This program defines how an equipment-response claim could be tested without turning a group average, a plausible shaft simulation, or a single favorable trial into a fitting rule. The executable example contains eight coded participants, two equipment conditions, three crossover cycles, and five trials per condition and cycle. Every observation and property is manufactured-synthetic; no person or commercial product was measured.
The current evidence provides no product or fitting recommendation and no coaching, clinical, design, causal, or population authority. It does not identify an optimal shaft, diagnose a golfer, validate a vendor category, or show that changing equipment causes a durable performance change. Human and product guidance remains unavailable pending the promotion gates below.
Primary-Source Register
| Worobets and Stefanyshyn (2012) (Worobets and Stefanyshyn 2012) |
Double-blind, subject-dependent shaft-stiffness response as a reason to retain individual effects |
One best stiffness or a transportable responder label |
| MacKenzie and Boucher (2017) (MacKenzie and Boucher 2017) |
Repeated within-golfer comparisons and the separation of group from individual results |
Treating a significant individual contrast as a fitting prescription |
| Betzler et al. (2012) (Betzler et al. 2012) |
Repeated shaft-strain, clubhead-presentation, and wrist-kinematic observations |
A universal biomechanical mechanism or causal pathway |
| Jones et al. (2019) (Jones et al. 2019) |
Within-golfer repeatability and between-golfer strain-pattern variation |
A validated responder taxonomy or population subgroup |
| Lacy et al. (2012) (Lacy et al. 2012) |
Designed manipulation of driver mass and shaft length |
This crossover, outcome, sample size, or individual advice |
| Cheong, Kang, and Jeong (2006) (Cheong et al. 2006) |
Mechanical shaft-property measurement and model-comparison precedent |
A qualified vendor specification or released design |
The sources motivate the questions and controls. None supplies the manufactured values below, validates this estimator, or licenses a conclusion about a particular golfer or club.
Equipment Property and Metrology Contract
An intervention is not the printed shaft label. Each coded condition requires the same ordered property manifest before allocation:
| Shaft structure |
Flexural-rigidity and torsional-rigidity profiles with station locations |
A single flex label hides spatial and directional variation |
| Mass distribution |
Shaft, head, grip, and total mass; balance point; club length |
Nominal component values do not close the assembled system |
| Head geometry |
Static loft, lie, face angle, and head inertia |
Delivery changes can be confounded with an unmeasured head state |
| Metrology |
Value, unit, standard uncertainty, method, and calibration revision |
Precision is claimed without traceability |
| Custody |
Seal, custodian role, code, transition, and condition IDs |
Analysts or participants can infer or alter the intervention |
The executable contract rejects missing, duplicated, reordered, nonfinite, or zero-uncertainty properties. The sample numbers are calibrated only against a manufactured software fixture. Real work requires traceable instruments, environmental conditions, as-found/as-left checks, and a signed chain of custody. A product name cannot substitute for those records.
Randomization, Blinding, and Washout
Protocol revision affinedrift.equipment-individual-response/v1 uses a declared seeded blocked permutation: four participants receive AB, four receive BA, with three cycles and five trials in each condition-cycle cell. Both the participant and the primary analyst receive condition codes. A ten-minute washout is a fixture declaration, not an empirically validated duration. Every trial records its period and elapsed minutes since the prior condition; the qualifier rejects a condition assigned to the wrong randomized period or a second period observed before the declared washout.
Counterbalancing separates treatment order from condition, but it does not erase learning, fatigue, expectation, warming, or condition-by-period effects. The software therefore rejects imbalance and a zero washout rather than quietly interpreting them as ordinary noise.
Intent Control and Adaptation
Each trial retains an intent-error signal and a carryover residual. A qualified study would declare the task cue, allowable speed or effort band, familiarization criterion, warm-up, rest, stopping rule, and method for measuring adherence. The fixture applies the gate before estimating a response:
- Keep every raw record, including excluded and adverse trials.
- Mark the participant result unavailable if the declared carryover or intent limit is exceeded.
- Do not impute a failed participant into the hierarchical model.
- Report period and cycle effects so adaptation cannot masquerade as equipment response.
The adverse fixture preserves all P08 trials but reports its response as unavailable because its carryover residual exceeds the preregistered limit.
Preregistered Estimands
The primary estimand is the within-participant target-minus-baseline change in clubhead speed at impact, in m/s. The practical threshold is 0.5 m/s. These choices are frozen before analyzing a real data set.
Distinct questions require distinct estimands:
| Did this coded participant differ under these conditions? |
Within-person mean contrast across qualified cycles |
Conditional on the task, equipment, session, and measurement envelope |
| Is the response stable? |
Cycle-specific contrasts and direction consistency |
Does not imply stability on another day or task |
| How heterogeneous are fixture responses? |
Between-participant variance after sampling-variance accounting |
Descriptive for this manufactured set only |
| Would a new participant benefit? |
Held-out predictive distribution |
unavailable in the current program |
| Did the property change cause the response? |
Preregistered causal contrast with exchangeability and adherence evidence |
unavailable until the intervention and confounders are qualified |
Changing from one row to another after seeing results is estimand drift and invalidates the confirmatory interpretation.
Hierarchical Participant-by-Equipment Analysis
For participant \(i\) and cycle \(c\), the fixture first computes
\[
d_{ic}=\overline{y}_{i,c,B}-\overline{y}_{i,c,A}.
\]
The raw individual contrast is \(\bar d_i\). A method-of-moments between-person variance separates observed dispersion from average sampling variance, and a partial-pooling estimate shrinks \(\bar d_i\) toward the group mean. Raw and shrunken values remain side by side; shrinkage never changes the stored trials or creates a recommendation.
The manufactured group mean is approximately 0.000 m/s while the estimated between-participant variance is 0.764 (m/s)\(^2\). Opposing individual directions cancel at group level, which is precisely why a near-zero mean cannot prove that everyone has no response.
| P01 |
1.400 |
1.360 to 1.440 |
Positive |
Yes |
| P03 |
-1.400 |
-1.440 to -1.360 |
Negative |
Yes |
| P05 |
0.000 |
-0.040 to 0.040 |
Null |
Yes |
| P07 |
0.200 |
-0.998 to 1.398 |
Indeterminate |
No |
| P08, adverse carryover fixture |
unavailable |
unavailable |
Unavailable |
No |
These exact numbers are regression fixtures. Their clean separation is evidence that the code can preserve outcome classes, not evidence about real response rates or effect sizes.
Within-Person Uncertainty
The interval combines cycle-to-cycle dispersion with declared measurement standard uncertainty. Increasing P01 measurement uncertainty from 0.08 to 0.80 m/s leaves the raw contrast unchanged but widens its interval. That contract blocks a precise-looking mean from outrunning instrument capability.
A human study must extend this calculation to calibration covariance, repeated days, trial autocorrelation, heteroscedasticity, missingness, analyst decisions, and sensitivity to hierarchical priors or variance estimators. A confidence or credible interval is conditional on its model; it is not a tolerance interval for all golfers.
The executable sensitivity record also recomputes the group mean after leaving out each fixture participant and compares raw-status classifications with the partially pooled estimates. Its leave-one-out group-mean range is -0.2 to +0.2 m/s, no fixture status changes under partial pooling, and mixed individual directions remain. This narrow check does not replace alternative priors, estimators, missing-data models, or held-out predictive assessment.
Responder Instability and Carryover
A responder label is not a permanent trait. P07 has cycle effects of +1.0, -1.0, and +0.6 m/s: its mean is positive but its interval crosses both the null region and the positive practical boundary. The result remains indeterminate, with stable_across_cycles = false.
Carryover is handled separately from instability. A large residual after condition A can contaminate condition B even when the trial values appear repeatable. The correct disposition is unavailable pending a qualified model or new collection—not deletion, favorable cycle selection, or imputation.
Practical Versus Statistical Significance
The result classes use the complete interval relative to ±0.5 m/s:
| Positive |
Entire interval exceeds +0.5 m/s |
Manufactured contrast only |
| Negative |
Entire interval is below -0.5 m/s |
Retained adverse direction, not failure of reporting |
| Null |
Entire interval lies inside -0.5 to +0.5 m/s |
Practically bounded for this fixture, not proof of exact zero |
| Indeterminate |
Interval crosses a practical boundary |
More precision or a better design may be needed |
| Unavailable |
Qualification or evidence gate fails |
No numerical substitute is permitted |
A small p-value does not establish practical importance. Conversely, a large but uncertain estimate does not become advice. Thresholds must be justified for the declared outcome before data collection and checked in sensitivity analyses.
Flexible-Shaft Prediction Linkage
This protocol does not duplicate an UpstreamDrift shaft solver. A future comparison should import an immutable, schema-validated UpstreamDrift prediction for each measured condition and bind it to the exact property, coordinate, frame, event, and source revisions. The planar-to-spatial model ladder identifies when flexible-shaft states are required; the hybrid impact-contact protocol identifies terminal-event uncertainty that can change the predicted outcome.
The club fitting simulation article describes forward models and interchange documents. A prediction is evaluated against locked measurements; it is not tuned on the same trials and then called validated. Model discrepancy, parameter uncertainty, numerical error, and measurement error remain separate. AffineDrift explains and audits the contract; UpstreamDrift owns the upstream computational implementation.
Negative, Null, Indeterminate, and Unavailable Results
The regression ledger deliberately contains one representative positive, negative, null, indeterminate, and unavailable outcome. Every available row retains manufactured-synthetic; the failed row retains unavailable. All five retain authorized_guidance = unavailable. This prevents an unfavorable or ambiguous response from disappearing between code, analysis, and publication.
No global recommendation is computed. Aggregation can summarize heterogeneity, but it cannot decide which product a person should use.
Reproducible Implementation
The declarations, manufactured fixtures, qualification, and analysis live in src/affine_control/equipment_response_protocol.py, equipment_response_fixtures.py, and equipment_response_analysis.py. Executable contracts live in tests/test_equipment_response_protocol.py and tests/test_equipment_response_content.py. The reviewed-route inventory binds those exact bytes by SHA-256. A digest proves review identity, not scientific truth or external validity.
References
Betzler, Nils F., Stuart A. Monk, Eric S. Wallace, and Steve R. Otto. 2012.
“Effects of Golf Shaft Stiffness on Strain, Clubhead Presentation and Wrist Kinematics.” Sports Biomechanics 11 (2): 223–38.
https://doi.org/10.1080/14763141.2012.681796.
Cheong, S. K., K. W. Kang, and S. K. Jeong. 2006.
“Evaluation of the Mechanical Performance of Golf Shafts.” Engineering Failure Analysis 13 (3): 464–73.
https://doi.org/10.1016/j.engfailanal.2004.12.035.
Jones, Kristian M., Nils F. Betzler, Eric S. Wallace, and Steve R. Otto. 2019.
“Differences in Shaft Strain Patterns During Golf Drives Due to Stiffness and Swing Effects.” Sports Engineering 22 (2): 14.
https://doi.org/10.1007/s12283-019-0308-3.
Lacy, Thomas E., Jaesang Yu, John Axe, and Tony Luczak. 2012.
“The Effect of Driver Mass and Shaft Length on Initial Golf Ball Launch Conditions: A Designed Experimental Study.” Procedia Engineering 34: 379–84.
https://doi.org/10.1016/j.proeng.2012.04.065.
MacKenzie, Sasho J., and Daniel E. Boucher. 2017.
“The Influence of Golf Shaft Stiffness on Grip and Clubhead Kinematics.” Journal of Sports Sciences 35 (2): 105–11.
https://doi.org/10.1080/02640414.2016.1157262.
Worobets, Jay, and Darren Stefanyshyn. 2012.
“The Influence of Golf Club Shaft Stiffness on Clubhead Kinematics at Ball Impact.” Sports Biomechanics 11 (2): 239–48.
https://doi.org/10.1080/14763141.2012.674154.