3 (longer flight time, more total exposure and more variation between shots).
Scatter simulation
The canvas uses Box-Muller transform to generate bivariate normal arrow positions at the computed σ. Each reshoot produces a new random session — realistic variation in what any given 10-arrow group might look like with these inputs. The dashed circle shows the projected group diameter.