Critique: Strokes Gained Limitations and Ecological Fallacy

Corrected critique distinguishing strokes-gained accounting from individual forecasting, hidden-state models, and tournament objectives.

Critique: Strokes Gained Limitations and Ecological Fallacy

Summary of Concern

Technical correction, September 10, 2026: The original critique correctly raised questions about forecasting a changing golfer and choosing tournament strategies. It incorrectly presented stationarity, full observation, and risk neutrality as requirements of strokes-gained accounting. Those claims are withdrawn. This correction preserves the critique’s identity and its governed open status; it does not silently adjudicate the trust ledger.

The revised article separates three questions: how recorded strokes are allocated, what a golfer is likely to do next, and what would change under an intervention. The remaining concern is whether a particular predictive or decision model has adequate states, validated transitions, an appropriate objective, and uncertainty estimates.

Location

• Article: articles/strokes-gained-limitations.qmd.
• Relevant Sections: Policy Evaluation; Individual Continuation and Category Boundaries; Heterogeneity, Selection, and Causal Inference; Hidden States and Tournament Objectives.

Nature of the Issue

For a fixed benchmark \(B\) and complete hole with counted costs \(c_t\),

\[ \sum_t[B(s_t)-c_t-B(s_{t+1})]=B(s_0)-\sum_t c_t, \]

because the final holed-state value is zero. This holds without assuming an optimal policy, stationary skill, or a Markov process. Omitted factors can limit how well the benchmark predicts or interprets individual shots without invalidating that cancellation.

A policy value \(V_i^\pi\) requires a specified continuation policy and transition model. Its state may need environmental conditions, player identity, history, or beliefs about hidden variables. A distance-and-lie conditional mean can still be defined when those observations are insufficient for a closed Markov recursion. Adding a symbol for confidence does not establish its causal effect.

Why This Is a Problem

The same physical leave can have different continuation values for different players. Yet “worse putter” does not establish a larger proximity benefit: probability levels do not order distance derivatives. A pooled regression also mixes state-dependent player weights and observed conditions. Calling that regression an individual treatment-response function needs justification beyond its fit to the observed data.

Time variation can undermine a static forecast, but an individual’s mean need not equal a heterogeneous population mean even under stationarity. Dependence alone does not establish non-ergodicity. The earlier argument conflated these distinct issues and provided no golf-specific stochastic model establishing its proposed non-ergodicity conclusion.

Evidence and References

• Broadie’s author preprint, Section 2 establishes the benchmark definition and additivity and describes the additional near-optimal-strategy approximation in its DP discussion.
• Sutton and Barto, Sections 3.5–3.6 distinguish policy evaluation from optimal values.
• Gelman (2006) separates predictive pooling from causal interpretation of observational coefficients.

The previous general references to fat tails, prospect theory, and optimal feedback control did not establish the claimed failure of SG accounting. They are not retained as evidence for those withdrawn assertions.

Severity

Medium, governed open. The concern is consequential when making individual forecasts or prescriptions. It is not evidence that complete SG totals cease to account for counted strokes.

Suggested Remedies

1. Test State Sufficiency

Compare predictions across relevant conditions and future time periods. Examine whether omitted history improves held-out predictions and whether measured changes support the proposed mechanism. Avoid interpreting a negative SG value as a diagnosis of anxiety or mechanical error.

2. State the Decision Objective

Expected-score minimization and maximizing the chance of beating a threshold can prefer different actions. The article’s constructed four-stroke safe outcome versus a three-or-seven risky outcome demonstrates this without assigning universal risk preferences to golfers. Counted score is a cost; worse expected scoring means a higher stroke count. SG can report either policy’s consequences without deciding which objective the golfer should use.

3. Separate Time Variation From Population Differences

Specify the process and time horizon before claiming nonstationarity or non-ergodicity. Use repeated measurements, time-ordered validation, and uncertainty that respects dependence. Personalization can improve forecasting; causal claims still require a defined intervention and an identification argument. The source and numerical review is tracked in issue #4358.

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