2021 — A review of forward-dynamics simulation models for predicting optimal technique

Source: full paper text, not abstract only.

READ THIS FILE FIRST if you want to know how much to trust any simulation-derived claim elsewhere in this catalogue. It is the authors’ own account of what their method can and cannot deliver, written with unusual candour about the limits.

Research theme

Identifying the optimum technique for a maximal-effort sporting task — especially for a specific individual — has been called the “holy grail” of sports biomechanics. Conventional research either compares groups (elite vs sub-elite) or correlates variables with outcomes; neither can establish cause and effect for one athlete, and conclusions drawn between individuals do not reliably apply to any individual. Forward-dynamics simulation offers a way out: build a mathematical model of the athlete, specify the driving forces, compute the resulting motion, then systematically perturb one factor at a time with everything else held constant.

This review asks whether that promise is actually delivered. It evaluates the field through a dynamical systems theory lens — the school of thought that says movement patterns emerge from self-organisation and the interaction of organismic, environmental and task constraints, and that therefore a top-down computed “optimum” may be something the athlete can never inhabit.

Structure: the four stages

Every forward-dynamics study follows the same pipeline, and the review is organised around it:

1. Model construction — how many segments, what joints, what actuators
2. Parameter determination — measuring this individual’s inertia, strength, soft-tissue and contact properties
3. Model evaluation — proving the model can reproduce recorded performances
4. Model application/optimisation — perturbing and optimising to find the “best” technique

Stages 1–3 are iterative: every change in complexity changes the parameter set to be determined.

The preconditions for a simulation prediction to be believable

This is the extractable caveat list. Every simulation-derived coaching claim in this catalogue should be checked against these.

1. Model evaluation — the accuracy threshold

• A model is considered a satisfactory representation when the evaluated simulation score/cost is less than 10%, or ideally less than 5%.
• Accepted differences are typically larger when kinetics (forces) are in the cost function than when kinematics alone are considered. So a “5%” that includes forces is a stronger result than a “5%” that doesn’t — always ask what went into the score.
• Evaluation should use different experimental trials from the ones the parameters were fitted on.
• Ideally evaluate against an elite performer capable of producing close to optimal performances, so the model is not extrapolated beyond where its accuracy is known.
• The crucial epistemic limit, stated repeatedly: evaluation “only confirms that the model can generate a movement pattern to recreate the recorded performance and does not guarantee that any subsequently optimized movement solution is possible by the individual.”

2. Subject-specific strength measurement — the reason models are 2D

• Torque-driven models are preferred for maximal-effort work precisely because individual-specific strength parameters can be measured in vivo on an isovelocity dynamometer, giving “assurance that torques exerted at each joint angle and velocity within any predicted optimal technique are realistic for the individual.”
• Muscle-driven models cannot do this: individual muscle parameters are hard to obtain non-invasively, so literature-scaled values are used, which are specific to nobody. Optimal performance at high movement velocities is sensitive to strength capabilities, so this matters.
• But: the dynamometer advantage “is therefore only true for two-dimensional representations.” No technique exists for determining subject-specific maximal torque profiles about three axes at the hip or shoulder. This is the single reason Felton’s cricket work is 2D.
• Monoarticular assumption is a known error source. Most models compute torque from the primary joint angle alone, ignoring two-joint muscles. Lewis et al. showed a biarticular representation of ankle plantar flexor torque had a weighted RMS difference of 3% against measured maximum torque, versus 19% for the single-joint function — and concluded a biarticular representation is necessary where the knee is flexed more than 40°. Monoarticular hip actuators may overestimate maximum flexion torque and underestimate maximum extension torque with the knee extended.

3. Objective function choice — the result depends on what you asked for

• The objective function “must represent the task objective of the modeled activity.”
• The worked cautionary example: in gymnastics upstart optimisation, minimising joint torques produced a solution that diverged from an elite gymnast’s actual movement, whereas maximising success in the presence of inherent movement variability produced a solution close to the gymnast’s real movement. Same model, different criterion, opposite verdict on what the athlete “should” do.
• Penalty functions should ramp up, not be all-or-nothing, so the optimiser can converge.
• Explicit warning about analysis flexibility: researchers should pre-register or at least pre-specify cost functions and evaluation criteria, to avoid “the modeling equivalent of p-hacking, where cost functions or criteria are adjusted until ‘satisfactory’ scores are achieved.”
• A true individual optimum likely depends on a combination of factors — spatial and temporal accuracy, robustness to internal and external variation, and musculoskeletal loading — and these should be in future cost functions.

4. Robustness — a one-off best is not an optimum

• Humans never repeat a movement exactly, so a predicted optimum “should be robust to perturbations and not simply a single greatest one-off performance.”
• Best-practice example: Hiley & Yeadon repeated each simulation 1000 times, varying the turning points of the angle-time histories according to experimentally recorded intra-individual variation, and declared optimal the solution that maximised success in that noisy environment.
• The review states plainly that this “should be utilized in future torque-driven models” — an admission that most torque-driven work, including the cricket bowling optimisations, has not done it.

5. Generalising from one athlete to another — don’t

• Application of conclusions drawn from between-individual comparisons to any specific individual is limited; lack of group-to-individual generalisability is flagged as “a threat to human subjects research.”
• Even in the best case: “Only predicting the optimal technique for an individual such as a world record holder with a technique considered close to optimal may come close, and even then, the evaluation results could not be extrapolated to other models of sub-elite athletes.”
• The defensible product of this method is cause-and-effect understanding of what generally limits performance in a hypothetical individual — which is preferable to “in general” group observations because cause and effect can be confidently inferred. The indefensible product is a transferable technique prescription.

6. The unquantifiable error — self-organisation and intrinsic dynamics

• “Intrinsic dynamics” — an athlete’s pre-existing preferred coordination patterns — determine how likely they are to be able to adopt and reliably reproduce a predicted optimum. These are currently extremely difficult to measure or model.
• This is named the main limitation from a dynamical systems perspective, and — critically — “The magnitude of errors introduced by this limitation cannot be quantified and evaluated”, because there is no “true” optimum to compare against. The whole point of the optimisation is to predict an unmeasurable performance.
• Consequence: “Forward-dynamics simulation models are unlikely to ever provide a perfect prediction of optimal technique since they are simplified representations of the human body and are always likely to incorporate various sources of systematic error. The overall magnitude of the optimal performance outcome measure should, therefore, clearly be treated with caution.”

7. The bottom line the authors themselves draw

Simulation models “may be used as indicative rather than prescriptive tools within a coaching framework.”

“The ‘optimal’ technique and performance outcome should not currently be viewed as a definitively achievable target against which an individual is judged.”

The athlete should work towards “the broadly indicated and mechanically justified differences in relation to their current technique.”

The example they give of what that looks like in practice is drawn straight from the cricket work: more extended front ankle and knee joint angles; increased trunk flexion; a longer delay in the onset of arm circumduction. That is the correct register for every simulation-derived coaching cue in this catalogue — direction, not target.

Other numbers worth having

• Segmental inertia: Yeadon’s geometric model uses 40 shapes and 95 anthropometric measurements (34 lengths, 41 perimeters, 17 widths, 3 depths); reported error 2.3% for total body mass, with segmental densities the only literature-assumed values. Errors within individual segments are not thereby avoided. DXA scanning could improve this.
• Wobbling masses (soft tissue modelled as a second rigid segment on springs) reduce loading on the system by up to 50% compared to an equivalent rigid model.
• Wobbling-mass compliance is probably too generous. Limits used in the literature: 5.0 cm shank, 7.5 cm thigh, 11.0 cm trunk. Recent experimental measurement of shank and thigh soft tissue displacement in drop landings: up to 1.4 cm. The trunk limit traces to a study of viscera displacement in hopping (max 8 cm) — and viscera are only one component of trunk soft tissue. Peak displacements of different trunk tissues are unlikely to be synchronous.
• Foot–ground compliance is probably too generous too. Measured maximum deformation: 11.5 mm (shoe sole), 12.7 mm (human heel pad). Simulation foot–ground interfaces have been allowed up to 56 mm of compliance, at the toe and MTP as well as the heel.
• The review’s explanation for both: excessive compliance in the wobbling masses and foot springs is compensating for missing compliance elsewhere — pin joints with no compression, the medial longitudinal arch, joint structures, vertebrae. The model is soft in the wrong places because it is rigid in the right ones.
• Eccentric muscle force rises to ~1.4–1.5× isometric (tetanic) or ~1.1–1.2× (voluntary).
• Series elastic stiffness is computed assuming 4% tendon stretch plus literature moment arms.
• Task constraint example from cricket: ensuring the elbow does not extend by more than 15° between the instant of horizontal upper arm and ball release (the throwing law), and constraining ball landing location while optimising ball release speed.
• Pin joints are a known simplification, “particularly questioned at the shoulder, where motion can occur at four different joints”, and they neglect the energy-dissipative properties of real compliant joint structures.
• Application is “mostly limited to ‘closed’ skills, where environmental and task constraints remain relatively constant.”

What this means for video and motion analysis

No direct coaching cue — this review is about the trustworthiness of a whole class of results. Translated for anyone building or trusting a motion-analysis system:

• Adopt their acceptance thresholds as your own. A validated model scores <10%, ideally <5%, on a cost function that includes kinetics, evaluated on trials it was not fitted to. If a system’s accuracy claim doesn’t tell you (a) what went into the score, (b) whether the test data was held out, and (c) whether elite or general performers were used, you cannot assess it.
• “Validated” and “predictive” are different claims, and the gap is not quantifiable. A model proven to reproduce what was recorded is not thereby proven to predict what was never recorded. The review says this four separate times. Any product that validates on reproduction and markets on prediction is making an unearned leap.
• Compliance parameters are the field’s known soft spot (in both senses). Wobbling-mass and foot–ground compliance are set 4–5× larger than measured values, explicitly as compensation for rigidity elsewhere. So any internal load estimate — joint forces, spinal loading — is standing on parameters chosen for a different reason than physiological realism. Kinematic outputs are far safer than internal-load outputs.
• Analysis flexibility is real and the authors say so. The p-hacking warning applies directly to anyone tuning a pipeline until the validation number looks acceptable. Fix the metric before you fix the model.
• Determinism is the wrong frame; robustness is the right one. The gymnastics result — that minimising torque diverged from the elite athlete while maximising success under noise converged on them — is the most important single finding here for practical use. A “best” number computed from one perfect execution is less informative than a solution that survives the variability a real athlete brings.
• One athlete’s optimum is one athlete’s optimum. A system that computes an “ideal” from a model built on one bowler and applies it to a user is doing exactly what the authors say cannot be done.

Caveats and limits

• A narrative review, not systematic. No stated search strategy, inclusion criteria, or PRISMA-style flow. Selection of the 176 references is the authors’ judgement.
• Substantial self-citation and conflict of perspective. All three authors are practitioners of the method being reviewed; King and Felton’s own models are among those evaluated. The review’s candour about limitations partly mitigates this, but it is a defence of the approach as well as a critique. The opposing dynamical-systems position (Glazier & Mehdizadeh, refs [1,2]) is represented through the authors’ summary, not on its own terms.
• No new data, no meta-analysis, no effect sizes. Numbers quoted are drawn from individual cited studies.
• Received no external funding; authors declare no conflict of interest.
• Published in Applied Sciences (MDPI).

Relationship to other Felton work

• This is the umbrella document for the whole catalogue. Everything in Fast Bowling Simulation & Optimisation inherits the caveat list above.
• Cites Felton, Yeadon & King (2019) [ref 118] as the current answer to the planarity problem, and presents planar-with-massless-segments as the route by which “planar models are likely to evolve” until subject-specific 3D strength measurement or individual-specific muscle parameters become available.
• Cites Felton, Yeadon & King (2020) [ref 13] — the front foot contact optimisation — repeatedly as an exemplar, and uses its output (“more extended front ankle and knee joint angles; increased trunk flexion; a longer delay in the onset of arm circumduction”) as the illustration of how a simulation result should be phrased to a coach.
• Cites Felton & King (2016), The effect of elbow hyperextension on ball speed in cricket fast bowling [ref 123], as the source of the viscoelastic elbow hyperextension representation.
• TENSION with Felton, Yeadon & King (2019): the 2019 paper presents the planar/massless-segment approach as a viable solution because full 3D is “non-viable”. This review, with Felton as an author, reframes the same fact as a temporary limitation — “considerable increases in the potential applications… will be achieved through either individual-specific maximal muscle parameters or three-dimensional torque functions.” Not a contradiction of fact, but a clear shift in how permanent the 2D restriction is taken to be.
• TENSION with the compliance limits used in Felton’s own 2019 model. That model permitted 4.5 cm shank / 7 cm thigh / 10 cm trunk wobbling-mass movement and 6 cm vertical front-foot displacement. This review argues such values “may be excessive”, citing measured soft-tissue displacement of up to 1.4 cm and heel-pad/shoe deformation of 11.5–12.7 mm. Felton is a co-author of the critique. This is a genuine, self-acknowledged weakness in the parameter choices underpinning the cricket force results — and it is consistent with the ~11–14% residual force errors reported in 2016/2017/2019.
• TENSION on robustness: the review states that optimisation under movement variability “should be utilized in future torque-driven models” and that its incorporation “has been sporadic”. The cricket fast bowling optimisations are torque-driven and did not do this. So by the review’s own best-practice standard, the cricket “optimal technique” predictions are single-best-performance optima, not noise-robust ones.