Opponent Archetype Classifier

Table of Contents

• [Example](#example)
• [Workflow](#workflow)
• [Common Patterns](#common-patterns)
• [Guardrails](#guardrails)
• [Quick Reference](#quick-reference)

Example

Scenario: Fantasy baseball league, Week 5. Classify opponent "Manager A" into one of six archetypes -- balanced, starsandscrubs, puntsv, puntsb, puntwinsqs, hitter_heavy.

Inputs (abbreviated; full taxonomy in [resources/template.md](resources/template.md#worked-example-6-archetype-fantasy-baseball-taxonomy)):

archetype_taxonomy:
  balanced:          {prior: 0.30, feature_distributions: {sp_roster_share: {mean: 0.40, std: 0.06}, closer_count: {mean: 2.0, std: 0.6}, sb_speed_count: {mean: 3.0, std: 1.0}, moves_per_week: {mean: 2.5, std: 1.0}, bid_aggression: {low: 0.5, high: 0.5}}}
  stars_and_scrubs:  {prior: 0.15, ...}
  punt_sv:           {prior: 0.15, feature_distributions: {closer_count: {mean: 0.3, std: 0.4}, ...}}
  punt_sb:           {prior: 0.15, feature_distributions: {sb_speed_count: {mean: 0.8, std: 0.7}, ...}}
  punt_wins_qs:      {prior: 0.10, feature_distributions: {sp_roster_share: {mean: 0.20, std: 0.05}, closer_count: {mean: 3.0, std: 0.8}, moves_per_week: {mean: 4.0, std: 1.2}, ...}}
  hitter_heavy:      {prior: 0.15, feature_distributions: {sp_roster_share: {mean: 0.28, std: 0.05}, ...}}

observed_features:
  sp_roster_share:   0.22    # low -- thin on starters
  closer_count:      3       # heavy RP
  sb_speed_count:    2       # moderate speed
  moves_per_week:    4.2     # high activity
  bid_aggression:    high    # active FAAB bidder

observation_weight: 0.7        # ~4 weeks of data

Computation (per-feature log-likelihood, summed, exponentiated, multiplied by prior, normalized):

Outputs:

posterior:
  balanced: 0.04
  stars_and_scrubs: 0.21
  punt_sv: 0.00
  punt_sb: 0.00
  punt_wins_qs: 0.68
  hitter_heavy: 0.16

map_archetype: punt_wins_qs

classification_confidence: 47.6     # = max_posterior (0.68) * observation_weight (0.7) * 100

best_response_hints:
  - "Concede K and QS; lock 6 of remaining 8 cats"
  - "Don't stream starting pitchers against them"
  - "They will dominate SV and ratios via all-RP staff; push hitting cats hard"

feature_contribution_breakdown:
  sp_roster_share:  {map_likelihood: 0.92, alternative_max: 0.15, likelihood_ratio: 6.1}   # low SP share -- strong punt_wins_qs signal
  closer_count:     {map_likelihood: 0.52, alternative_max: 0.46, likelihood_ratio: 1.1}   # 3 closers fits several archetypes
  sb_speed_count:   {map_likelihood: 0.38, alternative_max: 0.41, likelihood_ratio: 0.9}   # not discriminating
  moves_per_week:   {map_likelihood: 0.33, alternative_max: 0.28, likelihood_ratio: 1.2}
  bid_aggression:   {map_likelihood: 0.70, alternative_max: 0.60, likelihood_ratio: 1.2}

assumptions_flagged:
  - "Conditional independence across features assumed -- sp_roster_share and moves_per_week may be correlated (active punt strategy drives both)"
  - "Feature distributions are SME priors, not empirically fit -- refresh after season 1 with posterior data"

Note on confidence: posterior peaks at 0.68 but observation_weight=0.7 (only 4 weeks of data) dampens confidence to 47.6. Above the 40 threshold, so MAP is reported; but caller is advised that another 2-3 weeks of observation will sharpen the call.

Workflow

Copy this checklist and track progress:

Opponent Archetype Classification Progress:
- [ ] Step 1: Load archetype taxonomy (names, priors, feature distributions)
- [ ] Step 2: Collect observed features for the target opponent
- [ ] Step 3: Compute per-feature likelihood under each archetype
- [ ] Step 4: Combine likelihoods (assume conditional independence; flag it)
- [ ] Step 5: Apply Bayes rule, normalize posterior
- [ ] Step 6: Select MAP archetype; compute confidence
- [ ] Step 7: Check inconclusive threshold; report or defer
- [ ] Step 8: Produce feature-contribution breakdown and best-response hints

Step 1: Load archetype taxonomy

The caller supplies the taxonomy. See [resources/template.md](resources/template.md#archetype-taxonomy-schema) for required fields.

• Each archetype has a name, a prior probability, and a feature distribution per observable
• Priors sum to 1.0 (normalize if not)
• Each feature has either a parametric distribution (Gaussian with mean/std) or a categorical (value -> probability)
• Each archetype has a documented best_response string array

Step 2: Collect observed features

Observed features must match feature names in the taxonomy. Missing features are dropped (not imputed) and flagged.

• Feature names match taxonomy keys exactly
• Numeric features in the taxonomy's expected units
• Categorical features use the taxonomy's category labels
• observation_weight (0-1) supplied; rises with sample size -- see [methodology.md](resources/methodology.md#observation-weight-calibration)

Step 3: Compute per-feature likelihood

For each (archetype, feature) pair compute P(feature_value | archetype). See [methodology.md](resources/methodology.md#likelihood-function-design).

• Gaussian feature: L = (1/(stdsqrt(2pi))) exp(-0.5 ((x - mean)/std)^2)
• Categorical feature: L = P_archetype[category] with Laplace smoothing if zero
• Work in log-space (log L) to avoid underflow when combining 5+ features

Step 4: Combine likelihoods (conditional independence)

First-approximation assumption: features are conditionally independent given archetype. This is rarely exactly true; flag it.

• Sum log-likelihoods across features per archetype
• Flag correlated feature pairs (e.g., sprostershare and movesperweek in fantasy baseball)
• If two features are strongly correlated, consider merging them or down-weighting one; document the choice

Step 5: Apply Bayes rule, normalize

posterior_unnorm[a] = exp(sum_log_L[a]) * prior[a]
posterior[a] = posterior_unnorm[a] / sum_a(posterior_unnorm[a])

• Compute in log-space for numerical stability, then subtract max before exponentiating
• Verify sum(posterior) == 1.0 within rounding
• Document any archetype with posterior < 1e-6 as "ruled out"

Step 6: Select MAP archetype; compute confidence

map_archetype = argmax(posterior)
classification_confidence = max(posterior) * observation_weight * 100

• MAP is the most likely archetype, not the only possibility
• Confidence blends how peaked the posterior is with how much we trust the observation

Step 7: Inconclusive threshold

If classification_confidence < 40:

• Return map_archetype: "inconclusive"
• Return the full posterior anyway (caller may still act on the top-2)
• Advise: "Collect 2-3 more weeks of observation before committing to a classification"

Step 8: Feature-contribution breakdown + best-response hints

• For each feature compute likelihood ratio: L(feature | MAP) / max_{a != MAP} L(feature | a)
• Pull bestresponsehints from the MAP archetype's documented string array
• Return alongside the posterior so caller sees why this archetype was selected

Common Patterns

Pattern 1: Fantasy sports (baseball, basketball, hockey) manager archetypes

• Taxonomy: 5-8 archetypes like balanced, punt<cat>, starsand_scrubs, inactive covering category-league strategy.
• Features: roster composition by position, transaction frequency, FAAB aggression, lineup-setting accuracy.
• Conditional-independence risk: several features covary (an inactive manager has low moves AND low bids AND stale lineup). Down-weight or collapse.
• Observation weight: 0.3 by Week 2, 0.6 by Week 5, 0.85 by Week 10.

Pattern 2: Poker opponent archetypes

• Taxonomy: tightaggressive (TAG), looseaggressive (LAG), tightpassive (rock), loosepassive (calling station), maniac.
• Features: VPIP, PFR, 3-bet %, aggression factor, c-bet frequency, showdown frequency.
• Conditional-independence risk: VPIP and PFR are tightly linked; keep both but note the correlation.
• Observation weight: rises sharply with hand count -- 0.4 at 100 hands, 0.75 at 500 hands, 0.9 at 2000+.

Pattern 3: DFS lineup-construction archetypes

• Taxonomy: cashgameoptimizer, GPPceilingchaser, contrarianpivot, chalkherding.
• Features: average salary usage, stack count, ownership-vs-projection ratio, tournament vs cash entry split.
• Conditional-independence risk: stack count and ownership-vs-projection covary for GPP players.

Pattern 4: M&A / auction bidder archetypes

• Taxonomy: strategicpremiumbidder, financialdisciplinedbidder, fishingexpedition, structuredearnout_preferer.
• Features: announced bid count per quarter, strategic vs financial press-release language, premium multiple paid, deal structure (cash vs stock vs earnout).
• Observation weight: low at any single deal; rises with repeated bidding history.

Guardrails

1. Conditional independence is almost never exactly true. Always flag it. If two features are strongly correlated (|r| > 0.6), merge them into a single composite feature or down-weight one by 50%. Otherwise the confident archetype gets credited twice for the same underlying signal.

1. Priors matter when data is thin. Uniform priors are a choice, not a neutral default. Use domain-informed priors when the population distribution is known (e.g., in a 12-team fantasy league, inactive has a real base rate of ~1-2 managers, not 1/12).

1. Numeric stability: work in log-space. Multiplying 5+ small likelihoods underflows to 0 in float64. Sum log-likelihoods, subtract the max log-posterior before exponentiating, then normalize.

1. Laplace smoothing for categoricals. If an archetype has P(category=X) = 0 in its distribution and the observation is X, the posterior for that archetype becomes 0 -- permanently ruling it out on one data point. Apply add-epsilon smoothing (epsilon = 0.01 is typical).

1. Inconclusive is a feature, not a failure. A low-confidence classification is valuable information -- it tells the caller to gather more data before committing. Don't force a MAP when confidence is below 40.

1. Best-response hints come from the taxonomy, not the classifier. The skill should not invent strategy; it should retrieve what the taxonomy author documented for that archetype. If the taxonomy's best_response is empty, return an empty array and note that the taxonomy needs enrichment.

1. Posterior is a distribution, not a point estimate. When downstream agents consume the output, they should ideally consume the full posterior (and make expected-value decisions over it) rather than collapsing to MAP. Expose both.

1. Update sequentially as new observations arrive. The current week's posterior becomes next week's prior. See [methodology.md](resources/methodology.md#sequential-posterior-updating) for the recursive formula.

1. Feature contribution breakdown guards against overfitting. If one feature's likelihood ratio is > 10, that single feature is driving the classification -- verify the feature was measured correctly before trusting the result.

1. Refresh feature distributions with empirical data once available. Initial distributions are SME priors. After N opponents have been labelled and observed, fit the distributions empirically and replace the SME priors.

Quick Reference

Key formulas:

Gaussian likelihood:
  L(x | a) = (1 / (std_a * sqrt(2*pi))) * exp(-0.5 * ((x - mean_a) / std_a)^2)

Categorical likelihood (with Laplace smoothing, epsilon = 0.01):
  L(x = c | a) = (count_a[c] + epsilon) / (sum_c' count_a[c'] + epsilon * num_categories)

Joint likelihood (conditional independence assumption):
  L(features | a) = prod_f L(feature_f | a)

Log-space joint likelihood:
  log L(features | a) = sum_f log L(feature_f | a)

Bayes posterior:
  posterior(a) proportional to L(features | a) * prior(a)
  posterior(a) = posterior_unnorm(a) / sum_a' posterior_unnorm(a')

MAP selection:
  map_archetype = argmax_a posterior(a)

Classification confidence:
  confidence = max_a posterior(a) * observation_weight * 100
  if confidence < 40:
      map_archetype = "inconclusive"

Sequential update (week t):
  prior_t(a) = posterior_{t-1}(a)
  posterior_t(a) proportional to L(new_features_t | a) * prior_t(a)

Feature contribution (likelihood ratio):
  LR(feature_f) = L(feature_f | MAP) / max_{a != MAP} L(feature_f | a)

Confidence bands:

Key resources:

• [resources/template.md](resources/template.md): Archetype taxonomy schema (YAML), observed-features schema, output schema, fully worked 6-archetype fantasy baseball example.
• [resources/methodology.md](resources/methodology.md): Bayesian classification primer, likelihood function design, characteristic-feature distribution construction (empirical vs SME), conditional independence assumption and when it breaks, sequential posterior updating.
• [resources/evaluators/rubricopponentarchetypeclassifier.json](resources/evaluators/rubricopponentarchetypeclassifier.json): 10 quality criteria for evaluating the output.

Inputs required:

• archetypetaxonomy: dict of archetypename -> {prior, featuredistributions, bestresponse}
• observedfeatures: dict of featurename -> observed value
• observation_weight: 0-1, how much to trust the observation vs the prior
• archetypeprior (optional): dict of archetypename -> prior; defaults to taxonomy priors (or uniform)

Outputs produced:

• posterior: dict<archetype, probability>, sums to 1
• map_archetype: string, most likely archetype (or "inconclusive")
• classification_confidence: 0-100
• bestresponsehints: string[], pulled from the MAP archetype's documented best-response
• featurecontributionbreakdown: dict<feature, {maplikelihood, alternativemax, likelihood_ratio}>
• assumptions_flagged: string[], e.g., correlated features, smoothing applied, priors forced uniform