# S16 V3: corrected model, reproduction and all errors

[中文](model_report_zh_cn.md) · [English](model_report_en.md)

Predict per-game pick rate, active ban rate, presence and conditional mean selection position for the entire Worlds event. Roles come from played lineups; every role rate uses the same game denominator. Original V2 outputs/parameters are preserved; V3 is a separate version.

- Inputs: 2556 games / 1003 series / 40 events / 173 champions × 5 roles.
- Cutoff: 2026-10-09T19:20:41Z; patch 26.20; Data Dragon 16.20.1.
- Preserve the match archive, target teams, skill-importance and role-relevance assumptions. Correct the inference structure and the Rocketbelt haste sign uniformly. No champion-specific overrides or S16-based parameter selection.

## 1. Historical game weighting

`w(g) ∝ exp(-ln(2)·age_days/45 - 0.25·patch_gap) × importance(g) × exp(0.8·clip((Elo_before(g)-1500)/400,-1,1)) × event_games_before_cutoff^(-0.25) × first_game_factor`

Older games and larger patch gaps receive smaller weights. Importance: MSI1.8, EWC1.4, First Stand1.3, qualifiers/regional finals1.45, playoffs/grand finals1.35, KeSPA/DCGI0.75, promotion0.4, others1. Strength uses the two teams’ mean pre-game Elo, updated with K=20. Initial ratings: LCK1600, LPL1580, LEC1500, LCS1450, LCP/CBLOL1430, outside challengers1350. First games receive factor1.4; known Worlds-team history has mixture0.45, moderating deep Fearless pools.

## 2. Historical regression layer

`historical_candidate = V1_no_patch_baseline + blend × (intercept + standardized_features × coefficients)`

Six frequency ridge models cover five roles and bans; five position ridge models estimate conditional mean pick rank. Coefficients are shared across champions within each output; no champion-identity features. These 17 historical features use fitted means/scales (scale floor0.025):

`baseline_probability`, `recent14_rate`, `recent45_rate`, `season_rate`, `recent_minus_baseline`, `recent_squared`, `baseline_squared`, `qualified_rate`, `champion_ban_rate`, `champion_pick_rate`, `early_pick_fraction`, `early_ban_fraction`, `role_share`, `flex_entropy`, `attack_range`, `recent_role_partner_strength`, `qualified_team_coverage`

recent14/recent45 add exponential half-life weighting of14/45 days to the main weights; they are not hard windows. The dashboard’s recent45 comparator is a direct count in the hard45-day window. Historical co-selection partner strength is correlational, not a causal synergy claim.

`ridge=0.03; residual_blend=0.75; position_blend=0.5`

## 3. Role evidence and structural zeros

`support(c,r) = historical_pick_count_before_cutoff(c,r) > 0`

States without historical role picks stay exactly zero after regression and throughout projection; epsilon and intercepts cannot revive them. All865 states remain in error denominators. There are277 supported and588 unsupported states. Rare observed roles retain small forecasts: Aurora top has62 historical picks. No hero-name or subjective manual exclusion is used.

Zero means conservative abstention, not impossibility. Champions never picked in the archive receive no invented role pick rates, so novel debuts/flex roles can be missed. Their actual test picks still count as errors. At zero pick rate, conditional positions export/display as null/blank; if a first-time champion appears in a test, position metrics use the V1 conditional prior fallback instead of dropping the champion.

## 4. Separately applied patch priors

`delta(c,r) = clip(Σ favorable_log_change × skill_importance × role_relevance, -1.6, 1.6)`
`patched_pick(c,r) ∝ supported_historical_candidate(c,r) × exp(delta(c,r))`
`patched_ban(c) ∝ historical_ban(c) × exp(Σ supported_V1_role_share(c,r) × delta(c,r))`

Preserve V1 gain1 for numeric, mechanism and system effects. Numeric effects use favorable-direction log(new/old): cooldowns, costs and damage taken invert sign; attack speed uses total multipliers, mitigation uses remaining damage. Ability importance and role relevance remain declared priors. Patch26.19 is exposure-adjusted for older historical games;26.20 applies directly. Historical regression and support projection precede the patch multiplier and final projection, avoiding additive patch uplifts in unsupported roles.

Remove V2’s numeric_patch, mechanism_patch, system_patch, positive_patch_saturation and patch_x_low_frequency learned features. S15 historical target windows lack complete patch-change history and these columns are mostly near zero: Aurora-top saturation0.962 extrapolated far beyond training mean0.000077. Patch effects remain explicit priors above; their true elasticity has not been learned/validated. Rocketbelt haste20→10 uses negative log cast-frequency denominator120→110, corrected uniformly for13 affected champions.

## 5. Positions and marginal constraints

`Σ_c p(c,r)=2; Σ_(c,r) p(c,r)=10; Σ_c ban(c)=10; Σ_r p(c,r)+ban(c)≤1`
`E[BP_step] = E[pick_rank] + 6 + 4·P(pick_rank≥7)`

Projection preserves support/availability zeros. Pick rank lies in1–10 and full BP step in7–20; role position residuals cap at±2 ranks, then patch priority priors apply with valid moments enforced. Overall positions are weighted by predicted role picks. Bans have no observed final role and are not assigned fictitious lanes.

## 6. Training and retesting

V3 uses2392 pre-Worlds S15 games, forming39 event/patch target windows with1771 target games. The first27 of34 rolling windows select ridge∈{0.03,0.1,0.3,1,3}, residual blend∈{0.25,0.5,0.75,1} and position blend∈{0,0.25,0.5,0.75,1}:100 combinations. Loss=0.45×presence RMSE+0.30×pick RMSE+0.15×role RMSE+0.10×rank MAE. Every fold fits only target windows ending before its start; final shared coefficients fit all39. S15 Worlds labels are accessed only after selection/fitting for diagnostics.

In-sample errors across all39 S15 target windows (V3 only; not generalization evidence):

|Metric|V3|
|---|---:|
|Pick MAE / pp|2.4404|
|Pick RMSE / pp|4.0968|
|Ban MAE / pp|3.3445|
|Presence RMSE / pp|8.1483|
|Champion × role RMSE / pp|1.8726|
|Pick-weighted rank MAE|1.0736|
|Pick-weighted BP-step MAE|1.7664|

Mean errors on the first27 S15 development windows:

|Metric|V2|V3|
|---|---:|---:|
|Pick MAE / pp|2.5405|2.5047|
|Pick RMSE / pp|4.2391|4.2391|
|Ban MAE / pp|3.4241|3.4241|
|Presence RMSE / pp|8.4140|8.3976|
|Champion × role RMSE / pp|1.9416|1.9366|
|Pick-weighted rank MAE|1.0733|1.0719|
|Pick-weighted BP-step MAE|1.7432|1.7398|

Last7 S15 chronological checks (previously inspected, not fresh blind tests):

|Metric|V2|V3|
|---|---:|---:|
|Pick MAE / pp|2.4094|2.3951|
|Pick RMSE / pp|3.9120|3.9287|
|Ban MAE / pp|3.3145|3.3139|
|Presence RMSE / pp|7.8672|7.8514|
|Champion × role RMSE / pp|1.7825|1.7872|
|Pick-weighted rank MAE|1.0933|1.0919|
|Pick-weighted BP-step MAE|1.8103|1.8051|

S15 Worlds84-game pre-event reconstruction (retrospective diagnostic):

|Metric|V2|V3|
|---|---:|---:|
|Pick MAE / pp|2.6532|2.4051|
|Pick RMSE / pp|4.2359|3.9278|
|Ban MAE / pp|3.0384|3.0165|
|Presence RMSE / pp|8.4430|8.4203|
|Champion × role RMSE / pp|1.9162|1.8094|
|Pick-weighted rank MAE|0.9062|0.8500|
|Pick-weighted BP-step MAE|1.4947|1.4275|

Frozen S16 parameter transfer:13 windows/210 games:

|Metric|V2|V3|
|---|---:|---:|
|Pick MAE / pp|3.3161|3.2834|
|Pick RMSE / pp|5.3810|5.3696|
|Ban MAE / pp|3.7430|3.7435|
|Presence RMSE / pp|8.6146|8.5959|
|Champion × role RMSE / pp|2.4599|2.4542|
|Pick-weighted rank MAE|1.4622|1.4602|
|Pick-weighted BP-step MAE|2.4665|2.4612|

S16 uses identical whole-series splits and recomputes old V2 metrics to verify agreement. Event/patch groups require≥30 games, earlier65% whole series provide history, later≥10 games test; other events are cut off too, with no overlapping series. Metadata matches the historical patch; new-patch shocks are zero. These checks test within-patch continuation, not unseen26.19/26.20 shocks. Windows are equally averaged, not pooled independent samples.

Actual role picks missed by the support mask: S15 7 windows=8; S15 Worlds=0; S16=10/2100.
S16 gains are small; pick/role RMSE slightly worsen on the last7 S15 windows. Direct repair evidence is exact unsupported-role zeros and removal of extreme patch extrapolation, not universally large accuracy gains. S16 check outcomes do not tune the parameters.

## 7. Uncertainty, reproduction and handoff

80 bootstrap draws resample historical complete series with a fixed pre-cutoff support mask and fixed coefficients;95% intervals cover sampling variation only. Sensitivity removes all patch effects, scales numeric magnitude±25%, or removes mechanism/system priors. Four toggle combinations yield two-factor Shapley26.19/26.20 contributions: model sensitivity, not observed/causal patch effects. Novel roles, stage mix, future schedules and Fearless availability uncertainty are not fully in these intervals.

```powershell
python -X utf8 research/scripts/train_worlds_model_v3.py
python -X utf8 research/scripts/forecast_s16_worlds_v3.py
python -X utf8 research/scripts/render_s16_forecast_v3.py
python -X utf8 research/scripts/audit_s16_forecast_v3.py
node research/scripts/check_s16_dashboard.cjs s16_preparation/outputs_v3
```

Teammates need V3 source,17-feature order, coefficients/means/scales/hyperparameters, matching V1 parameters, support policy, corrected patch encoding and input hashes. Do not interchange22-feature V2 with17-feature V3 coefficients or copy S15 per-champion posteriors. The new bundle is experiments/s15_candidates/s15-v3-supported-roles; original frozen transfer_parameters remain unchanged.

- Event-specific disabled roster not obtained; all 173 champions assumed eligible.
- CBLOL-only games excluded by requested collection scope: LOS/FURIA team preferences are estimated from sparse cross-region observations.
- No completed 26.19/26.20 games in this dataset; target-patch shocks are extrapolations.
- Future series lengths, stage participation and within-series unavailable pools are not explicitly simulated; this is the same marginal whole-event model as S15. First-game weighting moderates observed Fearless depth.
- Independent game-level source checks cover only part of the archive; no claim of every draft step verified against video.
- Historical-series bootstrap measures sampling variation, not all model, patch or event-format uncertainty.
- Zero unsupported roles are conservative abstentions; novel professional flex roles and unseen champion debuts are not forecast as positive picks. All actual test roles remain in error denominators.
- The patch response is an assumed V1 multiplicative prior. S15 lacks complete historical patch shocks, so the five V2 learned patch features are removed; no claim of empirically validated 26.19/26.20 response.

- [Per-window S16 errors](temporal_validation.json)
- [S15 training and retrospective errors](s15_validation.json)
- [Forecast/input hashes](forecast_manifest.json)
- [Shared V3 coefficients](parameters_s16_prior.json)
- [Corrected patch facts](patch_change_features.json)
- [Patch 26.19](https://www.leagueoflegends.com/en-us/news/game-updates/league-of-legends-patch-26-19-notes/)
- [Patch 26.20](https://www.leagueoflegends.com/en-us/news/game-updates/league-of-legends-patch-26-20-notes/)